{
  "schemaVersion": 1,
  "topics": [
    {
      "id": "topic:origin",
      "titleEN": "Seam, origin and declared inputs",
      "summaryEN": "TFPT starts from the oriented seam normalization P1 (c3=1/(8π)) and the marked five-slot carrier P2. Integer anchors and later compiler readouts connect these inputs, but do not derive their physical origin or selection.",
      "orientation": {
        "role_en": "Starting point of the TFPT compiler: oriented seam normalization P1 and marked five-slot carrier P2. The graph tracks internal consequences separately from the still-declared origin assumptions.",
        "have_en": "P1 declares c3=1/(8π); P2 declares five carrier slots with a 3+2 marking. The (1,1,2) anchor organizes internal numerical relations.",
        "seek_en": "The open work is a non-circular source for these inputs, the physical seam, and derivations of their markings and readout rules.",
        "connection_en": "The declared seeds feed E8, clock, flavor, α, and scale readouts. Shared seeds make those outputs correlated.",
        "next_bridge_en": "A source rule must select P1/P2, allowed interventions, and physical readouts together; downstream matches cannot serve as their own origin."
      },
      "problemIds": [
        "problem:future-quotient-and-gns-reconstruction",
        "problem:common-source-state-event-selection",
        "problem:seam-family-connection-compatibility",
        "problem:physical-time-projector-transfer",
        "problem:flavor-ratio-amplitude-readout",
        "problem:alpha-fixed-input-root",
        "problem:gravity-flow-normalization",
        "problem:charged-twist-response-identifiability",
        "problem:native-charged-seam-selection",
        "problem:constructive-seam-lift-state",
        "problem:seam-partner-charge-state-time",
        "problem:automated-operator-source-synthesis",
        "problem:reverse-bootstrap-physical-field-dictionary",
        "problem:fundamental-process-classification",
        "problem:carrier-pascal-glue-formal-scope",
        "problem:atlas-clock-defect-and-operational-reconstruction",
        "problem:automatic-origin-response-decision"
      ],
      "findingIds": [
        "finding:future-equivalence-minimizes-declared-answer-process",
        "finding:positive-word-kernel-reconstructs-cyclic-gns",
        "finding:operational-seed-is-input",
        "finding:native-source-common-time-thermal-family",
        "finding:native-grade-carry-and-memory",
        "finding:even-seam-global-operator-factorization",
        "finding:source-generated-marking-classification",
        "finding:source-marking-field-realization-boundary",
        "finding:minimal-defect-uniqueness-not-proved",
        "finding:conditional-seam-field-state-time-reconstruction",
        "finding:continuous-hardy-seam-classification",
        "finding:same-source-seam-energy-selection",
        "finding:master-functional-presupposes-source-selection",
        "finding:geometric-deck-not-calderon-polarization",
        "finding:positive-compression-erases-carrier-minus-sector",
        "finding:higgs-determinant-does-not-discharge-carrier-map",
        "finding:primitive-invariant-does-not-select-rank-three",
        "finding:fixed-background-source-does-not-fix-mixed-vertex",
        "finding:local-quarter-inner-variation-is-connection",
        "finding:calderon-enlargement-does-not-select-higgs",
        "finding:finite-sm-higgs-variation-retains-seed",
        "finding:operator-skeleton-does-not-identify-insertion-algebra",
        "finding:internal-even-car-hodge-is-not-coordinate-algebra",
        "finding:minimum-rank-unique-primitive-channel-does-not-select-32",
        "finding:joint-selfconsistency-presupposes-minimal-algebra-fiber-selection",
        "finding:process-composition-and-cyclicity-do-not-select-algebra",
        "finding:quartic-shape-selects-32-only-with-source-sign",
        "finding:native-symmetric-quartic-erasure-common-object",
        "finding:joint-native-algebra-normalizer-and-response-orbit",
        "finding:native-galois-intertwiner-unique-logical-marked-orbit",
        "finding:native-reflection-full-four-five-generators-rate-injectivity",
        "finding:complete-logical-readout-native-covariant-residual-classification",
        "finding:original-polar-mark-clock-centralizer-orbit",
        "finding:actual-quartic-code-product-stabilizer-quarter-exclusion",
        "finding:original-decoder-versus-native-quarter-polynomial-erasure-test",
        "finding:original-decoder-product-time-and-all-unitary-erasure-lifts",
        "finding:native-clock-compatible-polar-fibre-and-canonical-distance",
        "finding:native-moment-parent-and-product-path-selection-boundary",
        "finding:original-e8-current-response-and-full-quarter-lifts",
        "finding:literal-charged-current-register-dictionary-fails-quarter",
        "finding:native-cartan-code-inner-e8-stabilizer-excludes-marked-quarter",
        "finding:native-code-neutral-weight-two-action-and-global-clock-exclusion",
        "finding:original-neutral-root-mixed-response-derived",
        "finding:actual-mixed-ordered-return-on-native-quartic-code",
        "finding:mixed-return-spectrum-does-not-select-original-polar-mark",
        "finding:actual-mixed-return-fails-native-trimer-erasure-lift",
        "finding:strict-trace-gap-excludes-positive-mixed-return-reweighting",
        "finding:original-source-erasure-ward-terms-derived",
        "finding:uncompressed-original-mixed-return-does-not-preserve-code",
        "finding:original-root-response-sum-also-leaks-from-code",
        "finding:original-full-source-return-exterior-feedback-derived",
        "finding:original-return-requires-memory-in-every-code-direction",
        "finding:native-conformal-primary-multiplicity-source-factorization",
        "finding:canonical-conformal-erasure-forces-primary-twenty-carry",
        "finding:all-canonical-stress-histories-scalar-on-native-code",
        "finding:original-local-current-ope-forces-erasure-and-carry",
        "finding:all-real-local-cartan-profiles-erasure-third-bound",
        "finding:closed-cartan-weyl-histories-only-logical-phase",
        "finding:full-existing-local-e8-hull-of-native-code",
        "finding:full-local-quartic-wick-ladder-and-unprojected-native-actions",
        "finding:unmarked-native-w6-simplex-from-full-quartic-ope",
        "finding:full-e8-current-products-fix-stress-and-exterior-ward-cancellation",
        "finding:full-source-simplex-does-not-select-original-polar-mark",
        "finding:original-full-field-event-gram-reconstructs-relative-polar-mark",
        "finding:raw-event-state-positivity-does-not-execute-polar-normalization",
        "finding:determinant-cover-not-literal-full-cartan-lattice-event",
        "finding:clock-free-quartic-product-spectral-sectors-and-native-five",
        "finding:six-complex-native-simplex-rays-from-holomorphic-product-quadrics",
        "finding:intrinsic-relative-response-covariance-and-state-boundary",
        "finding:intrinsic-event-composition-retains-shared-source-and-correlation-data",
        "finding:clock-free-event-geometry-fixes-clock-class-and-mark-orbit-not-member",
        "finding:original-charged-seam-character-recovers-global-native-event-pair",
        "finding:internal-seam-vacuum-and-original-neutral-tensor-do-not-select-flag-root",
        "finding:actual-quarter-fold-shift-removes-native-symmetry-obstruction-without-flag-selector",
        "finding:fold-shift-equivariance-needs-actual-source-response-map-not-another-symmetry-no-go",
        "finding:original-fold-covariance-current-counterterm-and-quartic-twisted-transport",
        "finding:fold-state-full-quartic-kernel-and-erasure-protected-low-order-response",
        "finding:original-fold-quartic-mean-and-spectral-responses-do-not-match-sixty-flags",
        "finding:original-winding-full-state-response-removes-vacuum-rank-two-shortcut",
        "finding:original-source-global-time-winding-history-factorization",
        "finding:original-local-density-folds-to-correlated-root-current-and-erasure-response",
        "finding:original-current-all-mode-energy-and-geometric-stress-bridge",
        "finding:original-current-geometric-response-pair-has-no-common-polar-sector",
        "finding:original-current-ordered-hall-kernel-and-actual-folded-field-products",
        "finding:original-seam-grades-full-density-geometric-products-and-energy-response",
        "finding:original-seam-complete-density-grading-not-sharp-32-input-sectors",
        "finding:original-density-all-profile-mean-work-scalar-on-native-packet",
        "finding:original-p1-gap-normalized-action-covector-and-scalar-holonomy-class",
        "finding:original-p1-gap-car-component-not-native-sharp-32-event",
        "finding:complete-positive-scalar-first-order-circle-source-normal-form",
        "finding:fixed-source-time-seam-ward-rigidifies-scalar-principal-symbol-with-carry",
        "finding:unit-spectral-flow-gap-and-four-marks-do-not-imply-fixed-source-ward",
        "finding:four-native-starts-have-distinct-original-fold-state-correlations",
        "finding:four-starts-full-joint-kernel-and-charged-covariant-transport",
        "finding:four-native-polar-marks-not-fixed-source-state-gauge-equivalent",
        "finding:original-pointer-template-requires-source-context-identification",
        "finding:four-polar-context-algebra-and-source-crosscoupling",
        "finding:every-native-quartic-has-all-eight-original-car-supports",
        "finding:bounded-proper-local-source-operation-cannot-exactly-prepare-positive-eigenpacket",
        "finding:full-original-erasure20-and-joint25-have-all-eight-source-supports",
        "finding:two-face-collar-fixes-face-current-phase-and-distinguishes-relative-endpoint-lift",
        "finding:full-dirac-cauchy-vector-cocycle-cancels-and-endpoint-domain-distinction",
        "finding:unchanged-qwz-full-finite-energy-spectral-exhaustion",
        "finding:uniform-z4-d8-locality-and-both-spinor-chirality-time-census",
        "finding:odd-spinor-global-refielding-and-unit-source-winding",
        "finding:sharp-half-flux-register-quotient-and-local-normality-exclusion",
        "finding:all-word-register-charged-local-field-limit-obstruction",
        "finding:exact-parity-gauss-locality-completion-of-register-source",
        "finding:cover-half-flux-not-fixed-charge-eightfold-spinor-twist",
        "finding:original-neutral-eightpreimage-parity-pair-has-uniform-cut-action",
        "finding:complete-dirac-vector-phase-pair-has-zero-spinor-Ward-charge",
        "finding:smooth-unitary-endpoint-removal-diverges-at-fixed-source-time",
        "finding:continuous-original-time-nonunitary-limits-stay-in-old-source-folium",
        "finding:common-register-vacuum-reference-uniform-and-local-grade-reduction",
        "finding:actual-heat-filtered-neutral-pair-full-state-time-and-separate-chiral-limit",
        "finding:holomorphic-kms-extension-assumes-charged-net-and-not-microscopic-generator",
        "finding:fixed-interval-rotation-modular-chain-fails-local-state-takesaki-repairs",
        "finding:source-winding-cartan-four-word-and-two-edge-kms-gso-discriminator",
        "finding:p1-parity-gauss-net-selection-undecidable-without-original-localization-map",
        "finding:original-minimality-does-not-reconstruct-operational-source",
        "finding:generic-first-order-relative-bound-zero-counterexample-and-correct-domain-repair",
        "finding:joint-discrete-data-vs-connection",
        "finding:parallelity-excludes-2plus2-only-conditionally",
        "finding:sign-projector-does-not-determine-time-magnitude",
        "finding:full-faithful-kms-or-transfer-recovers-magnitudes",
        "finding:full-two-face-collar-recovers-signed-operator",
        "finding:two-face-graph-state-time-same-datum",
        "finding:shared-register-gkls-embedding-exact-q-interval",
        "finding:marked-m4-channel-all-powers-homogeneous-gksl-excluded",
        "finding:flavor-ratio-closed-absolute-anchor-open",
        "finding:alpha-equation-is-fixed-input-closure",
        "finding:alpha-global-positive-root-unique",
        "finding:marked-e8-sector-grade-response-realizes-five-quarters",
        "finding:alpha-exact-coefficients-and-root-retain-specific-physical-ward-obligation",
        "finding:alpha-archive-term-provenance-and-master-functional-scope",
        "finding:matter-observations-do-not-fix-geometric-response",
        "finding:neutral-vacuum-allword-twist-blindness",
        "finding:eight-charged-responses-reconstruct-twist",
        "finding:native-invariant-response-not-fixed-chiral-twist",
        "finding:native-opposite-charge-response-symmetry",
        "finding:native-chemical-mark-visible-in-charged-corners",
        "finding:fixed-hopping-quarter-phases-retain-antiunitary-discriminator",
        "finding:constructive-phase-class-and-full-winding",
        "finding:constructive-positive-state-extension",
        "finding:constructive-current-group-selects-positive-p-lift",
        "finding:constructive-state-algebra-resolution-and-source-test",
        "finding:constructive-all-phases-fail-unchanged-source",
        "finding:partner-carrier-charges-and-state-types",
        "finding:partner-fixed-quarter-time-splits-sm-multiplet",
        "finding:partner-original-carrier-cross-sheet-conjugation",
        "finding:partner-chiral-quarter-conjugation-state-time",
        "finding:joint-bilinear-hermitian-correction",
        "finding:joint-quarter-transports-marking",
        "finding:joint-fixed-time-marking-repair-excluded",
        "finding:joint-spinor-not-source-coefficient",
        "finding:typed-operator-search-calibrated",
        "finding:positive-kernel-construction-with-exact-discriminator",
        "finding:source-typed-kernel-search-controls",
        "finding:collar-car-projection-multifield-ray",
        "finding:known-quarter-source-full-multifield-control",
        "finding:source-reference-amplitude-retained",
        "finding:joint-fermionic-source-schur-functional",
        "finding:quarter-circle-absolute-zeta-green-eta",
        "finding:quarter-sea-absolute-thermal-central-phase",
        "finding:original-operational-seed-and-given-green-pairing",
        "finding:order-one-infinitesimal-bound-inference-fails",
        "finding:joint-ward-two-field-data-miss-fixed-four-field-response",
        "finding:complete-car-kernel-fixes-nongaussian-link-functional",
        "finding:source-covariance-jet-and-mixed-face-interface",
        "finding:e8-grade-two-explicit-spinor-current-action",
        "finding:intrinsic-source-jet-removes-pure-field-frame-motion",
        "finding:unchanged-ns-vector-generators-cannot-create-d5-spinor-fields",
        "finding:two-face-noncommuting-geometric-response-calculus",
        "finding:raw-face-mask-fails-source-kernel-null-descent",
        "finding:action-response-sewing-does-not-select-lf-intervention",
        "finding:faithful-gns-completion-closes-automated-source-query-feedback",
        "finding:whole-quarter-channels-identified-by-exact-internal-kernel",
        "finding:actual-joint-insertion-hull-resolves-eight-coefficient-directions",
        "finding:e8-bare-trilinear-and-single-anchor-weyl-class-insufficient",
        "finding:complete-family-four-cycle-class-separates-native-clock-from-sm-preservation",
        "finding:native-clock-word-transpose-has-static-rank-four-counterexample",
        "finding:whole-constant-coupled-source-is-implementable-despite-isolated-insertion-domain",
        "finding:fixed-quarter-jloc-pfaffian-closure-fails-local-skew-test",
        "finding:same-collar-has-canonical-selfdual-kinetic-pairing-and-charged-determinant",
        "finding:quarter-cover-pairing-does-not-supply-local-normal-or-select-scale-measure",
        "finding:fixed-aps-source-has-whole-inverse-and-finite-boundary-correction",
        "finding:mass-only-deck-relative-heat-action-fails-free-infinite-trace",
        "finding:finite-antiperiodic-scalar-wall-has-no-exact-massless-normal-mode",
        "finding:spectral-heat-covariance-positivity-does-not-imply-time-rp",
        "finding:quaternionic-sm-mass-winding-is-not-normal-determinant-clutch",
        "finding:bounded-relative-trace-obstruction-and-whole-genuine-pair-heat-reader",
        "finding:normal-clutch-orbit-index-equivariantly-recovers-given-weak-module",
        "finding:normal-orbit-spin-family-index-and-signed-charge-balance",
        "finding:fixed-flavor-cartan-sign-cover-and-root-lift-parity",
        "finding:original-family-vector-action-is-not-cartan-rotation-or-spinlift-selection",
        "finding:actual-genus-two-sign-family-closes-common-parallel-k-connection",
        "finding:actual-q-quarter-extends-common-k-connection-and-real-coefficient-lifts",
        "finding:real-source-reflection-is-not-linear-duality-or-compact-clock-inversion",
        "finding:source-selected-spin-and-q-signs-have-three-explicit-global-kernels",
        "finding:source-s0-szego-point-legs-generate-q-kernels-with-typed-products",
        "finding:actual-spin-kernel-determinant-has-inverse-q-norm-character",
        "finding:closed-source-flavor-spin-has-functorial-pfaffline-with-charged-type-limit",
        "finding:original-relative-seam-has-explicit-whole-graph-fredholm-mismatch",
        "finding:whole-constant-coupled-clutch-defects-are-exact-internal-kernels",
        "finding:old-complex-scalar-clutch-separates-c0-and-product-reflection",
        "finding:scalar-defect-circle-character-does-not-select-projector-holonomy",
        "finding:source-spin-is-canonical-ramified-base-spin-pullback",
        "finding:original-v117-has-explicit-algebraic-q-cover-fundamental-frame",
        "finding:double-circle-reflection-does-not-fix-entire-cubic-cable-seam",
        "finding:actual-fuchs-real-map-transports-whole-given-finite-source-state-and-time",
        "finding:actual-e0-compensator-extends-whole-k-e8-with-transported-quarter",
        "finding:actual-v252-entire-real-basis-has-signed-p2-dual-dictionary",
        "finding:chiral-fuchs-source-transport-has-distinct-majorana-phase-and-torus-absorption",
        "finding:native-theta-composition-retains-conjugate-source-and-parity-square",
        "finding:single-graph-range-isometry-does-not-give-local-whole-seed-map",
        "finding:hard-holonomy-selfduality-leg-and-finite-character-phase-separation",
        "finding:original-z6-positive-structural-kernel-does-not-supply-oriented-phase-observable",
        "finding:original-genus-two-hexagonal-rotation-has-concrete-rho-hodge-line",
        "finding:original-mixed-spin-products-realize-positive-u6-cycle",
        "finding:actual-spin-quadratics-reach-original-hexagonal-hodge-line",
        "finding:spin-pair-car-transport-retains-parity-and-whole-source-types",
        "finding:real-total-trace-does-not-exclude-coherent-phase-reader",
        "finding:geometric-six-spin-clock-differs-from-marked-native-clock",
        "finding:whole-q-to-p-pullback-transports-given-source-state-and-time",
        "finding:actual-fixpoint-evaluation-keeps-coefficient-signs-and-source-type",
        "finding:original-source-naturality-needs-no-second-p-image-background",
        "finding:canonical-spin2-lift-carries-whole-annulus-source-with-reversed-time",
        "finding:geometric-spin-collar-map-closes-weighted-image-domain-with-total-deck-action",
        "finding:claude33-annulus-map-is-valid-distinct-type-not-unique-geometric-spin-selection",
        "finding:original-mixed-spin-products-already-have-complete-dual-hom-coefficients",
        "finding:whole-f5-graph-supplies-canonical-reverse-qp-hom-kernel",
        "finding:actual-spin-product-weight-has-canonical-trace-class-form-pairing",
        "finding:fully-descended-covariant-reverse-kernel-removes-rho-form-channel",
        "finding:original-a4-linear-quarter-does-not-supply-proposed-scalar-mu3-repair",
        "finding:offdiagonal-hom-matches-a4-family-six-but-not-two-triplet-e8-product",
        "finding:compact-e8-adjoint-completes-family-six-with-carrier-rank-retained",
        "finding:three-family-cx-recursion-closes-exact-d8-with-minimal-original-escape",
        "finding:original-weak-current-coefficient-has-explicit-finite-oneform-consumer",
        "finding:original-d5-zero-mode-closes-triplet-carrier-and-fixed-glue-is-minimal-escape",
        "finding:mixed-spin-full-deck-has-no-rank-three-projector",
        "finding:actual-reverse-hom-diagonal-supplies-global-q-hodge-response",
        "finding:bare-c3-kernel-diagonal-yukawas-have-common-real-frame",
        "finding:original-primitive-action-is-present-highpass-is-not-finite-selector",
        "finding:atlas-detail-retrieval-recovers-existing-d4-solution",
        "finding:original-poisson-normal-trace-fixes-whole-calderon-graph",
        "finding:induced-original-hardy-defect-gives-finite-whole-source-reader",
        "finding:original-weak-quartic-action-has-nonzero-nonlinear-response",
        "finding:all-common-leading-distance-clutches-fail-original-flavor-lengths",
        "finding:actual-hardy-response-has-weak-clifford-odd-and-ko-real-completion",
        "finding:two-entry-hardy-adjoint-hierarchy-fails-full-ko-and-su2",
        "finding:actual-fuchs-halfpath-has-canonical-g-metric-c6-kernel-map",
        "finding:original-real-delta-jet-reads-same-marked-hardy-open-word",
        "finding:four-actual-fuchs-spine-edges-recover-marked-meridians-and-nonzero-open-word",
        "finding:native-adjoint-quarter-clock-cannot-compensate-hardypair-odd-character",
        "finding:whole-cubic-gram-differential-retains-hardy-phase-and-cross-resonance",
        "finding:complete-original-mu01-hardy-reader-has-two-calibrated-entries",
        "finding:whole-six-original-hardy-inputs-generate-full-family-coefficient-algebra",
        "finding:actual-whole-hardy-alphabet-has-finite-particle-hole-wick-block",
        "finding:bare-unsmeared-mu-crossface-quadratic-fails-vacuum-domain",
        "finding:linear-spectral-centralization-does-not-replace-full-marked-hardy-source",
        "finding:original-admissibility-projector-is-explicit-penalties-do-not-read-retained-amplitudes",
        "finding:actual-original-inner-fluctuation-has-whole-noncommuting-two-face-response",
        "finding:fiber-only-primitive-split-and-frozen-gap-miss-original-action",
        "finding:oriented-resolvent-weights-do-not-identify-original-reflection-producer",
        "finding:current-odd-carrier-reader-is-lossless-on-whole-coupled-source",
        "finding:ap-spectral-formulas-do-not-force-normal-domain-or-complete-source",
        "finding:actual-weak-connection-transmits-family-orientation-to-both-faces",
        "finding:original-higgs-variation-is-not-independent-yukawa-stationarity",
        "finding:actual-weak-cap-converges-on-whole-quarter-circle",
        "finding:canonical-clifford-double-derives-normal-ap-and-typed-deck",
        "finding:universal-graded-source-reducing-images-do-not-fix-carrier-frame",
        "finding:whole-two-face-compression-projector-defect-detects-hidden-source-loss",
        "finding:actual-v252-quark-lepton-split-prevents-weak-grading-uniqueness-inference",
        "finding:actual-graded-hypercharge-trace-rejects-quark-lepton-sign-intertwiner",
        "finding:separable-normal-real-maps-compose-to-given-deck-and-quarter-image",
        "finding:actual-gauge-real-frames-leave-carrier-phase-as-coordinate-freedom",
        "finding:original-higgs-family-has-one-complex-kk-class-but-different-whole-sources",
        "finding:signed-one-particle-modular-weight-is-not-the-positive-even-heat-operator",
        "finding:three-moments-select-one-exponential-exactly-in-positive-laplace-class",
        "finding:existing-ap-positive-source-factor-has-oriented-poisson-heat-bridge",
        "finding:actual-v252-entire-compatibility-family-has-generic31-dimensional-quotient",
        "finding:full-memory-schur-reconstruction-preserves-every-ordered-word-under-nesting",
        "finding:original-return-and-native-j-have-minimal68-dimensional-all-word-memory",
        "finding:original-full-source-regulator-flow-retains-normalized-kernel-and-vacuum-factor",
        "finding:full-reflected-quadratic-regulator-cone-preserves-every-rp-source",
        "finding:original-shared-higgs-source-induces-fixed-yukawa-mixed-matter-words",
        "finding:local-even-yukawa-sewing-preserves-given-joint-graded-rp",
        "finding:whole-original-constant-higgs-orbit-has-reduced-majorana-spectral-response",
        "finding:archived-geometric-higgs-residue-bulk-needs-coefficient-identification-repair",
        "finding:original-local-higgs-residue-linear-coefficients-fail-same-trace-heat-ratio",
        "finding:whole-original-higgs-moments-fix-conditional-local-kinetic-mass-quartic",
        "finding:whole-variable-original-higgs-bound-reference-response-and-forced-clifford-factor",
        "finding:original-symmetric-scale-map-fails-simultaneous-higgs-einstein-repair",
        "finding:whole-original-higgs-inner-scale-and-affine-full-source-transport",
        "finding:normal-higgs-mode-type-and-exact-kernel-metric-require-actual-relative-operator-map",
        "finding:original-superconnection-grades-and-weighted-heat-retain-higgs-kinetic-excursions",
        "finding:whole-normal-reduction-preserves-relative-spectral-reader-and-higgs-jets",
        "finding:original-admissibility-own-spectral-reader-has-no-free-low-mode-residue-repair",
        "finding:whole-total-chiral-positive-spectrum-retains-higgs-kinetics-and-common-half-trace",
        "finding:whole-scale-energy-response-uniquely-reconstructs-normal-profile",
        "finding:original-relative-scale-flow-separates-residue-finite-part-and-local-anomaly",
        "finding:original-whole-green-produces-energy-response-with-correct-orthogonal-trace",
        "finding:whole-mixed-scale-source-reads-bosonic-insertion-before-higgs-average",
        "finding:current-original-spectral-action-triplet-fails-positive-laplace-class-unless-leading-relative-term-cancels",
        "finding:correct-current-argument-weights-link-whole-higgs-threshold-and-same-einstein-response",
        "finding:whole-original-spinor-curvature-a4-has-no-independent-scalaron-r-squared",
        "finding:whole-original-entropic-curvature-corrects-max-symmetric-scalar-scale",
        "finding:given-whole-higgs-source-fixes-radial-curvature-susceptibility-without-extra-scalar",
        "finding:actual-original-four-ghost-complex-preserves-base-selector-with-full-cohomology-and-distinct-traces",
        "finding:whole-original-admissibility-energy-source-recovers-constraints-but-cannot-replace-geometric-operator",
        "finding:original-moving-normal-kernel-fixes-induced-connection-and-full-scale-covariance",
        "finding:fixed-original-o1-source-rejects-nonconstant-normal-multiplier-and-fixes-placement-test",
        "finding:original-master-variation-keeps-spin-weight-and-active-source-route-typed",
        "finding:shared-original-higgs-mixture-has-invariant-color-fourpoint-wick-defect",
        "finding:bounded-fixed-rank-spectral-action-does-not-normalize-noncompact-higgs-volume",
        "finding:whole-original-quarter-source-bounds-higgs-weight-uniformly-through-joint-mode-ir-limits",
        "finding:original-o1-covariance-leaves-full-radial-higgs-law-and-exact-fourier-source-readout",
        "finding:whole-process-reconstruction-priority-and-original-locality-geometry-input-audit",
        "finding:actual-disjoint-local-weyls-acquire-spurious-commutator-under-bare-native-compression",
        "finding:actual-quarter-current-state-excludes-nontrivial-geometric-local-point-time",
        "finding:actual-elliptic-interval-car-source-produces-local-modular-generator",
        "finding:actual-proper-two-face-regions-do-not-contain-pure-local-source-double",
        "finding:actual-elliptic-whole-environment-fixes-regional-car-partner",
        "finding:actual-original-color-triplet-has-spectator-dependent-modular-field-law",
        "finding:actual-color-marginal-has-complete-finite-source-reader-and-mixture-criterion",
        "finding:two-and-four-field-words-do-not-complete-original-color-triplet-source",
        "finding:whole-original-quarter-occupation-tower-uniquely-reconstructs-common-radial-higgs-law",
        "finding:finite-original-tower-reader-and-existing-weak-symmetry-fix-shared-matter-responses",
        "finding:unchanged-free-quarter-source-cannot-be-nontrivial-integrated-higgs-mixture",
        "finding:actual-e8-record-doily-action-is-signed-p-plus-compatible-point-with-typed-sym2-lift",
        "finding:actual-e8-record-words-distinguish-order-and-retain-phase-beyond-fifteen-labels",
        "finding:literal-doily-incidence-output-and-strict-causal-order-on-fifteen-source-labels-excluded",
        "finding:actual-doily-context-record-characters-have-ranks-four-two-two-two",
        "finding:canonical-standard-split-localizes-original-source-record-words-with-full-descendant-companion",
        "finding:unchanged-global-sixty-event-source-fails-local-exterior-current-test",
        "finding:canonical-source-localization-changes-exterior-state-and-does-not-select-event-origin",
        "finding:original-elliptic-fixed-holonomy-insertion-gives-local-operation-on-unchanged-source",
        "finding:original-quarter-pair-fixes-square-charge-law-half-response-and-real-quillen-norm",
        "finding:actual-elliptic-source-determines-all-path-normalized-causal-current-response",
        "finding:original-higgs-quark-source-has-exact-whole-su3-counting-response",
        "finding:single-original-color-parity-separates-free-quillen-from-positive-higgs-integrated-source",
        "finding:whole-original-quarter-graph-color-response-is-relative-and-diagonal-singlet",
        "finding:original-center-selector-requires-typed-state-field-and-face-transport",
        "finding:original-color-center-fixes-whole-e6-a2-source-and-charged-ward-word-action",
        "finding:original-color-neutral-lattice-class-cannot-supply-odd-fields-by-inherited-superlattice-extension",
        "finding:original-color-center-extends-to-folded-ns-but-full-current-action-needs-spin-sector-transport",
        "finding:actual-color-spin-car-mixed-word-has-complete-thermal-source-and-cyclic-sewing",
        "finding:exact-original-ns-ramond-heat-equality-does-not-identify-fixed-color-restricted-source",
        "finding:original-scalar-cover-profile-cannot-implement-fixed-spin-cartan-loop",
        "finding:actual-spin-cartan-composite-source-retains-multi-arc-support-and-fails-additive-even-locality",
        "finding:actual-color-selector-admits-exactly-eighth-periodic-original-density-variations",
        "finding:actual-color-is-internal-exactly-on-eightfold-coordinate-source-regions",
        "finding:original-whole-two-face-multiplier-reduction-is-only-constant-residue-diagonal",
        "finding:original-two-face-local-fock-implementation-and-exact-source-variation-differ-from-reduction",
        "finding:whole-undecorated-transfer-does-not-determine-original-marked-field-source",
        "finding:volume-wise-injective-positive-transfer-does-not-prove-uniform-parent-gap",
        "finding:original-c6-half-power-has-exact-entire-positive-ordered-word-expansion",
        "finding:original-c6-whole-word-sewing-retains-source-amplitude-and-controlled-infinite-tail",
        "finding:historical-parent-and-actual-field-time-bridges-must-be-reused-before-new-source-models",
        "finding:actual-native-v990-full-timed-words-recover-kubo-response-distinct-from-instantaneous-variance",
        "finding:actual-original-higgs-force-has-complete-ordered-fermionic-determinant-source",
        "finding:finite-covariant-higgs-composites-have-no-nontrivial-positive-instantaneous-classical-law",
        "finding:actual-original-collective-mean-has-exact-ball-domain-and-relative-entropy-action",
        "finding:original-uniform-allmode-force-clt-is-nonzero-only-before-fixed-time-smearing",
        "finding:original-unscaled-time-smeared-force-has-selfadjoint-whole-ordered-source",
        "finding:original-local-higgs-force-has-whole-centered-hilbert-schmidt-determinant-source",
        "finding:given-original-circle-force-source-generates-an-exact-causal-local-net",
        "finding:literal-archived-global-rg-kernel-does-not-preserve-finite-measures",
        "finding:native-higgs-marginal-retains-induced-vertex-and-noether-response",
        "finding:isospectral-noether-orbit-does-not-supply-original-metric-higgs-variation",
        "finding:metric-dtn-form-bound-needs-transfer-comparison-for-gap",
        "finding:conditional-higgs-pair-winding-protection-in-common-circle-carrier",
        "finding:natural-five-clock-carrier-excludes-invariant-three-transfer-compression",
        "finding:shared-scalar-shift-whole-retained-higgs-sector-has-index-minus-eighteen",
        "finding:whole-coupled-quark-circle-common-shift-cancels-relative-winding",
        "finding:one-sided-shift-full-higgs-pair-is-hilbert-schmidt-not-trace-class",
        "finding:selective-coupled-higgs-reader-has-well-defined-det2",
        "finding:v311-population-reader-does-not-identify-quantum-channel",
        "finding:declared-charged-pair-relation-leaves-five-word-ambiguity",
        "finding:full-creator-relations-close-fixed-free-two-mode-ambiguity",
        "finding:comoving-diagnostic-clock-exact-response-but-nonlocal-mode-transport",
        "finding:free-quarter-two-face-response-strip-with-relative-zero-mode-defect",
        "finding:e8-hodge-event-perfectly-distinguishable-from-every-unitary",
        "finding:common-five-slot-transfer-preserves-e8-bracket-not-automatic-tp",
        "finding:comoving-clock-dynamic-higgs-connection-and-charged-flow",
        "finding:r064-sixty-record-channel-exact-distance-and-continuous-record-parent",
        "finding:two-syntheses-shared-source-priorities-and-typed-limits",
        "finding:weighted-index-trace-and-selfdual-theta-require-original-selection",
        "finding:ordered-quarter-fourfield-e8-record-and-charge-filters",
        "finding:r091-recovered-native-hodge-sewing-and-full96-quarter-complement",
        "finding:r092-fold-ward-target-neutral-source-and-smaller-creation-branch",
        "finding:r093-original-kink-time-response-distinguishes-quarter-states",
        "finding:r093-ordered-current-kink-and-eight-arc-locality",
        "finding:r094-original-five-excitations-distinct-from-clustering-vacuum",
        "finding:r096-joint-higgs-twoface-source-constraint",
        "finding:r096-positive-twoface-fourword-defect-bound",
        "finding:r096-unnormalized-mixed-source-linear-identity",
        "finding:r096-original-quark-crossing-negative-covariance",
        "finding:known-fourmark-system-has-three-and-five-canonical-views",
        "finding:reverse-bootstrap-retained-operator-scope",
        "finding:e8-current-dictionary-all-separated-responses",
        "finding:charged-scaling-microscopic-map-still-unspecified",
        "finding:original-slater-proxy-fitted-bound-fails-actual-norm",
        "finding:periodic-microscopic-zero-modes-distinguish-source-state",
        "finding:r097-original-q-twins-are-integrally-conjugate-before-fixed-source-form",
        "finding:replicated-deterministic-consistency-iff-influence-dag",
        "finding:three-binary-processes-two-copy-reversible-classification",
        "finding:independent-poset-information-composition-consequences",
        "finding:reset-diagnosis-not-global-tfpt-underdetermination",
        "finding:three-inequivalent-repeatable-observation-countermodels",
        "finding:repeatable-reports-do-not-imply-full-state-stability",
        "finding:finite-sequential-data-admit-classical-history-realization",
        "finding:pascal-carrier-rank-unique-unbounded-source-proof",
        "finding:finite-carrier-glue-elements-orbits-and-halfway",
        "finding:actual-clock-doily-ovoid-kernel-is-native-quartic-five",
        "finding:glue-clock-twisted-sectors-share-marked-quadratic-module",
        "finding:complete-native-six-effect-covariant-instrument-classification",
        "finding:native-six-effect-readout-on-existing-erasure-output",
        "finding:relational-quartic-singlet-and-invariant-density-separation",
        "finding:new-clock-feedback-origin-input-audit",
        "finding:native-event-channel-cone-intersection-is-tenth-to-half",
        "finding:native-six-ovoid-observation-first-occurs-at-tensor-degree-three",
        "finding:original-quartic-erasure-and-hamming-octic-share-marked-ovoid-response",
        "finding:native-octic-field-ray-is-explicit-but-retained-clock-stress-preparation-fails",
        "finding:actual-quarter-fold-stress-has-nonzero-octic-eighth-jet",
        "finding:native-octic-is-an-original-even-car-current-composite",
        "finding:original-geometric-source-jet-and-partial-p1-seed-closure",
        "finding:full-root-ope-has-normalized-native-octic-component",
        "finding:paper-microscopic-car-composes-with-native-octic-ward",
        "finding:microscopic-neutral-octic-has-controlled-smeared-limit",
        "finding:paper-seed-source-needs-local-image-not-global-equivalence",
        "finding:full-car-positive-time-forces-source-vacuum",
        "finding:original-winding-theorem-does-not-select-seam-ray",
        "finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel",
        "finding:original-os-step-needs-full-moments-not-connected-cumulants",
        "finding:graded-field-image-precedes-physical-observable-restriction",
        "finding:older-original-circle-representative-already-realizes-ward-and-index",
        "finding:old-quarter-heat-transfer-has-controlled-rank-one-limit-and-odd-product",
        "finding:historical-em-rank-one-and-full-heat-traces-have-different-contracts",
        "finding:older-frg-functional-already-supplies-formal-full-moment-parent",
        "finding:earliest-c3-route-quantizes-level-but-needs-physical-kinetic-normalization",
        "finding:canonical-positive-circle-half-selects-the-toeplitz-line-and-sixth-order-correction",
        "finding:old-seam-shift-canonically-gives-relative-car-line-and-fredholm-factor",
        "finding:old-index-coupling-removes-heat-map-and-has-sharp-residual-ward-test",
        "finding:original-admissibility-requires-image-membership-not-positive-half-or-commutation",
        "finding:old-closure-already-assumes-car-but-does-not-map-the-geometric-circle",
        "finding:historical-uv-map-infinite-mass-exclusion-already-proved-and-recovered",
        "finding:a4-spin-lift-fixes-local-ns-and-unordered-quarter-pair",
        "finding:cover-winding-exchanges-quarter-sectors-before-its-square",
        "finding:retained-winding-preserves-local-support-and-neutral-time",
        "finding:marked-glue-square-is-the-e8-fermionization-character",
        "finding:fixed-canonical-d8-is-not-transported-source-d8",
        "finding:actual-winding-has-four-module-e8-defect-extension",
        "finding:ramond-lift-sign-is-common-intertwiner-basis-gauge",
        "finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class",
        "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor",
        "finding:schur-carrier-plus-complement-preserves-original-relative-determinant",
        "finding:v258-forward-source-gap-is-reused-not-solved-by-inversion",
        "finding:one-sided-source-and-real-em-norm-need-response-map-not-chiral-phase",
        "finding:trace-class-pair-index-fixes-relative-factor-without-primitive-ray",
        "finding:matrix-clutch-degree-connects-weak-determinant-class-without-ray-selector",
        "finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index",
        "finding:inner-carrier-is-infinite-spacetime-module-not-finite-circle-cut",
        "finding:normal-spin-determinant-line-exactly-transports-whole-circle-in-given-product",
        "finding:normal-index-line-source-match-is-holonomy-condition-not-vertical-degree",
        "finding:full-normal-product-polarization-change-is-not-trace-class",
        "finding:massive-transverse-zero-index-retains-positive-determinant-response",
        "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel",
        "finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection",
        "finding:tetrahedral-quarter-face-phase-does-not-identify-original-quarter-marked-curve",
        "finding:existing-elliptic-cover-correspondence-has-exact-c6-image-and-retained-mixed-clock",
        "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
        "finding:global-split-joint-carrier-admits-parallel-native-c12-clock",
        "finding:pure-weak-clutch-clock-identification-fails-despite-quarter-matches",
        "finding:same-chern-clutch-native-compiler-does-not-select-physical-connection",
        "finding:native-gaussian-four-is-cartan-subspace-in-whole-sixtyfour",
        "finding:native-family-factor-is-not-gaussian-four-despite-symmetric-coincidences",
        "finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice",
        "finding:even-degree-pullback-removes-cartan-topology-without-selecting-clock-cover",
        "finding:global-cartan-choice-is-optional-for-original-scalar-source-fields",
        "finding:bare-native-octic-is-not-whole-e8-zero-mode-singlet",
        "finding:explicit-primary-e8-invariant-octic-completes-same-neutral-car-source",
        "finding:completed-octic-has-exact-old-root-ope-component-and-quarter-source-value",
        "finding:elliptic-normal-spin-pullback-doubles-index-and-deck-quarter-lifts-anticommute",
        "finding:exact-separated-w8-twopoint-in-original-quarter-current-source",
        "finding:unshifted-vacuum-fails-same-w8-source-state-time-dictionary",
        "finding:local-current-phase-and-conditional-cyclic-p1-w8-image",
        "finding:all-neutral-w8-correlations-identify-the-two-original-quarter-charges",
        "finding:original-w8-response-has-infinite-same-time-spectral-support",
        "finding:older-seam-equivalence-verifications-do-not-supply-marked-local-p1-map",
        "finding:full-original-c1-stress-cycle-reconstructs-neutral-w8-response",
        "finding:folded-c8-cycle-misses-intrinsic-w8-tangent-without-obstructing-original-stress",
        "finding:native-source-first-nonuniform-moment-is-four-with-literal-five",
        "finding:native-whole-five-ground-space-needs-four-register-interaction",
        "finding:old-cover-winding-reconstructs-local-quarter-current-net",
        "finding:untransported-independent-quarter-stress-pair-is-not-current",
        "finding:current-public-paper-bytes-and-binding-source-gaps-recovered",
        "finding:winding-charge-conjugation-descends-fixed-pin-domain-but-not-full-dirac-sea",
        "finding:native-fourth-root-frame-has-signed-collective-sixty-mode-dual",
        "finding:native-root-gram-spectrum-is-not-canonical-source-energy-selection",
        "finding:identical-overlapping-native-five-codes-have-no-common-state",
        "finding:horizontal-e8-invariant-octic-cannot-isolate-native-five-ground-space",
        "finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea",
        "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity",
        "finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp",
        "finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum",
        "finding:declared-recursive-native-som-is-u35-equivariant",
        "finding:declared-recursive-native-som-clocks-depend-on-chosen-rates",
        "finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower",
        "finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent",
        "finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms",
        "finding:finite-crosscap-cauchy-state-is-not-original-quarter-vacuum-by-normal-filtering",
        "finding:native-quartic-relative-arc-charge-excludes-additive-density-stress-insertion",
        "finding:retained-quarter-sea-finite-modular-transfer-preserves-integrated-native-cartan",
        "finding:original-neutral-interarc-fields-have-exact-connected-current-vertex-reconstruction",
        "finding:actual-pin-zero-branch-retains-quarter-car-state-time-but-no-uniform-scale-return",
        "finding:conformal-pin-source-geometry-fixes-exterior-return-and-unitary-memory",
        "finding:geometric-exterior-schur-response-transfers-proper-native-arc-charge-but-is-compact",
        "finding:actual-ns-half-cover-cauchy-graph-purifies-green-state-with-neutral-ground-time-obstruction",
        "finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots",
        "finding:full-marked-equatorial-pullback-is-ramified-graph-not-smooth-seam-circle",
        "finding:same-elliptic-szego-green-functional-has-all-word-free-rp-and-calderon-marginal",
        "finding:elliptic-scalar-spin-pushforward-has-original-holomorphic-p2-anchor",
        "finding:natural-elliptic-anchor-connection-is-not-original-p2-cusp-connection",
        "finding:actual-elliptic-gaussian-source-determines-full-quarter-current-functional",
        "finding:elliptic-current-state-differs-from-hardy-on-every-proper-current-interval",
        "finding:primitive-geometric-force-retains-coupled-reference-and-parity-variation",
        "finding:equal-finite-positive-heat-channel-values-do-not-fix-geometric-force",
        "finding:elliptic-ns-spin-trace-has-complete-global-quarter-kernel",
        "finding:source-induced-ramified-resolutions-do-not-select-quarter-circle-domain",
        "finding:fixed-native-and-fermat-c3-carriers-do-not-identify-marked-v117-pair",
        "finding:theta-square-modular-pair-reconstructs-v117-with-distinct-geometric-q",
        "finding:archived-d4-puncture-formula-fails-and-existing-v117-repairs-existence",
        "finding:geometric-square-clock-is-not-theta-v117-quarter-generator",
        "finding:canonical-conformal-boundary-trace-fixes-existing-elliptic-cauchy-state",
        "finding:conformal-factor-averaging-preserves-given-free-boundary-wick-words",
        "finding:retained-seam-defect-has-derived-causal-geometric-response-with-contact",
        "finding:same-final-pin-geometry-retains-history-while-relative-index-factor-is-fixed",
        "finding:full-projector-covariance-and-positivity-force-all-car-words",
        "finding:actual-two-face-projector-reduces-free-source-test-to-cross-coherence",
        "finding:retained-marked-quarter-compiler-has-no-local-geometric-wick-correction",
        "finding:changed-elliptic-modulus-has-derived-cauchy-response-and-neutral-fourfield-variance",
        "finding:actual-equatorial-half-form-trace-fixes-orthogonal-hardy-range",
        "finding:actual-holomorphic-quarter-cauchy-idempotents-are-not-positive-car-covariances",
        "finding:full-equatorial-checkerboard-free-algebra-fails-fixed-reflection-positivity",
        "finding:genuine-d4-orbifold-branch-has-unique-irreducible-v117-class",
        "finding:wall-weight-additivity-does-not-exclude-stable-v117-parabolic-bundle",
        "finding:recovered-september-c4-triangle-closes-original-a0star-monodromy",
        "finding:actual-a0star-connection-does-not-have-rational-base-inversion-lift",
        "finding:actual-v117-sign-lines-are-negative-weierstrass-triangle-two-torsion",
        "finding:antipodal-and-positive-sign-packets-fail-actual-marked-v117-ramification",
        "finding:common-cyclic-twelve-cover-does-not-trivialize-v117-unramified-sign-lines",
        "finding:negative-sign-packet-has-source-selected-quarter-clock-lift",
        "finding:original-root-and-sign-lines-have-minimal-degree48-common-cover",
        "finding:given-elliptic-flat-connection-family-has-explicit-quillen-norm-and-two-holonomies",
        "finding:bare-large-gauge-quillen-norm-does-not-equal-original-winding-counting-factor",
        "finding:existing-elliptic-half-period-has-canonical-graded-gns-intertwiner",
        "finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law",
        "finding:declared-recursive-machine-baseline-controls-and-recovery-are-finitely-measured",
        "finding:declared-recursive-machine-long-run-retains-motion-at-stable-aggregate-rank",
        "finding:recursive-kohonen-source-investigation-has-source-verified-atlas-handoff",
        "finding:chat-algorithmic-comparison-native-pauli-code-and-scoped-information-loss",
        "finding:chat-20261026-results-consolidated-with-corrected-assumptions",
        "finding:source-inversion-forces-six-line-theta-completion",
        "finding:literal-geometric-quarter-is-not-central-gaussian-quarter-on-labels",
        "finding:source-cubic-and-quarter-select-even-theta-and-spin-half-turn-lift",
        "finding:source-cubic-matches-native-pauli-translations-after-context-target-correction",
        "finding:joint-source-clock-relations-have-one-native-clifford-gauge-class",
        "finding:ordinary-theta-determinant-erases-selected-spin-central-character",
        "finding:marked-negative-point-norm-restores-required-spin-central-character",
        "finding:point-normalized-theta-family-correction-fails-original-cubic-action",
        "finding:source-spin-relative-poincare-normalization-closes-point-norm-family",
        "finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package",
        "finding:tfpt-origin-investigation-full-source-coverage-and-current-frontier",
        "finding:full-clock-norm-power-class-and-canonical-eighth-period",
        "finding:original-unit-winding-selects-one-inverse-norm-in-three-cabled-hardy-pair",
        "finding:original-boundary-audit-and-h1-point-restriction-limit",
        "finding:eta-phase-conventions-do-not-identify-relative-spin-reference-pair",
        "finding:same-spin-unit-shift-gives-native-module-class-with-odd-determinant-line",
        "finding:original-even-odd-operator-split-is-compatible-with-same-spin-seam-reference",
        "finding:elliptic-projector-and-weyl-results-retain-their-source-type-at-cubic-spin-bridge",
        "finding:cubic-spin-cauchy-range-is-three-hardy-with-strong-domain-distinction",
        "finding:original-negative-sea-three-mode-ket-is-dual-to-required-hardy-line",
        "finding:auxiliary-theta-route-needs-no-physical-cubic-bulk-or-eta-selected-dual",
        "finding:primitive-gaussian-theta-frame-constructs-e8-pair-with-retained-spin-action",
        "finding:existing-c12-lift-induces-coherent-two-object-e8-vertex-groupoid",
        "finding:actual-winding-functional-calculus-preserves-ns-ramond-split",
        "finding:single-chiral-cycle-exchange-selects-e8-in-four-extension-class",
        "finding:affine-source-involution-pairs-full-d8-sector-spectra",
        "finding:marked-local-e8-with-unchanged-source-time-fails-euclidean-clustering",
        "finding:original-parity-audit-does-not-supply-local-spinor-gauging",
        "finding:hypergraph-local-update-repaired-with-full-family-clock",
        "finding:petersen-polar-step-has-exact-double-cover-family-intertwiner",
        "finding:petersen-source-current-and-hodge-candidates-fail-physical-identification",
        "finding:a7-clock-direction-identifies-neutral-e7-zero-root",
        "finding:oriented-sewing-cocycle-distinguishes-continuation-and-reversal",
        "finding:calderon-single-face-compression-is-not-perron-projector",
        "finding:hodge-born-magnitudes-and-filtered-petersen-jump-match",
        "finding:five-complement-amplitudes-form-full-petersen-quantum-channel",
        "finding:original-twenty-events-factor-through-hodge-and-conditional-phase-record",
        "finding:actual-e8-mixed-current-response-is-full-clifford-channel",
        "finding:carrier-su5-centralizer-gives-direct-e8-petersen-response",
        "finding:su5-covariance-and-petersen-support-fix-complete-quantum-response",
        "finding:neutral-pair-witness-separates-old-events-and-hodge-response",
        "finding:original-degree-clock-is-not-carrier-slot-cycle-at-fixed-source",
        "finding:full-mark-transport-and-isospectrality-do-not-select-hodge-channel",
        "finding:original-pair-source-fixes-state-but-not-selected-epsilon-process",
        "finding:single-positive-process-saturation-selects-full-hodge-channel",
        "finding:original-five-slot-wedge-is-exact-e8-hodge-coefficient",
        "finding:native-pauli-f20-metric-and-quarter-bridge",
        "finding:two-actual-coherent-events-herald-hodge-at-one-over-twenty-five",
        "finding:original-color-center-removes-only-extra-h8-ground-state",
        "finding:marked-symplectic-functor-fixes-native-hodge-kraus-space",
        "finding:f20-record-repair-removes-chart-induced-three-plus-two",
        "finding:theta-scalar-square-lift-is-distinct-from-symplectic-f20-lift",
        "finding:full-admissibility-vacuum-test-needs-source-image-and-transfer-reduction",
        "finding:canonical-native-spin5-hodge-is-already-one-source-record-subchannel",
        "finding:native-hodge-record-selector-is-image-projector-not-kraus-kernel",
        "finding:irreducible-f20-four-cannot-host-original-independent-native-family-clock",
        "finding:native-hodge-is-exact-collective-five-current-action",
        "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
        "finding:six-hodge-responses-have-exact-full-current-barycenter",
        "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts",
        "finding:spin5-hodge-five-is-plucker-kernel-not-original-quartic-hessian",
        "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
        "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
        "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
        "finding:old-ward-root-generates-exact-charged-fifty-module",
        "finding:tp-charged-bracket-support-forces-entire-carrier-marginal",
        "finding:original-ward-and-p2-grading-select-smaller-creation-thirty",
        "finding:charged-source-quarter-recovers-inverse-internal-glue",
        "finding:state-independent-creation-branch-removes-whole-process-hodge-demand",
        "finding:given-source-current-constructs-half-kink-spinor-transport",
        "finding:neutral-ward-response-needs-no-spinor-observable-membership",
        "finding:actual-source-sector-transport-distinguishes-identical-hodge-marginals",
        "finding:ordinary-weyl-type-obstruction-to-single-chiral-os-anti-anti-reflection",
        "finding:given-two-face-source-derives-opposite-neutral-weyls-and-bounded-time-reflection",
        "finding:verification-recovery-preserves-local-source-chain-and-eight-gate-completeness",
        "finding:positive-spectral-reweighting-does-not-establish-original-source-rp",
        "finding:gapped-quarter-energy-cannot-be-same-borchers-translation",
        "finding:finite-ko6-pairing-does-not-supply-standalone-pfaffian-source",
        "finding:full-free-projector-forces-joint-commuting-source-factorization",
        "finding:actual-neutral-current-source-has-constructive-moebius-standard-pair",
        "finding:continuous-local-current-weyls-cannot-live-in-finite-coordinate-fibers",
        "finding:actual-folded-current-ward-and-state-determine-all-neutral-words",
        "finding:mixed-vector-axial-current-is-existing-full-car-subalgebra",
        "finding:constant-product-time-stable-current-level-is-kernel-index",
        "finding:paired-quarter-source-candidate-needs-original-filter-and-oriented-conjugation",
        "finding:graded-boundary-clifford-typing-transports-full-scalar-and-finite-coupled-source",
        "finding:actual-charge-j-transport-retains-full-dirac-and-distinct-pairings",
        "finding:fixed-graded-chart-transports-normal-dependent-source-and-given-mixed-moments",
        "finding:neutral-many-body-source-time-is-not-finite-summable-geometric-dirac",
        "finding:actual-product-reflection-and-same-time-have-full-positive-clifford-source-intertwiner",
        "finding:actual-v252-positive-grade-has-global-p2-wedge-dictionary",
        "finding:old-quarter-full-source-embeds-locally-exactly-on-decoupled-channel",
        "finding:petersen-population-full-cptp-p5-range-zero-to-ten",
        "finding:marked-sm-phase-p5-exact-range-and-response-collision",
        "finding:shared-epsilon-tp-process-fixes-hodge-marginal-even-for-correlated-inputs",
        "finding:puncture-meridians-have-one-glue-class-and-residue-duality-does-not-select-metric",
        "finding:joint-integral-unimodular-charge-closure-uniquely-selects-complete-invariant-metric",
        "finding:meridian-spinor-joint-source-product-has-actual-family-root-simple-pole",
        "finding:r098-withheld-response-search-has-exact-conditional-affine-certificates",
        "finding:r098-whole-finite-process-segment-preserves-2245-moments"
      ],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:528b3002ad6d3e8565e949a6"
      ]
    },
    {
      "id": "topic:e8",
      "titleEN": "Carrier, families and E8 closure",
      "summaryEN": "The finite compiler combines a five-slot carrier, a selected half-spinor action, D5×A3 and Z4 glue into an E8 lattice closure. This establishes a mathematical construction within its stated choices, not the physical gauge group or a first-principles origin.",
      "orientation": {
        "role_en": "Finite structural closure of the compiler: a concrete E8 lattice construction is built from the chosen carrier action and family side.",
        "have_en": "Under the stated actions, D5×A3 with Z4 glue gives the even unimodular rank-8 E8 lattice; the half-spinor reading depends on the chosen group action.",
        "seek_en": "Open items include physical boundary realization, a local interacting chiral 3+1D implementation, mirror decoupling, and derivation of the action from the origin.",
        "connection_en": "E8 carries internal clock, code, flavor, and arithmetic structures. Rank, representation, family count, and spacetime dimension remain distinct types.",
        "next_bridge_en": "The selected finite action must be realized inside the same local parent with a controlled limit."
      },
      "problemIds": [
        "problem:seam-family-connection-compatibility",
        "problem:flavor-ratio-amplitude-readout",
        "problem:alpha-fixed-input-root",
        "problem:clock-source-covariant-transport",
        "problem:constructive-seam-lift-state",
        "problem:seam-partner-charge-state-time",
        "problem:reverse-bootstrap-physical-field-dictionary",
        "problem:carrier-pascal-glue-formal-scope",
        "problem:marked-seam-monodromy-and-lattice-lifts",
        "problem:atlas-clock-defect-and-operational-reconstruction"
      ],
      "findingIds": [
        "finding:joint-discrete-data-vs-connection",
        "finding:parallelity-excludes-2plus2-only-conditionally",
        "finding:flavor-ratio-closed-absolute-anchor-open",
        "finding:alpha-equation-is-fixed-input-closure",
        "finding:alpha-global-positive-root-unique",
        "finding:marked-e8-sector-grade-response-realizes-five-quarters",
        "finding:alpha-exact-coefficients-and-root-retain-specific-physical-ward-obligation",
        "finding:alpha-archive-term-provenance-and-master-functional-scope",
        "finding:actual-j-covariant-source-transport",
        "finding:fixed-source-affine-j-obstruction",
        "finding:constructive-phase-class-and-full-winding",
        "finding:constructive-positive-state-extension",
        "finding:constructive-current-group-selects-positive-p-lift",
        "finding:constructive-state-algebra-resolution-and-source-test",
        "finding:constructive-all-phases-fail-unchanged-source",
        "finding:partner-carrier-charges-and-state-types",
        "finding:partner-fixed-quarter-time-splits-sm-multiplet",
        "finding:partner-original-carrier-cross-sheet-conjugation",
        "finding:partner-chiral-quarter-conjugation-state-time",
        "finding:joint-bilinear-hermitian-correction",
        "finding:joint-quarter-transports-marking",
        "finding:joint-fixed-time-marking-repair-excluded",
        "finding:joint-spinor-not-source-coefficient",
        "finding:known-fourmark-system-has-three-and-five-canonical-views",
        "finding:reverse-bootstrap-retained-operator-scope",
        "finding:e8-current-dictionary-all-separated-responses",
        "finding:charged-scaling-microscopic-map-still-unspecified",
        "finding:original-slater-proxy-fitted-bound-fails-actual-norm",
        "finding:periodic-microscopic-zero-modes-distinguish-source-state",
        "finding:r097-original-q-twins-are-integrally-conjugate-before-fixed-source-form",
        "finding:pascal-carrier-rank-unique-unbounded-source-proof",
        "finding:finite-carrier-glue-elements-orbits-and-halfway",
        "finding:marked-seam-category-and-character-valued-full-lift-factor",
        "finding:quarter-clock-sign-lift-complete-four-puncture-classification",
        "finding:quarter-lift-central-quotient-class-and-all-subgroup-restrictions",
        "finding:native-clock-reflection-full-factor-cocycle-trivialization",
        "finding:native-quartic-exterior-local-cohomology-distinguishes-clock-monodromies",
        "finding:orbifold-lift-criterion-and-determinant-eight-divisibility",
        "finding:original-g31-reflection-census-and-all-integral-cohomology",
        "finding:all62-original-clock-obstructions-and-central-variants",
        "finding:actual-sign-lift-g31-group-comparison",
        "finding:complete-g31-lift-invariants-and-explicit-collisions",
        "finding:e7-quarter-pairs-literal-native-g31-reflections",
        "finding:e6-root-subsystem-quarter-clock-discriminant-obstruction",
        "finding:e-series-square-cover-family-and-quarter-descent",
        "finding:e-series-integral-glue-and-normalization-nonidentifiability",
        "finding:global-original-g31-character-lift-nonsplitting",
        "finding:all62-original-character-clock-lifts-complete",
        "finding:all17-original-character-monodromy-lifts-complete",
        "finding:e7-pair-full-lattice-field-character-torsor",
        "finding:e-series-complete-native-compiler-cut-dictionary",
        "finding:common-cover-clock-and-maximal-integral-phi12-intertwiner",
        "finding:native-four-cut-projectors-unify48-fourthirds-fivequarters",
        "finding:complete-covariant-compiler-voa-source-and-weyl-closure",
        "finding:complete-fixed-jhat-cyclic-field-lift-and-associated-clock",
        "finding:relative-native-burau-clock-hom-faithful12-transport",
        "finding:e6-vertex-nonselection-survives-full-field-clock-phases",
        "finding:marked-c4-glue-unique-local-e8-vacuum-source",
        "finding:canonical-vacuum-clock-preserves-e6-nonselection",
        "finding:marked-generator-forces-e8-without-support-multiplicity-or-minimality-input",
        "finding:native-reflection-rotation-lift-classes-and-forgetful-images",
        "finding:quarter-clock-pure-mapping-class-complete-quotient",
        "finding:e8-cut-five-orbital-incidence-algebra-complete",
        "finding:compiler-d8-frame-requires-full-d5-a3-flag",
        "finding:tetrahedron-incidence-lossless-e6-reconstruction",
        "finding:restricted-clock-lift-and-global-cover-audit-reconciled",
        "finding:double-scalar-quarter-is-marked-glue-with-two-step-index",
        "finding:scalar-quarter-two-involutive-e8-extensions",
        "finding:native-quarter-glue-inner-conjugacy-and-oriented-tetrahedron-flags",
        "finding:native-cyclic-compiler-inner-conjugacy",
        "finding:recovered-e6-closed-81-current-module-and-unique-source-cubic",
        "finding:e-series-operational-role-review-and-source-time-centralizer",
        "finding:actual-clock-doily-ovoid-kernel-is-native-quartic-five",
        "finding:glue-clock-twisted-sectors-share-marked-quadratic-module",
        "finding:complete-native-six-effect-covariant-instrument-classification",
        "finding:native-six-effect-readout-on-existing-erasure-output",
        "finding:relational-quartic-singlet-and-invariant-density-separation",
        "finding:new-clock-feedback-origin-input-audit",
        "finding:native-event-channel-cone-intersection-is-tenth-to-half",
        "finding:native-six-ovoid-observation-first-occurs-at-tensor-degree-three",
        "finding:original-quartic-erasure-and-hamming-octic-share-marked-ovoid-response",
        "finding:native-octic-field-ray-is-explicit-but-retained-clock-stress-preparation-fails",
        "finding:actual-quarter-fold-stress-has-nonzero-octic-eighth-jet",
        "finding:native-octic-is-an-original-even-car-current-composite",
        "finding:original-geometric-source-jet-and-partial-p1-seed-closure",
        "finding:full-root-ope-has-normalized-native-octic-component",
        "finding:paper-microscopic-car-composes-with-native-octic-ward",
        "finding:microscopic-neutral-octic-has-controlled-smeared-limit",
        "finding:paper-seed-source-needs-local-image-not-global-equivalence",
        "finding:full-car-positive-time-forces-source-vacuum",
        "finding:original-winding-theorem-does-not-select-seam-ray",
        "finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel",
        "finding:original-os-step-needs-full-moments-not-connected-cumulants",
        "finding:graded-field-image-precedes-physical-observable-restriction",
        "finding:older-original-circle-representative-already-realizes-ward-and-index",
        "finding:old-quarter-heat-transfer-has-controlled-rank-one-limit-and-odd-product",
        "finding:historical-em-rank-one-and-full-heat-traces-have-different-contracts",
        "finding:older-frg-functional-already-supplies-formal-full-moment-parent",
        "finding:earliest-c3-route-quantizes-level-but-needs-physical-kinetic-normalization",
        "finding:canonical-positive-circle-half-selects-the-toeplitz-line-and-sixth-order-correction",
        "finding:old-seam-shift-canonically-gives-relative-car-line-and-fredholm-factor",
        "finding:old-index-coupling-removes-heat-map-and-has-sharp-residual-ward-test",
        "finding:original-admissibility-requires-image-membership-not-positive-half-or-commutation",
        "finding:old-closure-already-assumes-car-but-does-not-map-the-geometric-circle",
        "finding:historical-uv-map-infinite-mass-exclusion-already-proved-and-recovered",
        "finding:a4-spin-lift-fixes-local-ns-and-unordered-quarter-pair",
        "finding:cover-winding-exchanges-quarter-sectors-before-its-square",
        "finding:retained-winding-preserves-local-support-and-neutral-time",
        "finding:marked-glue-square-is-the-e8-fermionization-character",
        "finding:fixed-canonical-d8-is-not-transported-source-d8",
        "finding:actual-winding-has-four-module-e8-defect-extension",
        "finding:ramond-lift-sign-is-common-intertwiner-basis-gauge",
        "finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class",
        "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor",
        "finding:schur-carrier-plus-complement-preserves-original-relative-determinant",
        "finding:v258-forward-source-gap-is-reused-not-solved-by-inversion",
        "finding:one-sided-source-and-real-em-norm-need-response-map-not-chiral-phase",
        "finding:trace-class-pair-index-fixes-relative-factor-without-primitive-ray",
        "finding:matrix-clutch-degree-connects-weak-determinant-class-without-ray-selector",
        "finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index",
        "finding:inner-carrier-is-infinite-spacetime-module-not-finite-circle-cut",
        "finding:normal-spin-determinant-line-exactly-transports-whole-circle-in-given-product",
        "finding:normal-index-line-source-match-is-holonomy-condition-not-vertical-degree",
        "finding:full-normal-product-polarization-change-is-not-trace-class",
        "finding:massive-transverse-zero-index-retains-positive-determinant-response",
        "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel",
        "finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection",
        "finding:tetrahedral-quarter-face-phase-does-not-identify-original-quarter-marked-curve",
        "finding:existing-elliptic-cover-correspondence-has-exact-c6-image-and-retained-mixed-clock",
        "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
        "finding:global-split-joint-carrier-admits-parallel-native-c12-clock",
        "finding:pure-weak-clutch-clock-identification-fails-despite-quarter-matches",
        "finding:same-chern-clutch-native-compiler-does-not-select-physical-connection",
        "finding:native-gaussian-four-is-cartan-subspace-in-whole-sixtyfour",
        "finding:native-family-factor-is-not-gaussian-four-despite-symmetric-coincidences",
        "finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice",
        "finding:even-degree-pullback-removes-cartan-topology-without-selecting-clock-cover",
        "finding:global-cartan-choice-is-optional-for-original-scalar-source-fields",
        "finding:bare-native-octic-is-not-whole-e8-zero-mode-singlet",
        "finding:explicit-primary-e8-invariant-octic-completes-same-neutral-car-source",
        "finding:completed-octic-has-exact-old-root-ope-component-and-quarter-source-value",
        "finding:elliptic-normal-spin-pullback-doubles-index-and-deck-quarter-lifts-anticommute",
        "finding:exact-separated-w8-twopoint-in-original-quarter-current-source",
        "finding:unshifted-vacuum-fails-same-w8-source-state-time-dictionary",
        "finding:local-current-phase-and-conditional-cyclic-p1-w8-image",
        "finding:all-neutral-w8-correlations-identify-the-two-original-quarter-charges",
        "finding:original-w8-response-has-infinite-same-time-spectral-support",
        "finding:older-seam-equivalence-verifications-do-not-supply-marked-local-p1-map",
        "finding:full-original-c1-stress-cycle-reconstructs-neutral-w8-response",
        "finding:folded-c8-cycle-misses-intrinsic-w8-tangent-without-obstructing-original-stress",
        "finding:native-source-first-nonuniform-moment-is-four-with-literal-five",
        "finding:native-whole-five-ground-space-needs-four-register-interaction",
        "finding:old-cover-winding-reconstructs-local-quarter-current-net",
        "finding:untransported-independent-quarter-stress-pair-is-not-current",
        "finding:current-public-paper-bytes-and-binding-source-gaps-recovered",
        "finding:winding-charge-conjugation-descends-fixed-pin-domain-but-not-full-dirac-sea",
        "finding:native-fourth-root-frame-has-signed-collective-sixty-mode-dual",
        "finding:native-root-gram-spectrum-is-not-canonical-source-energy-selection",
        "finding:identical-overlapping-native-five-codes-have-no-common-state",
        "finding:horizontal-e8-invariant-octic-cannot-isolate-native-five-ground-space",
        "finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea",
        "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity",
        "finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp",
        "finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum",
        "finding:declared-recursive-native-som-is-u35-equivariant",
        "finding:declared-recursive-native-som-clocks-depend-on-chosen-rates",
        "finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower",
        "finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent",
        "finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms",
        "finding:finite-crosscap-cauchy-state-is-not-original-quarter-vacuum-by-normal-filtering",
        "finding:native-quartic-relative-arc-charge-excludes-additive-density-stress-insertion",
        "finding:retained-quarter-sea-finite-modular-transfer-preserves-integrated-native-cartan",
        "finding:original-neutral-interarc-fields-have-exact-connected-current-vertex-reconstruction",
        "finding:actual-pin-zero-branch-retains-quarter-car-state-time-but-no-uniform-scale-return",
        "finding:conformal-pin-source-geometry-fixes-exterior-return-and-unitary-memory",
        "finding:geometric-exterior-schur-response-transfers-proper-native-arc-charge-but-is-compact",
        "finding:actual-ns-half-cover-cauchy-graph-purifies-green-state-with-neutral-ground-time-obstruction",
        "finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots",
        "finding:full-marked-equatorial-pullback-is-ramified-graph-not-smooth-seam-circle",
        "finding:same-elliptic-szego-green-functional-has-all-word-free-rp-and-calderon-marginal",
        "finding:elliptic-scalar-spin-pushforward-has-original-holomorphic-p2-anchor",
        "finding:natural-elliptic-anchor-connection-is-not-original-p2-cusp-connection",
        "finding:actual-elliptic-gaussian-source-determines-full-quarter-current-functional",
        "finding:elliptic-current-state-differs-from-hardy-on-every-proper-current-interval",
        "finding:primitive-geometric-force-retains-coupled-reference-and-parity-variation",
        "finding:equal-finite-positive-heat-channel-values-do-not-fix-geometric-force",
        "finding:elliptic-ns-spin-trace-has-complete-global-quarter-kernel",
        "finding:source-induced-ramified-resolutions-do-not-select-quarter-circle-domain",
        "finding:fixed-native-and-fermat-c3-carriers-do-not-identify-marked-v117-pair",
        "finding:theta-square-modular-pair-reconstructs-v117-with-distinct-geometric-q",
        "finding:archived-d4-puncture-formula-fails-and-existing-v117-repairs-existence",
        "finding:geometric-square-clock-is-not-theta-v117-quarter-generator",
        "finding:canonical-conformal-boundary-trace-fixes-existing-elliptic-cauchy-state",
        "finding:conformal-factor-averaging-preserves-given-free-boundary-wick-words",
        "finding:retained-seam-defect-has-derived-causal-geometric-response-with-contact",
        "finding:same-final-pin-geometry-retains-history-while-relative-index-factor-is-fixed",
        "finding:full-projector-covariance-and-positivity-force-all-car-words",
        "finding:actual-two-face-projector-reduces-free-source-test-to-cross-coherence",
        "finding:retained-marked-quarter-compiler-has-no-local-geometric-wick-correction",
        "finding:changed-elliptic-modulus-has-derived-cauchy-response-and-neutral-fourfield-variance",
        "finding:actual-equatorial-half-form-trace-fixes-orthogonal-hardy-range",
        "finding:actual-holomorphic-quarter-cauchy-idempotents-are-not-positive-car-covariances",
        "finding:full-equatorial-checkerboard-free-algebra-fails-fixed-reflection-positivity",
        "finding:genuine-d4-orbifold-branch-has-unique-irreducible-v117-class",
        "finding:wall-weight-additivity-does-not-exclude-stable-v117-parabolic-bundle",
        "finding:recovered-september-c4-triangle-closes-original-a0star-monodromy",
        "finding:actual-a0star-connection-does-not-have-rational-base-inversion-lift",
        "finding:actual-v117-sign-lines-are-negative-weierstrass-triangle-two-torsion",
        "finding:antipodal-and-positive-sign-packets-fail-actual-marked-v117-ramification",
        "finding:common-cyclic-twelve-cover-does-not-trivialize-v117-unramified-sign-lines",
        "finding:negative-sign-packet-has-source-selected-quarter-clock-lift",
        "finding:original-root-and-sign-lines-have-minimal-degree48-common-cover",
        "finding:given-elliptic-flat-connection-family-has-explicit-quillen-norm-and-two-holonomies",
        "finding:bare-large-gauge-quillen-norm-does-not-equal-original-winding-counting-factor",
        "finding:existing-elliptic-half-period-has-canonical-graded-gns-intertwiner",
        "finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law",
        "finding:declared-recursive-machine-baseline-controls-and-recovery-are-finitely-measured",
        "finding:declared-recursive-machine-long-run-retains-motion-at-stable-aggregate-rank",
        "finding:recursive-kohonen-source-investigation-has-source-verified-atlas-handoff",
        "finding:chat-algorithmic-comparison-native-pauli-code-and-scoped-information-loss",
        "finding:chat-20261026-results-consolidated-with-corrected-assumptions",
        "finding:source-inversion-forces-six-line-theta-completion",
        "finding:literal-geometric-quarter-is-not-central-gaussian-quarter-on-labels",
        "finding:source-cubic-and-quarter-select-even-theta-and-spin-half-turn-lift",
        "finding:source-cubic-matches-native-pauli-translations-after-context-target-correction",
        "finding:joint-source-clock-relations-have-one-native-clifford-gauge-class",
        "finding:ordinary-theta-determinant-erases-selected-spin-central-character",
        "finding:marked-negative-point-norm-restores-required-spin-central-character",
        "finding:point-normalized-theta-family-correction-fails-original-cubic-action",
        "finding:source-spin-relative-poincare-normalization-closes-point-norm-family",
        "finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package",
        "finding:tfpt-origin-investigation-full-source-coverage-and-current-frontier",
        "finding:full-clock-norm-power-class-and-canonical-eighth-period",
        "finding:original-unit-winding-selects-one-inverse-norm-in-three-cabled-hardy-pair",
        "finding:original-boundary-audit-and-h1-point-restriction-limit",
        "finding:eta-phase-conventions-do-not-identify-relative-spin-reference-pair",
        "finding:same-spin-unit-shift-gives-native-module-class-with-odd-determinant-line",
        "finding:original-even-odd-operator-split-is-compatible-with-same-spin-seam-reference",
        "finding:elliptic-projector-and-weyl-results-retain-their-source-type-at-cubic-spin-bridge",
        "finding:cubic-spin-cauchy-range-is-three-hardy-with-strong-domain-distinction",
        "finding:original-negative-sea-three-mode-ket-is-dual-to-required-hardy-line",
        "finding:auxiliary-theta-route-needs-no-physical-cubic-bulk-or-eta-selected-dual",
        "finding:primitive-gaussian-theta-frame-constructs-e8-pair-with-retained-spin-action",
        "finding:existing-c12-lift-induces-coherent-two-object-e8-vertex-groupoid",
        "finding:actual-winding-functional-calculus-preserves-ns-ramond-split",
        "finding:single-chiral-cycle-exchange-selects-e8-in-four-extension-class",
        "finding:affine-source-involution-pairs-full-d8-sector-spectra",
        "finding:marked-local-e8-with-unchanged-source-time-fails-euclidean-clustering",
        "finding:original-parity-audit-does-not-supply-local-spinor-gauging",
        "finding:hypergraph-local-update-repaired-with-full-family-clock",
        "finding:petersen-polar-step-has-exact-double-cover-family-intertwiner",
        "finding:petersen-source-current-and-hodge-candidates-fail-physical-identification",
        "finding:a7-clock-direction-identifies-neutral-e7-zero-root",
        "finding:oriented-sewing-cocycle-distinguishes-continuation-and-reversal",
        "finding:calderon-single-face-compression-is-not-perron-projector",
        "finding:hodge-born-magnitudes-and-filtered-petersen-jump-match",
        "finding:five-complement-amplitudes-form-full-petersen-quantum-channel",
        "finding:original-twenty-events-factor-through-hodge-and-conditional-phase-record",
        "finding:actual-e8-mixed-current-response-is-full-clifford-channel",
        "finding:carrier-su5-centralizer-gives-direct-e8-petersen-response",
        "finding:su5-covariance-and-petersen-support-fix-complete-quantum-response",
        "finding:neutral-pair-witness-separates-old-events-and-hodge-response",
        "finding:original-degree-clock-is-not-carrier-slot-cycle-at-fixed-source",
        "finding:full-mark-transport-and-isospectrality-do-not-select-hodge-channel",
        "finding:original-pair-source-fixes-state-but-not-selected-epsilon-process",
        "finding:single-positive-process-saturation-selects-full-hodge-channel",
        "finding:original-five-slot-wedge-is-exact-e8-hodge-coefficient",
        "finding:native-pauli-f20-metric-and-quarter-bridge",
        "finding:two-actual-coherent-events-herald-hodge-at-one-over-twenty-five",
        "finding:original-color-center-removes-only-extra-h8-ground-state",
        "finding:marked-symplectic-functor-fixes-native-hodge-kraus-space",
        "finding:f20-record-repair-removes-chart-induced-three-plus-two",
        "finding:theta-scalar-square-lift-is-distinct-from-symplectic-f20-lift",
        "finding:full-admissibility-vacuum-test-needs-source-image-and-transfer-reduction",
        "finding:canonical-native-spin5-hodge-is-already-one-source-record-subchannel",
        "finding:native-hodge-record-selector-is-image-projector-not-kraus-kernel",
        "finding:irreducible-f20-four-cannot-host-original-independent-native-family-clock",
        "finding:native-hodge-is-exact-collective-five-current-action",
        "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
        "finding:six-hodge-responses-have-exact-full-current-barycenter",
        "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts",
        "finding:spin5-hodge-five-is-plucker-kernel-not-original-quartic-hessian",
        "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
        "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
        "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
        "finding:old-ward-root-generates-exact-charged-fifty-module",
        "finding:tp-charged-bracket-support-forces-entire-carrier-marginal",
        "finding:original-ward-and-p2-grading-select-smaller-creation-thirty",
        "finding:charged-source-quarter-recovers-inverse-internal-glue",
        "finding:state-independent-creation-branch-removes-whole-process-hodge-demand",
        "finding:given-source-current-constructs-half-kink-spinor-transport",
        "finding:neutral-ward-response-needs-no-spinor-observable-membership",
        "finding:actual-source-sector-transport-distinguishes-identical-hodge-marginals",
        "finding:ordinary-weyl-type-obstruction-to-single-chiral-os-anti-anti-reflection",
        "finding:given-two-face-source-derives-opposite-neutral-weyls-and-bounded-time-reflection",
        "finding:verification-recovery-preserves-local-source-chain-and-eight-gate-completeness",
        "finding:positive-spectral-reweighting-does-not-establish-original-source-rp",
        "finding:gapped-quarter-energy-cannot-be-same-borchers-translation",
        "finding:finite-ko6-pairing-does-not-supply-standalone-pfaffian-source",
        "finding:full-free-projector-forces-joint-commuting-source-factorization",
        "finding:actual-neutral-current-source-has-constructive-moebius-standard-pair",
        "finding:continuous-local-current-weyls-cannot-live-in-finite-coordinate-fibers",
        "finding:actual-folded-current-ward-and-state-determine-all-neutral-words",
        "finding:mixed-vector-axial-current-is-existing-full-car-subalgebra",
        "finding:constant-product-time-stable-current-level-is-kernel-index",
        "finding:paired-quarter-source-candidate-needs-original-filter-and-oriented-conjugation",
        "finding:graded-boundary-clifford-typing-transports-full-scalar-and-finite-coupled-source",
        "finding:actual-charge-j-transport-retains-full-dirac-and-distinct-pairings",
        "finding:fixed-graded-chart-transports-normal-dependent-source-and-given-mixed-moments",
        "finding:neutral-many-body-source-time-is-not-finite-summable-geometric-dirac",
        "finding:actual-product-reflection-and-same-time-have-full-positive-clifford-source-intertwiner",
        "finding:actual-v252-positive-grade-has-global-p2-wedge-dictionary",
        "finding:old-quarter-full-source-embeds-locally-exactly-on-decoupled-channel",
        "finding:petersen-population-full-cptp-p5-range-zero-to-ten",
        "finding:marked-sm-phase-p5-exact-range-and-response-collision",
        "finding:shared-epsilon-tp-process-fixes-hodge-marginal-even-for-correlated-inputs",
        "finding:puncture-meridians-have-one-glue-class-and-residue-duality-does-not-select-metric",
        "finding:joint-integral-unimodular-charge-closure-uniquely-selects-complete-invariant-metric",
        "finding:meridian-spinor-joint-source-product-has-actual-family-root-simple-pole"
      ],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:846edbe1e4e0a19bbe25c851",
        "semantic-source:4f98197613fed96709f08c93"
      ]
    },
    {
      "id": "topic:clocks",
      "titleEN": "Interlocking clocks",
      "summaryEN": "TFPT uses several distinct algebraic clocks and transfers: Coxeter period 30, phase automorphisms, an order-12 compiler action, and separate relaxation factors. Their mathematical periods do not by themselves define physical duration.",
      "orientation": {
        "role_en": "Connects discrete symmetry actions, readout periods, and transfer/relaxation rules without collapsing them into one physical time.",
        "have_en": "Known structures include finite actions: Coxeter number 30, μ4 on phase data, an order-12 compiler action, and separate relaxation rates.",
        "seek_en": "The open work is a common source derivation, event interpretation, and a parent realizing one time rule for matter, boundary, and instruments.",
        "connection_en": "Clock actions organize E8/code readouts and event sequences; algebraic orders are neither measured seconds nor proofs of dynamics.",
        "next_bridge_en": "An explicit source rule must connect discrete steps to records and repeated physical interventions."
      },
      "problemIds": [
        "problem:common-source-state-event-selection",
        "problem:physical-time-projector-transfer",
        "problem:clock-linked-neutral-response-reconstruction",
        "problem:clock-source-covariant-transport",
        "problem:charged-twist-response-identifiability",
        "problem:native-charged-seam-selection",
        "problem:constructive-seam-lift-state",
        "problem:seam-partner-charge-state-time",
        "problem:marked-seam-monodromy-and-lattice-lifts",
        "problem:atlas-clock-defect-and-operational-reconstruction"
      ],
      "findingIds": [
        "finding:operational-seed-is-input",
        "finding:native-source-common-time-thermal-family",
        "finding:native-grade-carry-and-memory",
        "finding:even-seam-global-operator-factorization",
        "finding:source-generated-marking-classification",
        "finding:source-marking-field-realization-boundary",
        "finding:minimal-defect-uniqueness-not-proved",
        "finding:conditional-seam-field-state-time-reconstruction",
        "finding:continuous-hardy-seam-classification",
        "finding:same-source-seam-energy-selection",
        "finding:master-functional-presupposes-source-selection",
        "finding:geometric-deck-not-calderon-polarization",
        "finding:positive-compression-erases-carrier-minus-sector",
        "finding:higgs-determinant-does-not-discharge-carrier-map",
        "finding:primitive-invariant-does-not-select-rank-three",
        "finding:fixed-background-source-does-not-fix-mixed-vertex",
        "finding:local-quarter-inner-variation-is-connection",
        "finding:calderon-enlargement-does-not-select-higgs",
        "finding:finite-sm-higgs-variation-retains-seed",
        "finding:operator-skeleton-does-not-identify-insertion-algebra",
        "finding:internal-even-car-hodge-is-not-coordinate-algebra",
        "finding:minimum-rank-unique-primitive-channel-does-not-select-32",
        "finding:joint-selfconsistency-presupposes-minimal-algebra-fiber-selection",
        "finding:process-composition-and-cyclicity-do-not-select-algebra",
        "finding:quartic-shape-selects-32-only-with-source-sign",
        "finding:native-symmetric-quartic-erasure-common-object",
        "finding:joint-native-algebra-normalizer-and-response-orbit",
        "finding:native-galois-intertwiner-unique-logical-marked-orbit",
        "finding:native-reflection-full-four-five-generators-rate-injectivity",
        "finding:complete-logical-readout-native-covariant-residual-classification",
        "finding:original-polar-mark-clock-centralizer-orbit",
        "finding:actual-quartic-code-product-stabilizer-quarter-exclusion",
        "finding:original-decoder-versus-native-quarter-polynomial-erasure-test",
        "finding:original-decoder-product-time-and-all-unitary-erasure-lifts",
        "finding:native-clock-compatible-polar-fibre-and-canonical-distance",
        "finding:native-moment-parent-and-product-path-selection-boundary",
        "finding:original-e8-current-response-and-full-quarter-lifts",
        "finding:literal-charged-current-register-dictionary-fails-quarter",
        "finding:native-cartan-code-inner-e8-stabilizer-excludes-marked-quarter",
        "finding:native-code-neutral-weight-two-action-and-global-clock-exclusion",
        "finding:original-neutral-root-mixed-response-derived",
        "finding:actual-mixed-ordered-return-on-native-quartic-code",
        "finding:mixed-return-spectrum-does-not-select-original-polar-mark",
        "finding:actual-mixed-return-fails-native-trimer-erasure-lift",
        "finding:strict-trace-gap-excludes-positive-mixed-return-reweighting",
        "finding:original-source-erasure-ward-terms-derived",
        "finding:uncompressed-original-mixed-return-does-not-preserve-code",
        "finding:original-root-response-sum-also-leaks-from-code",
        "finding:original-full-source-return-exterior-feedback-derived",
        "finding:original-return-requires-memory-in-every-code-direction",
        "finding:native-conformal-primary-multiplicity-source-factorization",
        "finding:canonical-conformal-erasure-forces-primary-twenty-carry",
        "finding:all-canonical-stress-histories-scalar-on-native-code",
        "finding:original-local-current-ope-forces-erasure-and-carry",
        "finding:all-real-local-cartan-profiles-erasure-third-bound",
        "finding:closed-cartan-weyl-histories-only-logical-phase",
        "finding:full-existing-local-e8-hull-of-native-code",
        "finding:full-local-quartic-wick-ladder-and-unprojected-native-actions",
        "finding:unmarked-native-w6-simplex-from-full-quartic-ope",
        "finding:full-e8-current-products-fix-stress-and-exterior-ward-cancellation",
        "finding:full-source-simplex-does-not-select-original-polar-mark",
        "finding:original-full-field-event-gram-reconstructs-relative-polar-mark",
        "finding:raw-event-state-positivity-does-not-execute-polar-normalization",
        "finding:determinant-cover-not-literal-full-cartan-lattice-event",
        "finding:clock-free-quartic-product-spectral-sectors-and-native-five",
        "finding:six-complex-native-simplex-rays-from-holomorphic-product-quadrics",
        "finding:intrinsic-relative-response-covariance-and-state-boundary",
        "finding:intrinsic-event-composition-retains-shared-source-and-correlation-data",
        "finding:clock-free-event-geometry-fixes-clock-class-and-mark-orbit-not-member",
        "finding:original-charged-seam-character-recovers-global-native-event-pair",
        "finding:internal-seam-vacuum-and-original-neutral-tensor-do-not-select-flag-root",
        "finding:actual-quarter-fold-shift-removes-native-symmetry-obstruction-without-flag-selector",
        "finding:fold-shift-equivariance-needs-actual-source-response-map-not-another-symmetry-no-go",
        "finding:original-fold-covariance-current-counterterm-and-quartic-twisted-transport",
        "finding:fold-state-full-quartic-kernel-and-erasure-protected-low-order-response",
        "finding:original-fold-quartic-mean-and-spectral-responses-do-not-match-sixty-flags",
        "finding:original-winding-full-state-response-removes-vacuum-rank-two-shortcut",
        "finding:original-source-global-time-winding-history-factorization",
        "finding:original-local-density-folds-to-correlated-root-current-and-erasure-response",
        "finding:original-current-all-mode-energy-and-geometric-stress-bridge",
        "finding:original-current-geometric-response-pair-has-no-common-polar-sector",
        "finding:original-current-ordered-hall-kernel-and-actual-folded-field-products",
        "finding:original-seam-grades-full-density-geometric-products-and-energy-response",
        "finding:original-seam-complete-density-grading-not-sharp-32-input-sectors",
        "finding:original-density-all-profile-mean-work-scalar-on-native-packet",
        "finding:original-p1-gap-normalized-action-covector-and-scalar-holonomy-class",
        "finding:original-p1-gap-car-component-not-native-sharp-32-event",
        "finding:complete-positive-scalar-first-order-circle-source-normal-form",
        "finding:fixed-source-time-seam-ward-rigidifies-scalar-principal-symbol-with-carry",
        "finding:unit-spectral-flow-gap-and-four-marks-do-not-imply-fixed-source-ward",
        "finding:four-native-starts-have-distinct-original-fold-state-correlations",
        "finding:four-starts-full-joint-kernel-and-charged-covariant-transport",
        "finding:four-native-polar-marks-not-fixed-source-state-gauge-equivalent",
        "finding:original-pointer-template-requires-source-context-identification",
        "finding:four-polar-context-algebra-and-source-crosscoupling",
        "finding:every-native-quartic-has-all-eight-original-car-supports",
        "finding:bounded-proper-local-source-operation-cannot-exactly-prepare-positive-eigenpacket",
        "finding:full-original-erasure20-and-joint25-have-all-eight-source-supports",
        "finding:two-face-collar-fixes-face-current-phase-and-distinguishes-relative-endpoint-lift",
        "finding:full-dirac-cauchy-vector-cocycle-cancels-and-endpoint-domain-distinction",
        "finding:unchanged-qwz-full-finite-energy-spectral-exhaustion",
        "finding:uniform-z4-d8-locality-and-both-spinor-chirality-time-census",
        "finding:odd-spinor-global-refielding-and-unit-source-winding",
        "finding:sharp-half-flux-register-quotient-and-local-normality-exclusion",
        "finding:all-word-register-charged-local-field-limit-obstruction",
        "finding:exact-parity-gauss-locality-completion-of-register-source",
        "finding:cover-half-flux-not-fixed-charge-eightfold-spinor-twist",
        "finding:original-neutral-eightpreimage-parity-pair-has-uniform-cut-action",
        "finding:complete-dirac-vector-phase-pair-has-zero-spinor-Ward-charge",
        "finding:smooth-unitary-endpoint-removal-diverges-at-fixed-source-time",
        "finding:continuous-original-time-nonunitary-limits-stay-in-old-source-folium",
        "finding:common-register-vacuum-reference-uniform-and-local-grade-reduction",
        "finding:actual-heat-filtered-neutral-pair-full-state-time-and-separate-chiral-limit",
        "finding:holomorphic-kms-extension-assumes-charged-net-and-not-microscopic-generator",
        "finding:fixed-interval-rotation-modular-chain-fails-local-state-takesaki-repairs",
        "finding:source-winding-cartan-four-word-and-two-edge-kms-gso-discriminator",
        "finding:p1-parity-gauss-net-selection-undecidable-without-original-localization-map",
        "finding:original-minimality-does-not-reconstruct-operational-source",
        "finding:generic-first-order-relative-bound-zero-counterexample-and-correct-domain-repair",
        "finding:sign-projector-does-not-determine-time-magnitude",
        "finding:full-faithful-kms-or-transfer-recovers-magnitudes",
        "finding:full-two-face-collar-recovers-signed-operator",
        "finding:two-face-graph-state-time-same-datum",
        "finding:shared-register-gkls-embedding-exact-q-interval",
        "finding:marked-m4-channel-all-powers-homogeneous-gksl-excluded",
        "finding:four-clock-fields-complete-quadratic-response",
        "finding:actual-j-covariant-source-transport",
        "finding:fixed-source-affine-j-obstruction",
        "finding:neutral-vacuum-allword-twist-blindness",
        "finding:eight-charged-responses-reconstruct-twist",
        "finding:native-invariant-response-not-fixed-chiral-twist",
        "finding:native-opposite-charge-response-symmetry",
        "finding:native-chemical-mark-visible-in-charged-corners",
        "finding:fixed-hopping-quarter-phases-retain-antiunitary-discriminator",
        "finding:constructive-phase-class-and-full-winding",
        "finding:constructive-positive-state-extension",
        "finding:constructive-current-group-selects-positive-p-lift",
        "finding:constructive-state-algebra-resolution-and-source-test",
        "finding:constructive-all-phases-fail-unchanged-source",
        "finding:partner-carrier-charges-and-state-types",
        "finding:partner-fixed-quarter-time-splits-sm-multiplet",
        "finding:partner-original-carrier-cross-sheet-conjugation",
        "finding:partner-chiral-quarter-conjugation-state-time",
        "finding:joint-bilinear-hermitian-correction",
        "finding:joint-quarter-transports-marking",
        "finding:joint-fixed-time-marking-repair-excluded",
        "finding:joint-spinor-not-source-coefficient",
        "finding:marked-seam-category-and-character-valued-full-lift-factor",
        "finding:quarter-clock-sign-lift-complete-four-puncture-classification",
        "finding:quarter-lift-central-quotient-class-and-all-subgroup-restrictions",
        "finding:native-clock-reflection-full-factor-cocycle-trivialization",
        "finding:native-quartic-exterior-local-cohomology-distinguishes-clock-monodromies",
        "finding:orbifold-lift-criterion-and-determinant-eight-divisibility",
        "finding:original-g31-reflection-census-and-all-integral-cohomology",
        "finding:all62-original-clock-obstructions-and-central-variants",
        "finding:actual-sign-lift-g31-group-comparison",
        "finding:complete-g31-lift-invariants-and-explicit-collisions",
        "finding:e7-quarter-pairs-literal-native-g31-reflections",
        "finding:e6-root-subsystem-quarter-clock-discriminant-obstruction",
        "finding:e-series-square-cover-family-and-quarter-descent",
        "finding:e-series-integral-glue-and-normalization-nonidentifiability",
        "finding:global-original-g31-character-lift-nonsplitting",
        "finding:all62-original-character-clock-lifts-complete",
        "finding:all17-original-character-monodromy-lifts-complete",
        "finding:e7-pair-full-lattice-field-character-torsor",
        "finding:e-series-complete-native-compiler-cut-dictionary",
        "finding:common-cover-clock-and-maximal-integral-phi12-intertwiner",
        "finding:native-four-cut-projectors-unify48-fourthirds-fivequarters",
        "finding:complete-covariant-compiler-voa-source-and-weyl-closure",
        "finding:complete-fixed-jhat-cyclic-field-lift-and-associated-clock",
        "finding:relative-native-burau-clock-hom-faithful12-transport",
        "finding:e6-vertex-nonselection-survives-full-field-clock-phases",
        "finding:marked-c4-glue-unique-local-e8-vacuum-source",
        "finding:canonical-vacuum-clock-preserves-e6-nonselection",
        "finding:marked-generator-forces-e8-without-support-multiplicity-or-minimality-input",
        "finding:native-reflection-rotation-lift-classes-and-forgetful-images",
        "finding:quarter-clock-pure-mapping-class-complete-quotient",
        "finding:e8-cut-five-orbital-incidence-algebra-complete",
        "finding:compiler-d8-frame-requires-full-d5-a3-flag",
        "finding:tetrahedron-incidence-lossless-e6-reconstruction",
        "finding:restricted-clock-lift-and-global-cover-audit-reconciled",
        "finding:double-scalar-quarter-is-marked-glue-with-two-step-index",
        "finding:scalar-quarter-two-involutive-e8-extensions",
        "finding:native-quarter-glue-inner-conjugacy-and-oriented-tetrahedron-flags",
        "finding:native-cyclic-compiler-inner-conjugacy",
        "finding:recovered-e6-closed-81-current-module-and-unique-source-cubic",
        "finding:e-series-operational-role-review-and-source-time-centralizer",
        "finding:actual-clock-doily-ovoid-kernel-is-native-quartic-five",
        "finding:glue-clock-twisted-sectors-share-marked-quadratic-module",
        "finding:complete-native-six-effect-covariant-instrument-classification",
        "finding:native-six-effect-readout-on-existing-erasure-output",
        "finding:relational-quartic-singlet-and-invariant-density-separation",
        "finding:new-clock-feedback-origin-input-audit",
        "finding:native-event-channel-cone-intersection-is-tenth-to-half",
        "finding:native-six-ovoid-observation-first-occurs-at-tensor-degree-three",
        "finding:original-quartic-erasure-and-hamming-octic-share-marked-ovoid-response",
        "finding:native-octic-field-ray-is-explicit-but-retained-clock-stress-preparation-fails",
        "finding:actual-quarter-fold-stress-has-nonzero-octic-eighth-jet",
        "finding:native-octic-is-an-original-even-car-current-composite",
        "finding:original-geometric-source-jet-and-partial-p1-seed-closure",
        "finding:full-root-ope-has-normalized-native-octic-component",
        "finding:paper-microscopic-car-composes-with-native-octic-ward",
        "finding:microscopic-neutral-octic-has-controlled-smeared-limit",
        "finding:paper-seed-source-needs-local-image-not-global-equivalence",
        "finding:full-car-positive-time-forces-source-vacuum",
        "finding:original-winding-theorem-does-not-select-seam-ray",
        "finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel",
        "finding:original-os-step-needs-full-moments-not-connected-cumulants",
        "finding:graded-field-image-precedes-physical-observable-restriction",
        "finding:older-original-circle-representative-already-realizes-ward-and-index",
        "finding:old-quarter-heat-transfer-has-controlled-rank-one-limit-and-odd-product",
        "finding:historical-em-rank-one-and-full-heat-traces-have-different-contracts",
        "finding:older-frg-functional-already-supplies-formal-full-moment-parent",
        "finding:earliest-c3-route-quantizes-level-but-needs-physical-kinetic-normalization",
        "finding:canonical-positive-circle-half-selects-the-toeplitz-line-and-sixth-order-correction",
        "finding:old-seam-shift-canonically-gives-relative-car-line-and-fredholm-factor",
        "finding:old-index-coupling-removes-heat-map-and-has-sharp-residual-ward-test",
        "finding:original-admissibility-requires-image-membership-not-positive-half-or-commutation",
        "finding:old-closure-already-assumes-car-but-does-not-map-the-geometric-circle",
        "finding:historical-uv-map-infinite-mass-exclusion-already-proved-and-recovered",
        "finding:a4-spin-lift-fixes-local-ns-and-unordered-quarter-pair",
        "finding:cover-winding-exchanges-quarter-sectors-before-its-square",
        "finding:retained-winding-preserves-local-support-and-neutral-time",
        "finding:marked-glue-square-is-the-e8-fermionization-character",
        "finding:fixed-canonical-d8-is-not-transported-source-d8",
        "finding:actual-winding-has-four-module-e8-defect-extension",
        "finding:ramond-lift-sign-is-common-intertwiner-basis-gauge",
        "finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class",
        "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor",
        "finding:schur-carrier-plus-complement-preserves-original-relative-determinant",
        "finding:v258-forward-source-gap-is-reused-not-solved-by-inversion",
        "finding:one-sided-source-and-real-em-norm-need-response-map-not-chiral-phase",
        "finding:trace-class-pair-index-fixes-relative-factor-without-primitive-ray",
        "finding:matrix-clutch-degree-connects-weak-determinant-class-without-ray-selector",
        "finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index",
        "finding:inner-carrier-is-infinite-spacetime-module-not-finite-circle-cut",
        "finding:normal-spin-determinant-line-exactly-transports-whole-circle-in-given-product",
        "finding:normal-index-line-source-match-is-holonomy-condition-not-vertical-degree",
        "finding:full-normal-product-polarization-change-is-not-trace-class",
        "finding:massive-transverse-zero-index-retains-positive-determinant-response",
        "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel",
        "finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection",
        "finding:tetrahedral-quarter-face-phase-does-not-identify-original-quarter-marked-curve",
        "finding:existing-elliptic-cover-correspondence-has-exact-c6-image-and-retained-mixed-clock",
        "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
        "finding:global-split-joint-carrier-admits-parallel-native-c12-clock",
        "finding:pure-weak-clutch-clock-identification-fails-despite-quarter-matches",
        "finding:same-chern-clutch-native-compiler-does-not-select-physical-connection",
        "finding:native-gaussian-four-is-cartan-subspace-in-whole-sixtyfour",
        "finding:native-family-factor-is-not-gaussian-four-despite-symmetric-coincidences",
        "finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice",
        "finding:even-degree-pullback-removes-cartan-topology-without-selecting-clock-cover",
        "finding:global-cartan-choice-is-optional-for-original-scalar-source-fields",
        "finding:bare-native-octic-is-not-whole-e8-zero-mode-singlet",
        "finding:explicit-primary-e8-invariant-octic-completes-same-neutral-car-source",
        "finding:completed-octic-has-exact-old-root-ope-component-and-quarter-source-value",
        "finding:elliptic-normal-spin-pullback-doubles-index-and-deck-quarter-lifts-anticommute",
        "finding:exact-separated-w8-twopoint-in-original-quarter-current-source",
        "finding:unshifted-vacuum-fails-same-w8-source-state-time-dictionary",
        "finding:local-current-phase-and-conditional-cyclic-p1-w8-image",
        "finding:all-neutral-w8-correlations-identify-the-two-original-quarter-charges",
        "finding:original-w8-response-has-infinite-same-time-spectral-support",
        "finding:older-seam-equivalence-verifications-do-not-supply-marked-local-p1-map",
        "finding:full-original-c1-stress-cycle-reconstructs-neutral-w8-response",
        "finding:folded-c8-cycle-misses-intrinsic-w8-tangent-without-obstructing-original-stress",
        "finding:native-source-first-nonuniform-moment-is-four-with-literal-five",
        "finding:native-whole-five-ground-space-needs-four-register-interaction",
        "finding:old-cover-winding-reconstructs-local-quarter-current-net",
        "finding:untransported-independent-quarter-stress-pair-is-not-current",
        "finding:current-public-paper-bytes-and-binding-source-gaps-recovered",
        "finding:winding-charge-conjugation-descends-fixed-pin-domain-but-not-full-dirac-sea",
        "finding:native-fourth-root-frame-has-signed-collective-sixty-mode-dual",
        "finding:native-root-gram-spectrum-is-not-canonical-source-energy-selection",
        "finding:identical-overlapping-native-five-codes-have-no-common-state",
        "finding:horizontal-e8-invariant-octic-cannot-isolate-native-five-ground-space",
        "finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea",
        "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity",
        "finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp",
        "finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum",
        "finding:declared-recursive-native-som-is-u35-equivariant",
        "finding:declared-recursive-native-som-clocks-depend-on-chosen-rates",
        "finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower",
        "finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent",
        "finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms",
        "finding:finite-crosscap-cauchy-state-is-not-original-quarter-vacuum-by-normal-filtering",
        "finding:native-quartic-relative-arc-charge-excludes-additive-density-stress-insertion",
        "finding:retained-quarter-sea-finite-modular-transfer-preserves-integrated-native-cartan",
        "finding:original-neutral-interarc-fields-have-exact-connected-current-vertex-reconstruction",
        "finding:actual-pin-zero-branch-retains-quarter-car-state-time-but-no-uniform-scale-return",
        "finding:conformal-pin-source-geometry-fixes-exterior-return-and-unitary-memory",
        "finding:geometric-exterior-schur-response-transfers-proper-native-arc-charge-but-is-compact",
        "finding:actual-ns-half-cover-cauchy-graph-purifies-green-state-with-neutral-ground-time-obstruction",
        "finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots",
        "finding:full-marked-equatorial-pullback-is-ramified-graph-not-smooth-seam-circle",
        "finding:same-elliptic-szego-green-functional-has-all-word-free-rp-and-calderon-marginal",
        "finding:elliptic-scalar-spin-pushforward-has-original-holomorphic-p2-anchor",
        "finding:natural-elliptic-anchor-connection-is-not-original-p2-cusp-connection",
        "finding:actual-elliptic-gaussian-source-determines-full-quarter-current-functional",
        "finding:elliptic-current-state-differs-from-hardy-on-every-proper-current-interval",
        "finding:primitive-geometric-force-retains-coupled-reference-and-parity-variation",
        "finding:equal-finite-positive-heat-channel-values-do-not-fix-geometric-force",
        "finding:elliptic-ns-spin-trace-has-complete-global-quarter-kernel",
        "finding:source-induced-ramified-resolutions-do-not-select-quarter-circle-domain",
        "finding:fixed-native-and-fermat-c3-carriers-do-not-identify-marked-v117-pair",
        "finding:theta-square-modular-pair-reconstructs-v117-with-distinct-geometric-q",
        "finding:archived-d4-puncture-formula-fails-and-existing-v117-repairs-existence",
        "finding:geometric-square-clock-is-not-theta-v117-quarter-generator",
        "finding:canonical-conformal-boundary-trace-fixes-existing-elliptic-cauchy-state",
        "finding:conformal-factor-averaging-preserves-given-free-boundary-wick-words",
        "finding:retained-seam-defect-has-derived-causal-geometric-response-with-contact",
        "finding:same-final-pin-geometry-retains-history-while-relative-index-factor-is-fixed",
        "finding:full-projector-covariance-and-positivity-force-all-car-words",
        "finding:actual-two-face-projector-reduces-free-source-test-to-cross-coherence",
        "finding:retained-marked-quarter-compiler-has-no-local-geometric-wick-correction",
        "finding:changed-elliptic-modulus-has-derived-cauchy-response-and-neutral-fourfield-variance",
        "finding:actual-equatorial-half-form-trace-fixes-orthogonal-hardy-range",
        "finding:actual-holomorphic-quarter-cauchy-idempotents-are-not-positive-car-covariances",
        "finding:full-equatorial-checkerboard-free-algebra-fails-fixed-reflection-positivity",
        "finding:genuine-d4-orbifold-branch-has-unique-irreducible-v117-class",
        "finding:wall-weight-additivity-does-not-exclude-stable-v117-parabolic-bundle",
        "finding:recovered-september-c4-triangle-closes-original-a0star-monodromy",
        "finding:actual-a0star-connection-does-not-have-rational-base-inversion-lift",
        "finding:actual-v117-sign-lines-are-negative-weierstrass-triangle-two-torsion",
        "finding:antipodal-and-positive-sign-packets-fail-actual-marked-v117-ramification",
        "finding:common-cyclic-twelve-cover-does-not-trivialize-v117-unramified-sign-lines",
        "finding:negative-sign-packet-has-source-selected-quarter-clock-lift",
        "finding:original-root-and-sign-lines-have-minimal-degree48-common-cover",
        "finding:given-elliptic-flat-connection-family-has-explicit-quillen-norm-and-two-holonomies",
        "finding:bare-large-gauge-quillen-norm-does-not-equal-original-winding-counting-factor",
        "finding:existing-elliptic-half-period-has-canonical-graded-gns-intertwiner",
        "finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law",
        "finding:declared-recursive-machine-baseline-controls-and-recovery-are-finitely-measured",
        "finding:declared-recursive-machine-long-run-retains-motion-at-stable-aggregate-rank",
        "finding:recursive-kohonen-source-investigation-has-source-verified-atlas-handoff",
        "finding:chat-algorithmic-comparison-native-pauli-code-and-scoped-information-loss",
        "finding:chat-20261026-results-consolidated-with-corrected-assumptions",
        "finding:source-inversion-forces-six-line-theta-completion",
        "finding:literal-geometric-quarter-is-not-central-gaussian-quarter-on-labels",
        "finding:source-cubic-and-quarter-select-even-theta-and-spin-half-turn-lift",
        "finding:source-cubic-matches-native-pauli-translations-after-context-target-correction",
        "finding:joint-source-clock-relations-have-one-native-clifford-gauge-class",
        "finding:ordinary-theta-determinant-erases-selected-spin-central-character",
        "finding:marked-negative-point-norm-restores-required-spin-central-character",
        "finding:point-normalized-theta-family-correction-fails-original-cubic-action",
        "finding:source-spin-relative-poincare-normalization-closes-point-norm-family",
        "finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package",
        "finding:tfpt-origin-investigation-full-source-coverage-and-current-frontier",
        "finding:full-clock-norm-power-class-and-canonical-eighth-period",
        "finding:original-unit-winding-selects-one-inverse-norm-in-three-cabled-hardy-pair",
        "finding:original-boundary-audit-and-h1-point-restriction-limit",
        "finding:eta-phase-conventions-do-not-identify-relative-spin-reference-pair",
        "finding:same-spin-unit-shift-gives-native-module-class-with-odd-determinant-line",
        "finding:original-even-odd-operator-split-is-compatible-with-same-spin-seam-reference",
        "finding:elliptic-projector-and-weyl-results-retain-their-source-type-at-cubic-spin-bridge",
        "finding:cubic-spin-cauchy-range-is-three-hardy-with-strong-domain-distinction",
        "finding:original-negative-sea-three-mode-ket-is-dual-to-required-hardy-line",
        "finding:auxiliary-theta-route-needs-no-physical-cubic-bulk-or-eta-selected-dual",
        "finding:primitive-gaussian-theta-frame-constructs-e8-pair-with-retained-spin-action",
        "finding:existing-c12-lift-induces-coherent-two-object-e8-vertex-groupoid",
        "finding:actual-winding-functional-calculus-preserves-ns-ramond-split",
        "finding:single-chiral-cycle-exchange-selects-e8-in-four-extension-class",
        "finding:affine-source-involution-pairs-full-d8-sector-spectra",
        "finding:marked-local-e8-with-unchanged-source-time-fails-euclidean-clustering",
        "finding:original-parity-audit-does-not-supply-local-spinor-gauging",
        "finding:hypergraph-local-update-repaired-with-full-family-clock",
        "finding:petersen-polar-step-has-exact-double-cover-family-intertwiner",
        "finding:petersen-source-current-and-hodge-candidates-fail-physical-identification",
        "finding:a7-clock-direction-identifies-neutral-e7-zero-root",
        "finding:oriented-sewing-cocycle-distinguishes-continuation-and-reversal",
        "finding:calderon-single-face-compression-is-not-perron-projector",
        "finding:hodge-born-magnitudes-and-filtered-petersen-jump-match",
        "finding:five-complement-amplitudes-form-full-petersen-quantum-channel",
        "finding:original-twenty-events-factor-through-hodge-and-conditional-phase-record",
        "finding:actual-e8-mixed-current-response-is-full-clifford-channel",
        "finding:carrier-su5-centralizer-gives-direct-e8-petersen-response",
        "finding:su5-covariance-and-petersen-support-fix-complete-quantum-response",
        "finding:neutral-pair-witness-separates-old-events-and-hodge-response",
        "finding:original-degree-clock-is-not-carrier-slot-cycle-at-fixed-source",
        "finding:full-mark-transport-and-isospectrality-do-not-select-hodge-channel",
        "finding:original-pair-source-fixes-state-but-not-selected-epsilon-process",
        "finding:single-positive-process-saturation-selects-full-hodge-channel",
        "finding:original-five-slot-wedge-is-exact-e8-hodge-coefficient",
        "finding:native-pauli-f20-metric-and-quarter-bridge",
        "finding:two-actual-coherent-events-herald-hodge-at-one-over-twenty-five",
        "finding:original-color-center-removes-only-extra-h8-ground-state",
        "finding:marked-symplectic-functor-fixes-native-hodge-kraus-space",
        "finding:f20-record-repair-removes-chart-induced-three-plus-two",
        "finding:theta-scalar-square-lift-is-distinct-from-symplectic-f20-lift",
        "finding:full-admissibility-vacuum-test-needs-source-image-and-transfer-reduction",
        "finding:canonical-native-spin5-hodge-is-already-one-source-record-subchannel",
        "finding:native-hodge-record-selector-is-image-projector-not-kraus-kernel",
        "finding:irreducible-f20-four-cannot-host-original-independent-native-family-clock",
        "finding:native-hodge-is-exact-collective-five-current-action",
        "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
        "finding:six-hodge-responses-have-exact-full-current-barycenter",
        "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts",
        "finding:spin5-hodge-five-is-plucker-kernel-not-original-quartic-hessian",
        "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
        "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
        "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
        "finding:old-ward-root-generates-exact-charged-fifty-module",
        "finding:tp-charged-bracket-support-forces-entire-carrier-marginal",
        "finding:original-ward-and-p2-grading-select-smaller-creation-thirty",
        "finding:charged-source-quarter-recovers-inverse-internal-glue",
        "finding:state-independent-creation-branch-removes-whole-process-hodge-demand",
        "finding:given-source-current-constructs-half-kink-spinor-transport",
        "finding:neutral-ward-response-needs-no-spinor-observable-membership",
        "finding:actual-source-sector-transport-distinguishes-identical-hodge-marginals",
        "finding:ordinary-weyl-type-obstruction-to-single-chiral-os-anti-anti-reflection",
        "finding:given-two-face-source-derives-opposite-neutral-weyls-and-bounded-time-reflection",
        "finding:verification-recovery-preserves-local-source-chain-and-eight-gate-completeness",
        "finding:positive-spectral-reweighting-does-not-establish-original-source-rp",
        "finding:gapped-quarter-energy-cannot-be-same-borchers-translation",
        "finding:finite-ko6-pairing-does-not-supply-standalone-pfaffian-source",
        "finding:full-free-projector-forces-joint-commuting-source-factorization",
        "finding:actual-neutral-current-source-has-constructive-moebius-standard-pair",
        "finding:continuous-local-current-weyls-cannot-live-in-finite-coordinate-fibers",
        "finding:actual-folded-current-ward-and-state-determine-all-neutral-words",
        "finding:mixed-vector-axial-current-is-existing-full-car-subalgebra",
        "finding:constant-product-time-stable-current-level-is-kernel-index",
        "finding:paired-quarter-source-candidate-needs-original-filter-and-oriented-conjugation",
        "finding:graded-boundary-clifford-typing-transports-full-scalar-and-finite-coupled-source",
        "finding:actual-charge-j-transport-retains-full-dirac-and-distinct-pairings",
        "finding:fixed-graded-chart-transports-normal-dependent-source-and-given-mixed-moments",
        "finding:neutral-many-body-source-time-is-not-finite-summable-geometric-dirac",
        "finding:actual-product-reflection-and-same-time-have-full-positive-clifford-source-intertwiner",
        "finding:actual-v252-positive-grade-has-global-p2-wedge-dictionary",
        "finding:old-quarter-full-source-embeds-locally-exactly-on-decoupled-channel",
        "finding:petersen-population-full-cptp-p5-range-zero-to-ten",
        "finding:marked-sm-phase-p5-exact-range-and-response-collision",
        "finding:shared-epsilon-tp-process-fixes-hodge-marginal-even-for-correlated-inputs",
        "finding:puncture-meridians-have-one-glue-class-and-residue-duality-does-not-select-metric",
        "finding:joint-integral-unimodular-charge-closure-uniquely-selects-complete-invariant-metric",
        "finding:meridian-spinor-joint-source-product-has-actual-family-root-simple-pole"
      ],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ]
    },
    {
      "id": "topic:flavor",
      "titleEN": "Standard Model and flavor",
      "summaryEN": "Family lattices, residue operators, windings, and shared seeds produce algebraic flavor structures and source-mass readouts. Their mapping to normalized, interacting 3+1D particle masses and full neutrino dynamics remains a separate bridge.",
      "orientation": {
        "role_en": "Translates compiler and family structures into flavor operators and conditional mass outputs.",
        "have_en": "The corpus contains family rank 3, discrete residues and operators, and selected ratio/source-mass readouts; φ0/λC are shared across sectors.",
        "seek_en": "Open items are physical Yukawa and neutrino dynamics, absolute normalization, threshold/pole-mass transfer, and mapping to interacting 3+1D fields.",
        "connection_en": "Shared seeds with α and other sectors produce correlated predictions, not independent confirmations.",
        "next_bridge_en": "The next bridge is a state and interaction rule derived from the same parent, with scale and renormalization transfer."
      },
      "problemIds": [
        "problem:seam-family-connection-compatibility",
        "problem:flavor-ratio-amplitude-readout"
      ],
      "findingIds": [
        "finding:joint-discrete-data-vs-connection",
        "finding:parallelity-excludes-2plus2-only-conditionally",
        "finding:flavor-ratio-closed-absolute-anchor-open"
      ],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:b39e451a05162da745b19d27"
      ]
    },
    {
      "id": "topic:alpha",
      "titleEN": "Fine-structure constant",
      "summaryEN": "The α program contains an explicit fixed-point equation, determinant-line reformulations, and precise finite checks. A positive root is exhibited for the specified equation; finite checks do not establish global uniqueness. make_F ignores c3 and Nfac=8 is selected, so physical origin and transfer to Thomson α remain open.",
      "orientation": {
        "role_en": "Examines a specific electromagnetic fixed-point readout and its formal reformulations; it is a readout branch, not a derivation of the full coupling origin.",
        "have_en": "The specified equation has a positive solution. v3 finite tests support only their checked cases; make_F ignores c3 and Nfac=8 is selected. They do not prove global uniqueness.",
        "seek_en": "The open work is a source derivation of the function and its parameters, determinant/Ward origin, and a justified transfer to Thomson α.",
        "connection_en": "φ0 and other architectural inputs connect the α branch to flavor and other outputs; this shared dependence limits the independence of matches.",
        "next_bridge_en": "First clarify the selection and c3-independent structure of make_F against its source contract; then derive a physical renormalization/measurement bridge."
      },
      "problemIds": [
        "problem:alpha-fixed-input-root",
        "problem:clock-linked-neutral-response-reconstruction"
      ],
      "findingIds": [
        "finding:alpha-equation-is-fixed-input-closure",
        "finding:alpha-global-positive-root-unique",
        "finding:marked-e8-sector-grade-response-realizes-five-quarters",
        "finding:alpha-exact-coefficients-and-root-retain-specific-physical-ward-obligation",
        "finding:alpha-archive-term-provenance-and-master-functional-scope",
        "finding:four-clock-fields-complete-quadratic-response"
      ],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:55e544ffff08c43dfd9f418e"
      ]
    },
    {
      "id": "topic:quantum",
      "titleEN": "Quantum and boundary structure",
      "summaryEN": "Finite E8, Pauli/Clifford, code, state, covariance, and instrument constructions supply internal quantum models and scoped guarantees. A code or successful channel is not yet a selected, repeatable physical source with the same parent dynamics.",
      "orientation": {
        "role_en": "Organizes finite codes, states, instruments, and quantum channels as checkable submodels.",
        "have_en": "Concrete finite code and operator structures exist, with local results within explicitly specified source and instrument menus.",
        "seek_en": "Open items include common physical preparation, source, interaction, repetition, record preservation, and connection to the TFPT parent.",
        "connection_en": "Codes and clocks specify internal information and symmetry structures; gravity additionally requires local geometry and dynamics.",
        "next_bridge_en": "A common source construction must reproduce all allowed interventions and records, including controlled counterexamples."
      },
      "problemIds": [
        "problem:future-quotient-and-gns-reconstruction",
        "problem:common-source-state-event-selection",
        "problem:physical-time-projector-transfer",
        "problem:gravity-flow-normalization",
        "problem:clock-linked-neutral-response-reconstruction",
        "problem:clock-source-covariant-transport",
        "problem:charged-twist-response-identifiability",
        "problem:native-charged-seam-selection",
        "problem:constructive-seam-lift-state",
        "problem:seam-partner-charge-state-time",
        "problem:automated-operator-source-synthesis",
        "problem:reverse-bootstrap-physical-field-dictionary",
        "problem:fundamental-process-classification",
        "problem:atlas-clock-defect-and-operational-reconstruction",
        "problem:automatic-origin-response-decision"
      ],
      "findingIds": [
        "finding:future-equivalence-minimizes-declared-answer-process",
        "finding:positive-word-kernel-reconstructs-cyclic-gns",
        "finding:operational-seed-is-input",
        "finding:native-source-common-time-thermal-family",
        "finding:native-grade-carry-and-memory",
        "finding:even-seam-global-operator-factorization",
        "finding:source-generated-marking-classification",
        "finding:source-marking-field-realization-boundary",
        "finding:minimal-defect-uniqueness-not-proved",
        "finding:conditional-seam-field-state-time-reconstruction",
        "finding:continuous-hardy-seam-classification",
        "finding:same-source-seam-energy-selection",
        "finding:master-functional-presupposes-source-selection",
        "finding:geometric-deck-not-calderon-polarization",
        "finding:positive-compression-erases-carrier-minus-sector",
        "finding:higgs-determinant-does-not-discharge-carrier-map",
        "finding:primitive-invariant-does-not-select-rank-three",
        "finding:fixed-background-source-does-not-fix-mixed-vertex",
        "finding:local-quarter-inner-variation-is-connection",
        "finding:calderon-enlargement-does-not-select-higgs",
        "finding:finite-sm-higgs-variation-retains-seed",
        "finding:operator-skeleton-does-not-identify-insertion-algebra",
        "finding:internal-even-car-hodge-is-not-coordinate-algebra",
        "finding:minimum-rank-unique-primitive-channel-does-not-select-32",
        "finding:joint-selfconsistency-presupposes-minimal-algebra-fiber-selection",
        "finding:process-composition-and-cyclicity-do-not-select-algebra",
        "finding:quartic-shape-selects-32-only-with-source-sign",
        "finding:native-symmetric-quartic-erasure-common-object",
        "finding:joint-native-algebra-normalizer-and-response-orbit",
        "finding:native-galois-intertwiner-unique-logical-marked-orbit",
        "finding:native-reflection-full-four-five-generators-rate-injectivity",
        "finding:complete-logical-readout-native-covariant-residual-classification",
        "finding:original-polar-mark-clock-centralizer-orbit",
        "finding:actual-quartic-code-product-stabilizer-quarter-exclusion",
        "finding:original-decoder-versus-native-quarter-polynomial-erasure-test",
        "finding:original-decoder-product-time-and-all-unitary-erasure-lifts",
        "finding:native-clock-compatible-polar-fibre-and-canonical-distance",
        "finding:native-moment-parent-and-product-path-selection-boundary",
        "finding:original-e8-current-response-and-full-quarter-lifts",
        "finding:literal-charged-current-register-dictionary-fails-quarter",
        "finding:native-cartan-code-inner-e8-stabilizer-excludes-marked-quarter",
        "finding:native-code-neutral-weight-two-action-and-global-clock-exclusion",
        "finding:original-neutral-root-mixed-response-derived",
        "finding:actual-mixed-ordered-return-on-native-quartic-code",
        "finding:mixed-return-spectrum-does-not-select-original-polar-mark",
        "finding:actual-mixed-return-fails-native-trimer-erasure-lift",
        "finding:strict-trace-gap-excludes-positive-mixed-return-reweighting",
        "finding:original-source-erasure-ward-terms-derived",
        "finding:uncompressed-original-mixed-return-does-not-preserve-code",
        "finding:original-root-response-sum-also-leaks-from-code",
        "finding:original-full-source-return-exterior-feedback-derived",
        "finding:original-return-requires-memory-in-every-code-direction",
        "finding:native-conformal-primary-multiplicity-source-factorization",
        "finding:canonical-conformal-erasure-forces-primary-twenty-carry",
        "finding:all-canonical-stress-histories-scalar-on-native-code",
        "finding:original-local-current-ope-forces-erasure-and-carry",
        "finding:all-real-local-cartan-profiles-erasure-third-bound",
        "finding:closed-cartan-weyl-histories-only-logical-phase",
        "finding:full-existing-local-e8-hull-of-native-code",
        "finding:full-local-quartic-wick-ladder-and-unprojected-native-actions",
        "finding:unmarked-native-w6-simplex-from-full-quartic-ope",
        "finding:full-e8-current-products-fix-stress-and-exterior-ward-cancellation",
        "finding:full-source-simplex-does-not-select-original-polar-mark",
        "finding:original-full-field-event-gram-reconstructs-relative-polar-mark",
        "finding:raw-event-state-positivity-does-not-execute-polar-normalization",
        "finding:determinant-cover-not-literal-full-cartan-lattice-event",
        "finding:clock-free-quartic-product-spectral-sectors-and-native-five",
        "finding:six-complex-native-simplex-rays-from-holomorphic-product-quadrics",
        "finding:intrinsic-relative-response-covariance-and-state-boundary",
        "finding:intrinsic-event-composition-retains-shared-source-and-correlation-data",
        "finding:clock-free-event-geometry-fixes-clock-class-and-mark-orbit-not-member",
        "finding:original-charged-seam-character-recovers-global-native-event-pair",
        "finding:internal-seam-vacuum-and-original-neutral-tensor-do-not-select-flag-root",
        "finding:actual-quarter-fold-shift-removes-native-symmetry-obstruction-without-flag-selector",
        "finding:fold-shift-equivariance-needs-actual-source-response-map-not-another-symmetry-no-go",
        "finding:original-fold-covariance-current-counterterm-and-quartic-twisted-transport",
        "finding:fold-state-full-quartic-kernel-and-erasure-protected-low-order-response",
        "finding:original-fold-quartic-mean-and-spectral-responses-do-not-match-sixty-flags",
        "finding:original-winding-full-state-response-removes-vacuum-rank-two-shortcut",
        "finding:original-source-global-time-winding-history-factorization",
        "finding:original-local-density-folds-to-correlated-root-current-and-erasure-response",
        "finding:original-current-all-mode-energy-and-geometric-stress-bridge",
        "finding:original-current-geometric-response-pair-has-no-common-polar-sector",
        "finding:original-current-ordered-hall-kernel-and-actual-folded-field-products",
        "finding:original-seam-grades-full-density-geometric-products-and-energy-response",
        "finding:original-seam-complete-density-grading-not-sharp-32-input-sectors",
        "finding:original-density-all-profile-mean-work-scalar-on-native-packet",
        "finding:original-p1-gap-normalized-action-covector-and-scalar-holonomy-class",
        "finding:original-p1-gap-car-component-not-native-sharp-32-event",
        "finding:complete-positive-scalar-first-order-circle-source-normal-form",
        "finding:fixed-source-time-seam-ward-rigidifies-scalar-principal-symbol-with-carry",
        "finding:unit-spectral-flow-gap-and-four-marks-do-not-imply-fixed-source-ward",
        "finding:four-native-starts-have-distinct-original-fold-state-correlations",
        "finding:four-starts-full-joint-kernel-and-charged-covariant-transport",
        "finding:four-native-polar-marks-not-fixed-source-state-gauge-equivalent",
        "finding:original-pointer-template-requires-source-context-identification",
        "finding:four-polar-context-algebra-and-source-crosscoupling",
        "finding:every-native-quartic-has-all-eight-original-car-supports",
        "finding:bounded-proper-local-source-operation-cannot-exactly-prepare-positive-eigenpacket",
        "finding:full-original-erasure20-and-joint25-have-all-eight-source-supports",
        "finding:two-face-collar-fixes-face-current-phase-and-distinguishes-relative-endpoint-lift",
        "finding:full-dirac-cauchy-vector-cocycle-cancels-and-endpoint-domain-distinction",
        "finding:unchanged-qwz-full-finite-energy-spectral-exhaustion",
        "finding:uniform-z4-d8-locality-and-both-spinor-chirality-time-census",
        "finding:odd-spinor-global-refielding-and-unit-source-winding",
        "finding:sharp-half-flux-register-quotient-and-local-normality-exclusion",
        "finding:all-word-register-charged-local-field-limit-obstruction",
        "finding:exact-parity-gauss-locality-completion-of-register-source",
        "finding:cover-half-flux-not-fixed-charge-eightfold-spinor-twist",
        "finding:original-neutral-eightpreimage-parity-pair-has-uniform-cut-action",
        "finding:complete-dirac-vector-phase-pair-has-zero-spinor-Ward-charge",
        "finding:smooth-unitary-endpoint-removal-diverges-at-fixed-source-time",
        "finding:continuous-original-time-nonunitary-limits-stay-in-old-source-folium",
        "finding:common-register-vacuum-reference-uniform-and-local-grade-reduction",
        "finding:actual-heat-filtered-neutral-pair-full-state-time-and-separate-chiral-limit",
        "finding:holomorphic-kms-extension-assumes-charged-net-and-not-microscopic-generator",
        "finding:fixed-interval-rotation-modular-chain-fails-local-state-takesaki-repairs",
        "finding:source-winding-cartan-four-word-and-two-edge-kms-gso-discriminator",
        "finding:p1-parity-gauss-net-selection-undecidable-without-original-localization-map",
        "finding:original-minimality-does-not-reconstruct-operational-source",
        "finding:generic-first-order-relative-bound-zero-counterexample-and-correct-domain-repair",
        "finding:sign-projector-does-not-determine-time-magnitude",
        "finding:full-faithful-kms-or-transfer-recovers-magnitudes",
        "finding:full-two-face-collar-recovers-signed-operator",
        "finding:two-face-graph-state-time-same-datum",
        "finding:shared-register-gkls-embedding-exact-q-interval",
        "finding:marked-m4-channel-all-powers-homogeneous-gksl-excluded",
        "finding:matter-observations-do-not-fix-geometric-response",
        "finding:four-clock-fields-complete-quadratic-response",
        "finding:actual-j-covariant-source-transport",
        "finding:fixed-source-affine-j-obstruction",
        "finding:neutral-vacuum-allword-twist-blindness",
        "finding:eight-charged-responses-reconstruct-twist",
        "finding:native-invariant-response-not-fixed-chiral-twist",
        "finding:native-opposite-charge-response-symmetry",
        "finding:native-chemical-mark-visible-in-charged-corners",
        "finding:fixed-hopping-quarter-phases-retain-antiunitary-discriminator",
        "finding:constructive-phase-class-and-full-winding",
        "finding:constructive-positive-state-extension",
        "finding:constructive-current-group-selects-positive-p-lift",
        "finding:constructive-state-algebra-resolution-and-source-test",
        "finding:constructive-all-phases-fail-unchanged-source",
        "finding:partner-carrier-charges-and-state-types",
        "finding:partner-fixed-quarter-time-splits-sm-multiplet",
        "finding:partner-original-carrier-cross-sheet-conjugation",
        "finding:partner-chiral-quarter-conjugation-state-time",
        "finding:joint-bilinear-hermitian-correction",
        "finding:joint-quarter-transports-marking",
        "finding:joint-fixed-time-marking-repair-excluded",
        "finding:joint-spinor-not-source-coefficient",
        "finding:typed-operator-search-calibrated",
        "finding:positive-kernel-construction-with-exact-discriminator",
        "finding:source-typed-kernel-search-controls",
        "finding:collar-car-projection-multifield-ray",
        "finding:known-quarter-source-full-multifield-control",
        "finding:source-reference-amplitude-retained",
        "finding:joint-fermionic-source-schur-functional",
        "finding:quarter-circle-absolute-zeta-green-eta",
        "finding:quarter-sea-absolute-thermal-central-phase",
        "finding:original-operational-seed-and-given-green-pairing",
        "finding:order-one-infinitesimal-bound-inference-fails",
        "finding:joint-ward-two-field-data-miss-fixed-four-field-response",
        "finding:complete-car-kernel-fixes-nongaussian-link-functional",
        "finding:source-covariance-jet-and-mixed-face-interface",
        "finding:e8-grade-two-explicit-spinor-current-action",
        "finding:intrinsic-source-jet-removes-pure-field-frame-motion",
        "finding:unchanged-ns-vector-generators-cannot-create-d5-spinor-fields",
        "finding:two-face-noncommuting-geometric-response-calculus",
        "finding:raw-face-mask-fails-source-kernel-null-descent",
        "finding:action-response-sewing-does-not-select-lf-intervention",
        "finding:faithful-gns-completion-closes-automated-source-query-feedback",
        "finding:whole-quarter-channels-identified-by-exact-internal-kernel",
        "finding:actual-joint-insertion-hull-resolves-eight-coefficient-directions",
        "finding:e8-bare-trilinear-and-single-anchor-weyl-class-insufficient",
        "finding:complete-family-four-cycle-class-separates-native-clock-from-sm-preservation",
        "finding:native-clock-word-transpose-has-static-rank-four-counterexample",
        "finding:whole-constant-coupled-source-is-implementable-despite-isolated-insertion-domain",
        "finding:fixed-quarter-jloc-pfaffian-closure-fails-local-skew-test",
        "finding:same-collar-has-canonical-selfdual-kinetic-pairing-and-charged-determinant",
        "finding:quarter-cover-pairing-does-not-supply-local-normal-or-select-scale-measure",
        "finding:fixed-aps-source-has-whole-inverse-and-finite-boundary-correction",
        "finding:mass-only-deck-relative-heat-action-fails-free-infinite-trace",
        "finding:finite-antiperiodic-scalar-wall-has-no-exact-massless-normal-mode",
        "finding:spectral-heat-covariance-positivity-does-not-imply-time-rp",
        "finding:quaternionic-sm-mass-winding-is-not-normal-determinant-clutch",
        "finding:bounded-relative-trace-obstruction-and-whole-genuine-pair-heat-reader",
        "finding:normal-clutch-orbit-index-equivariantly-recovers-given-weak-module",
        "finding:normal-orbit-spin-family-index-and-signed-charge-balance",
        "finding:fixed-flavor-cartan-sign-cover-and-root-lift-parity",
        "finding:original-family-vector-action-is-not-cartan-rotation-or-spinlift-selection",
        "finding:actual-genus-two-sign-family-closes-common-parallel-k-connection",
        "finding:actual-q-quarter-extends-common-k-connection-and-real-coefficient-lifts",
        "finding:real-source-reflection-is-not-linear-duality-or-compact-clock-inversion",
        "finding:source-selected-spin-and-q-signs-have-three-explicit-global-kernels",
        "finding:source-s0-szego-point-legs-generate-q-kernels-with-typed-products",
        "finding:actual-spin-kernel-determinant-has-inverse-q-norm-character",
        "finding:closed-source-flavor-spin-has-functorial-pfaffline-with-charged-type-limit",
        "finding:original-relative-seam-has-explicit-whole-graph-fredholm-mismatch",
        "finding:whole-constant-coupled-clutch-defects-are-exact-internal-kernels",
        "finding:old-complex-scalar-clutch-separates-c0-and-product-reflection",
        "finding:scalar-defect-circle-character-does-not-select-projector-holonomy",
        "finding:source-spin-is-canonical-ramified-base-spin-pullback",
        "finding:original-v117-has-explicit-algebraic-q-cover-fundamental-frame",
        "finding:double-circle-reflection-does-not-fix-entire-cubic-cable-seam",
        "finding:actual-fuchs-real-map-transports-whole-given-finite-source-state-and-time",
        "finding:actual-e0-compensator-extends-whole-k-e8-with-transported-quarter",
        "finding:actual-v252-entire-real-basis-has-signed-p2-dual-dictionary",
        "finding:chiral-fuchs-source-transport-has-distinct-majorana-phase-and-torus-absorption",
        "finding:native-theta-composition-retains-conjugate-source-and-parity-square",
        "finding:single-graph-range-isometry-does-not-give-local-whole-seed-map",
        "finding:hard-holonomy-selfduality-leg-and-finite-character-phase-separation",
        "finding:original-z6-positive-structural-kernel-does-not-supply-oriented-phase-observable",
        "finding:original-genus-two-hexagonal-rotation-has-concrete-rho-hodge-line",
        "finding:original-mixed-spin-products-realize-positive-u6-cycle",
        "finding:actual-spin-quadratics-reach-original-hexagonal-hodge-line",
        "finding:spin-pair-car-transport-retains-parity-and-whole-source-types",
        "finding:real-total-trace-does-not-exclude-coherent-phase-reader",
        "finding:geometric-six-spin-clock-differs-from-marked-native-clock",
        "finding:whole-q-to-p-pullback-transports-given-source-state-and-time",
        "finding:actual-fixpoint-evaluation-keeps-coefficient-signs-and-source-type",
        "finding:original-source-naturality-needs-no-second-p-image-background",
        "finding:canonical-spin2-lift-carries-whole-annulus-source-with-reversed-time",
        "finding:geometric-spin-collar-map-closes-weighted-image-domain-with-total-deck-action",
        "finding:claude33-annulus-map-is-valid-distinct-type-not-unique-geometric-spin-selection",
        "finding:original-mixed-spin-products-already-have-complete-dual-hom-coefficients",
        "finding:whole-f5-graph-supplies-canonical-reverse-qp-hom-kernel",
        "finding:actual-spin-product-weight-has-canonical-trace-class-form-pairing",
        "finding:fully-descended-covariant-reverse-kernel-removes-rho-form-channel",
        "finding:original-a4-linear-quarter-does-not-supply-proposed-scalar-mu3-repair",
        "finding:offdiagonal-hom-matches-a4-family-six-but-not-two-triplet-e8-product",
        "finding:compact-e8-adjoint-completes-family-six-with-carrier-rank-retained",
        "finding:three-family-cx-recursion-closes-exact-d8-with-minimal-original-escape",
        "finding:original-weak-current-coefficient-has-explicit-finite-oneform-consumer",
        "finding:original-d5-zero-mode-closes-triplet-carrier-and-fixed-glue-is-minimal-escape",
        "finding:mixed-spin-full-deck-has-no-rank-three-projector",
        "finding:actual-reverse-hom-diagonal-supplies-global-q-hodge-response",
        "finding:bare-c3-kernel-diagonal-yukawas-have-common-real-frame",
        "finding:original-primitive-action-is-present-highpass-is-not-finite-selector",
        "finding:atlas-detail-retrieval-recovers-existing-d4-solution",
        "finding:original-poisson-normal-trace-fixes-whole-calderon-graph",
        "finding:induced-original-hardy-defect-gives-finite-whole-source-reader",
        "finding:original-weak-quartic-action-has-nonzero-nonlinear-response",
        "finding:all-common-leading-distance-clutches-fail-original-flavor-lengths",
        "finding:actual-hardy-response-has-weak-clifford-odd-and-ko-real-completion",
        "finding:two-entry-hardy-adjoint-hierarchy-fails-full-ko-and-su2",
        "finding:actual-fuchs-halfpath-has-canonical-g-metric-c6-kernel-map",
        "finding:original-real-delta-jet-reads-same-marked-hardy-open-word",
        "finding:four-actual-fuchs-spine-edges-recover-marked-meridians-and-nonzero-open-word",
        "finding:native-adjoint-quarter-clock-cannot-compensate-hardypair-odd-character",
        "finding:whole-cubic-gram-differential-retains-hardy-phase-and-cross-resonance",
        "finding:complete-original-mu01-hardy-reader-has-two-calibrated-entries",
        "finding:whole-six-original-hardy-inputs-generate-full-family-coefficient-algebra",
        "finding:actual-whole-hardy-alphabet-has-finite-particle-hole-wick-block",
        "finding:bare-unsmeared-mu-crossface-quadratic-fails-vacuum-domain",
        "finding:linear-spectral-centralization-does-not-replace-full-marked-hardy-source",
        "finding:original-admissibility-projector-is-explicit-penalties-do-not-read-retained-amplitudes",
        "finding:actual-original-inner-fluctuation-has-whole-noncommuting-two-face-response",
        "finding:fiber-only-primitive-split-and-frozen-gap-miss-original-action",
        "finding:oriented-resolvent-weights-do-not-identify-original-reflection-producer",
        "finding:current-odd-carrier-reader-is-lossless-on-whole-coupled-source",
        "finding:ap-spectral-formulas-do-not-force-normal-domain-or-complete-source",
        "finding:actual-weak-connection-transmits-family-orientation-to-both-faces",
        "finding:original-higgs-variation-is-not-independent-yukawa-stationarity",
        "finding:actual-weak-cap-converges-on-whole-quarter-circle",
        "finding:canonical-clifford-double-derives-normal-ap-and-typed-deck",
        "finding:universal-graded-source-reducing-images-do-not-fix-carrier-frame",
        "finding:whole-two-face-compression-projector-defect-detects-hidden-source-loss",
        "finding:actual-v252-quark-lepton-split-prevents-weak-grading-uniqueness-inference",
        "finding:actual-graded-hypercharge-trace-rejects-quark-lepton-sign-intertwiner",
        "finding:separable-normal-real-maps-compose-to-given-deck-and-quarter-image",
        "finding:actual-gauge-real-frames-leave-carrier-phase-as-coordinate-freedom",
        "finding:original-higgs-family-has-one-complex-kk-class-but-different-whole-sources",
        "finding:signed-one-particle-modular-weight-is-not-the-positive-even-heat-operator",
        "finding:three-moments-select-one-exponential-exactly-in-positive-laplace-class",
        "finding:existing-ap-positive-source-factor-has-oriented-poisson-heat-bridge",
        "finding:actual-v252-entire-compatibility-family-has-generic31-dimensional-quotient",
        "finding:full-memory-schur-reconstruction-preserves-every-ordered-word-under-nesting",
        "finding:original-return-and-native-j-have-minimal68-dimensional-all-word-memory",
        "finding:original-full-source-regulator-flow-retains-normalized-kernel-and-vacuum-factor",
        "finding:full-reflected-quadratic-regulator-cone-preserves-every-rp-source",
        "finding:original-shared-higgs-source-induces-fixed-yukawa-mixed-matter-words",
        "finding:local-even-yukawa-sewing-preserves-given-joint-graded-rp",
        "finding:whole-original-constant-higgs-orbit-has-reduced-majorana-spectral-response",
        "finding:archived-geometric-higgs-residue-bulk-needs-coefficient-identification-repair",
        "finding:original-local-higgs-residue-linear-coefficients-fail-same-trace-heat-ratio",
        "finding:whole-original-higgs-moments-fix-conditional-local-kinetic-mass-quartic",
        "finding:whole-variable-original-higgs-bound-reference-response-and-forced-clifford-factor",
        "finding:original-symmetric-scale-map-fails-simultaneous-higgs-einstein-repair",
        "finding:whole-original-higgs-inner-scale-and-affine-full-source-transport",
        "finding:normal-higgs-mode-type-and-exact-kernel-metric-require-actual-relative-operator-map",
        "finding:original-superconnection-grades-and-weighted-heat-retain-higgs-kinetic-excursions",
        "finding:whole-normal-reduction-preserves-relative-spectral-reader-and-higgs-jets",
        "finding:original-admissibility-own-spectral-reader-has-no-free-low-mode-residue-repair",
        "finding:whole-total-chiral-positive-spectrum-retains-higgs-kinetics-and-common-half-trace",
        "finding:whole-scale-energy-response-uniquely-reconstructs-normal-profile",
        "finding:original-relative-scale-flow-separates-residue-finite-part-and-local-anomaly",
        "finding:original-whole-green-produces-energy-response-with-correct-orthogonal-trace",
        "finding:whole-mixed-scale-source-reads-bosonic-insertion-before-higgs-average",
        "finding:current-original-spectral-action-triplet-fails-positive-laplace-class-unless-leading-relative-term-cancels",
        "finding:correct-current-argument-weights-link-whole-higgs-threshold-and-same-einstein-response",
        "finding:whole-original-spinor-curvature-a4-has-no-independent-scalaron-r-squared",
        "finding:whole-original-entropic-curvature-corrects-max-symmetric-scalar-scale",
        "finding:given-whole-higgs-source-fixes-radial-curvature-susceptibility-without-extra-scalar",
        "finding:actual-original-four-ghost-complex-preserves-base-selector-with-full-cohomology-and-distinct-traces",
        "finding:whole-original-admissibility-energy-source-recovers-constraints-but-cannot-replace-geometric-operator",
        "finding:original-moving-normal-kernel-fixes-induced-connection-and-full-scale-covariance",
        "finding:fixed-original-o1-source-rejects-nonconstant-normal-multiplier-and-fixes-placement-test",
        "finding:original-master-variation-keeps-spin-weight-and-active-source-route-typed",
        "finding:shared-original-higgs-mixture-has-invariant-color-fourpoint-wick-defect",
        "finding:bounded-fixed-rank-spectral-action-does-not-normalize-noncompact-higgs-volume",
        "finding:whole-original-quarter-source-bounds-higgs-weight-uniformly-through-joint-mode-ir-limits",
        "finding:original-o1-covariance-leaves-full-radial-higgs-law-and-exact-fourier-source-readout",
        "finding:whole-process-reconstruction-priority-and-original-locality-geometry-input-audit",
        "finding:actual-disjoint-local-weyls-acquire-spurious-commutator-under-bare-native-compression",
        "finding:actual-quarter-current-state-excludes-nontrivial-geometric-local-point-time",
        "finding:actual-elliptic-interval-car-source-produces-local-modular-generator",
        "finding:actual-proper-two-face-regions-do-not-contain-pure-local-source-double",
        "finding:actual-elliptic-whole-environment-fixes-regional-car-partner",
        "finding:actual-original-color-triplet-has-spectator-dependent-modular-field-law",
        "finding:actual-color-marginal-has-complete-finite-source-reader-and-mixture-criterion",
        "finding:two-and-four-field-words-do-not-complete-original-color-triplet-source",
        "finding:whole-original-quarter-occupation-tower-uniquely-reconstructs-common-radial-higgs-law",
        "finding:finite-original-tower-reader-and-existing-weak-symmetry-fix-shared-matter-responses",
        "finding:unchanged-free-quarter-source-cannot-be-nontrivial-integrated-higgs-mixture",
        "finding:actual-e8-record-doily-action-is-signed-p-plus-compatible-point-with-typed-sym2-lift",
        "finding:actual-e8-record-words-distinguish-order-and-retain-phase-beyond-fifteen-labels",
        "finding:literal-doily-incidence-output-and-strict-causal-order-on-fifteen-source-labels-excluded",
        "finding:actual-doily-context-record-characters-have-ranks-four-two-two-two",
        "finding:canonical-standard-split-localizes-original-source-record-words-with-full-descendant-companion",
        "finding:unchanged-global-sixty-event-source-fails-local-exterior-current-test",
        "finding:canonical-source-localization-changes-exterior-state-and-does-not-select-event-origin",
        "finding:original-elliptic-fixed-holonomy-insertion-gives-local-operation-on-unchanged-source",
        "finding:original-quarter-pair-fixes-square-charge-law-half-response-and-real-quillen-norm",
        "finding:actual-elliptic-source-determines-all-path-normalized-causal-current-response",
        "finding:original-higgs-quark-source-has-exact-whole-su3-counting-response",
        "finding:single-original-color-parity-separates-free-quillen-from-positive-higgs-integrated-source",
        "finding:whole-original-quarter-graph-color-response-is-relative-and-diagonal-singlet",
        "finding:original-center-selector-requires-typed-state-field-and-face-transport",
        "finding:original-color-center-fixes-whole-e6-a2-source-and-charged-ward-word-action",
        "finding:original-color-neutral-lattice-class-cannot-supply-odd-fields-by-inherited-superlattice-extension",
        "finding:original-color-center-extends-to-folded-ns-but-full-current-action-needs-spin-sector-transport",
        "finding:actual-color-spin-car-mixed-word-has-complete-thermal-source-and-cyclic-sewing",
        "finding:exact-original-ns-ramond-heat-equality-does-not-identify-fixed-color-restricted-source",
        "finding:original-scalar-cover-profile-cannot-implement-fixed-spin-cartan-loop",
        "finding:actual-spin-cartan-composite-source-retains-multi-arc-support-and-fails-additive-even-locality",
        "finding:actual-color-selector-admits-exactly-eighth-periodic-original-density-variations",
        "finding:actual-color-is-internal-exactly-on-eightfold-coordinate-source-regions",
        "finding:original-whole-two-face-multiplier-reduction-is-only-constant-residue-diagonal",
        "finding:original-two-face-local-fock-implementation-and-exact-source-variation-differ-from-reduction",
        "finding:whole-undecorated-transfer-does-not-determine-original-marked-field-source",
        "finding:volume-wise-injective-positive-transfer-does-not-prove-uniform-parent-gap",
        "finding:original-c6-half-power-has-exact-entire-positive-ordered-word-expansion",
        "finding:original-c6-whole-word-sewing-retains-source-amplitude-and-controlled-infinite-tail",
        "finding:historical-parent-and-actual-field-time-bridges-must-be-reused-before-new-source-models",
        "finding:actual-native-v990-full-timed-words-recover-kubo-response-distinct-from-instantaneous-variance",
        "finding:actual-original-higgs-force-has-complete-ordered-fermionic-determinant-source",
        "finding:finite-covariant-higgs-composites-have-no-nontrivial-positive-instantaneous-classical-law",
        "finding:actual-original-collective-mean-has-exact-ball-domain-and-relative-entropy-action",
        "finding:original-uniform-allmode-force-clt-is-nonzero-only-before-fixed-time-smearing",
        "finding:original-unscaled-time-smeared-force-has-selfadjoint-whole-ordered-source",
        "finding:original-local-higgs-force-has-whole-centered-hilbert-schmidt-determinant-source",
        "finding:given-original-circle-force-source-generates-an-exact-causal-local-net",
        "finding:literal-archived-global-rg-kernel-does-not-preserve-finite-measures",
        "finding:native-higgs-marginal-retains-induced-vertex-and-noether-response",
        "finding:isospectral-noether-orbit-does-not-supply-original-metric-higgs-variation",
        "finding:metric-dtn-form-bound-needs-transfer-comparison-for-gap",
        "finding:conditional-higgs-pair-winding-protection-in-common-circle-carrier",
        "finding:natural-five-clock-carrier-excludes-invariant-three-transfer-compression",
        "finding:shared-scalar-shift-whole-retained-higgs-sector-has-index-minus-eighteen",
        "finding:whole-coupled-quark-circle-common-shift-cancels-relative-winding",
        "finding:one-sided-shift-full-higgs-pair-is-hilbert-schmidt-not-trace-class",
        "finding:selective-coupled-higgs-reader-has-well-defined-det2",
        "finding:v311-population-reader-does-not-identify-quantum-channel",
        "finding:declared-charged-pair-relation-leaves-five-word-ambiguity",
        "finding:full-creator-relations-close-fixed-free-two-mode-ambiguity",
        "finding:comoving-diagnostic-clock-exact-response-but-nonlocal-mode-transport",
        "finding:free-quarter-two-face-response-strip-with-relative-zero-mode-defect",
        "finding:e8-hodge-event-perfectly-distinguishable-from-every-unitary",
        "finding:common-five-slot-transfer-preserves-e8-bracket-not-automatic-tp",
        "finding:comoving-clock-dynamic-higgs-connection-and-charged-flow",
        "finding:r064-sixty-record-channel-exact-distance-and-continuous-record-parent",
        "finding:two-syntheses-shared-source-priorities-and-typed-limits",
        "finding:weighted-index-trace-and-selfdual-theta-require-original-selection",
        "finding:ordered-quarter-fourfield-e8-record-and-charge-filters",
        "finding:r091-recovered-native-hodge-sewing-and-full96-quarter-complement",
        "finding:r092-fold-ward-target-neutral-source-and-smaller-creation-branch",
        "finding:r093-original-kink-time-response-distinguishes-quarter-states",
        "finding:r093-ordered-current-kink-and-eight-arc-locality",
        "finding:r094-original-five-excitations-distinct-from-clustering-vacuum",
        "finding:r096-joint-higgs-twoface-source-constraint",
        "finding:r096-positive-twoface-fourword-defect-bound",
        "finding:r096-unnormalized-mixed-source-linear-identity",
        "finding:r096-original-quark-crossing-negative-covariance",
        "finding:known-fourmark-system-has-three-and-five-canonical-views",
        "finding:reverse-bootstrap-retained-operator-scope",
        "finding:e8-current-dictionary-all-separated-responses",
        "finding:charged-scaling-microscopic-map-still-unspecified",
        "finding:original-slater-proxy-fitted-bound-fails-actual-norm",
        "finding:periodic-microscopic-zero-modes-distinguish-source-state",
        "finding:r097-original-q-twins-are-integrally-conjugate-before-fixed-source-form",
        "finding:replicated-deterministic-consistency-iff-influence-dag",
        "finding:three-binary-processes-two-copy-reversible-classification",
        "finding:independent-poset-information-composition-consequences",
        "finding:reset-diagnosis-not-global-tfpt-underdetermination",
        "finding:three-inequivalent-repeatable-observation-countermodels",
        "finding:repeatable-reports-do-not-imply-full-state-stability",
        "finding:finite-sequential-data-admit-classical-history-realization",
        "finding:actual-clock-doily-ovoid-kernel-is-native-quartic-five",
        "finding:glue-clock-twisted-sectors-share-marked-quadratic-module",
        "finding:complete-native-six-effect-covariant-instrument-classification",
        "finding:native-six-effect-readout-on-existing-erasure-output",
        "finding:relational-quartic-singlet-and-invariant-density-separation",
        "finding:new-clock-feedback-origin-input-audit",
        "finding:native-event-channel-cone-intersection-is-tenth-to-half",
        "finding:native-six-ovoid-observation-first-occurs-at-tensor-degree-three",
        "finding:original-quartic-erasure-and-hamming-octic-share-marked-ovoid-response",
        "finding:native-octic-field-ray-is-explicit-but-retained-clock-stress-preparation-fails",
        "finding:actual-quarter-fold-stress-has-nonzero-octic-eighth-jet",
        "finding:native-octic-is-an-original-even-car-current-composite",
        "finding:original-geometric-source-jet-and-partial-p1-seed-closure",
        "finding:full-root-ope-has-normalized-native-octic-component",
        "finding:paper-microscopic-car-composes-with-native-octic-ward",
        "finding:microscopic-neutral-octic-has-controlled-smeared-limit",
        "finding:paper-seed-source-needs-local-image-not-global-equivalence",
        "finding:full-car-positive-time-forces-source-vacuum",
        "finding:original-winding-theorem-does-not-select-seam-ray",
        "finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel",
        "finding:original-os-step-needs-full-moments-not-connected-cumulants",
        "finding:graded-field-image-precedes-physical-observable-restriction",
        "finding:older-original-circle-representative-already-realizes-ward-and-index",
        "finding:old-quarter-heat-transfer-has-controlled-rank-one-limit-and-odd-product",
        "finding:historical-em-rank-one-and-full-heat-traces-have-different-contracts",
        "finding:older-frg-functional-already-supplies-formal-full-moment-parent",
        "finding:earliest-c3-route-quantizes-level-but-needs-physical-kinetic-normalization",
        "finding:canonical-positive-circle-half-selects-the-toeplitz-line-and-sixth-order-correction",
        "finding:old-seam-shift-canonically-gives-relative-car-line-and-fredholm-factor",
        "finding:old-index-coupling-removes-heat-map-and-has-sharp-residual-ward-test",
        "finding:original-admissibility-requires-image-membership-not-positive-half-or-commutation",
        "finding:old-closure-already-assumes-car-but-does-not-map-the-geometric-circle",
        "finding:historical-uv-map-infinite-mass-exclusion-already-proved-and-recovered",
        "finding:a4-spin-lift-fixes-local-ns-and-unordered-quarter-pair",
        "finding:cover-winding-exchanges-quarter-sectors-before-its-square",
        "finding:retained-winding-preserves-local-support-and-neutral-time",
        "finding:marked-glue-square-is-the-e8-fermionization-character",
        "finding:fixed-canonical-d8-is-not-transported-source-d8",
        "finding:actual-winding-has-four-module-e8-defect-extension",
        "finding:ramond-lift-sign-is-common-intertwiner-basis-gauge",
        "finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class",
        "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor",
        "finding:schur-carrier-plus-complement-preserves-original-relative-determinant",
        "finding:v258-forward-source-gap-is-reused-not-solved-by-inversion",
        "finding:one-sided-source-and-real-em-norm-need-response-map-not-chiral-phase",
        "finding:trace-class-pair-index-fixes-relative-factor-without-primitive-ray",
        "finding:matrix-clutch-degree-connects-weak-determinant-class-without-ray-selector",
        "finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index",
        "finding:inner-carrier-is-infinite-spacetime-module-not-finite-circle-cut",
        "finding:normal-spin-determinant-line-exactly-transports-whole-circle-in-given-product",
        "finding:normal-index-line-source-match-is-holonomy-condition-not-vertical-degree",
        "finding:full-normal-product-polarization-change-is-not-trace-class",
        "finding:massive-transverse-zero-index-retains-positive-determinant-response",
        "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel",
        "finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection",
        "finding:tetrahedral-quarter-face-phase-does-not-identify-original-quarter-marked-curve",
        "finding:existing-elliptic-cover-correspondence-has-exact-c6-image-and-retained-mixed-clock",
        "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
        "finding:global-split-joint-carrier-admits-parallel-native-c12-clock",
        "finding:pure-weak-clutch-clock-identification-fails-despite-quarter-matches",
        "finding:same-chern-clutch-native-compiler-does-not-select-physical-connection",
        "finding:native-gaussian-four-is-cartan-subspace-in-whole-sixtyfour",
        "finding:native-family-factor-is-not-gaussian-four-despite-symmetric-coincidences",
        "finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice",
        "finding:even-degree-pullback-removes-cartan-topology-without-selecting-clock-cover",
        "finding:global-cartan-choice-is-optional-for-original-scalar-source-fields",
        "finding:bare-native-octic-is-not-whole-e8-zero-mode-singlet",
        "finding:explicit-primary-e8-invariant-octic-completes-same-neutral-car-source",
        "finding:completed-octic-has-exact-old-root-ope-component-and-quarter-source-value",
        "finding:elliptic-normal-spin-pullback-doubles-index-and-deck-quarter-lifts-anticommute",
        "finding:exact-separated-w8-twopoint-in-original-quarter-current-source",
        "finding:unshifted-vacuum-fails-same-w8-source-state-time-dictionary",
        "finding:local-current-phase-and-conditional-cyclic-p1-w8-image",
        "finding:all-neutral-w8-correlations-identify-the-two-original-quarter-charges",
        "finding:original-w8-response-has-infinite-same-time-spectral-support",
        "finding:older-seam-equivalence-verifications-do-not-supply-marked-local-p1-map",
        "finding:full-original-c1-stress-cycle-reconstructs-neutral-w8-response",
        "finding:folded-c8-cycle-misses-intrinsic-w8-tangent-without-obstructing-original-stress",
        "finding:native-source-first-nonuniform-moment-is-four-with-literal-five",
        "finding:native-whole-five-ground-space-needs-four-register-interaction",
        "finding:old-cover-winding-reconstructs-local-quarter-current-net",
        "finding:untransported-independent-quarter-stress-pair-is-not-current",
        "finding:current-public-paper-bytes-and-binding-source-gaps-recovered",
        "finding:winding-charge-conjugation-descends-fixed-pin-domain-but-not-full-dirac-sea",
        "finding:native-fourth-root-frame-has-signed-collective-sixty-mode-dual",
        "finding:native-root-gram-spectrum-is-not-canonical-source-energy-selection",
        "finding:identical-overlapping-native-five-codes-have-no-common-state",
        "finding:horizontal-e8-invariant-octic-cannot-isolate-native-five-ground-space",
        "finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea",
        "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity",
        "finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp",
        "finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum",
        "finding:declared-recursive-native-som-is-u35-equivariant",
        "finding:declared-recursive-native-som-clocks-depend-on-chosen-rates",
        "finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower",
        "finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent",
        "finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms",
        "finding:finite-crosscap-cauchy-state-is-not-original-quarter-vacuum-by-normal-filtering",
        "finding:native-quartic-relative-arc-charge-excludes-additive-density-stress-insertion",
        "finding:retained-quarter-sea-finite-modular-transfer-preserves-integrated-native-cartan",
        "finding:original-neutral-interarc-fields-have-exact-connected-current-vertex-reconstruction",
        "finding:actual-pin-zero-branch-retains-quarter-car-state-time-but-no-uniform-scale-return",
        "finding:conformal-pin-source-geometry-fixes-exterior-return-and-unitary-memory",
        "finding:geometric-exterior-schur-response-transfers-proper-native-arc-charge-but-is-compact",
        "finding:actual-ns-half-cover-cauchy-graph-purifies-green-state-with-neutral-ground-time-obstruction",
        "finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots",
        "finding:full-marked-equatorial-pullback-is-ramified-graph-not-smooth-seam-circle",
        "finding:same-elliptic-szego-green-functional-has-all-word-free-rp-and-calderon-marginal",
        "finding:elliptic-scalar-spin-pushforward-has-original-holomorphic-p2-anchor",
        "finding:natural-elliptic-anchor-connection-is-not-original-p2-cusp-connection",
        "finding:actual-elliptic-gaussian-source-determines-full-quarter-current-functional",
        "finding:elliptic-current-state-differs-from-hardy-on-every-proper-current-interval",
        "finding:primitive-geometric-force-retains-coupled-reference-and-parity-variation",
        "finding:equal-finite-positive-heat-channel-values-do-not-fix-geometric-force",
        "finding:elliptic-ns-spin-trace-has-complete-global-quarter-kernel",
        "finding:source-induced-ramified-resolutions-do-not-select-quarter-circle-domain",
        "finding:fixed-native-and-fermat-c3-carriers-do-not-identify-marked-v117-pair",
        "finding:theta-square-modular-pair-reconstructs-v117-with-distinct-geometric-q",
        "finding:archived-d4-puncture-formula-fails-and-existing-v117-repairs-existence",
        "finding:geometric-square-clock-is-not-theta-v117-quarter-generator",
        "finding:canonical-conformal-boundary-trace-fixes-existing-elliptic-cauchy-state",
        "finding:conformal-factor-averaging-preserves-given-free-boundary-wick-words",
        "finding:retained-seam-defect-has-derived-causal-geometric-response-with-contact",
        "finding:same-final-pin-geometry-retains-history-while-relative-index-factor-is-fixed",
        "finding:full-projector-covariance-and-positivity-force-all-car-words",
        "finding:actual-two-face-projector-reduces-free-source-test-to-cross-coherence",
        "finding:retained-marked-quarter-compiler-has-no-local-geometric-wick-correction",
        "finding:changed-elliptic-modulus-has-derived-cauchy-response-and-neutral-fourfield-variance",
        "finding:actual-equatorial-half-form-trace-fixes-orthogonal-hardy-range",
        "finding:actual-holomorphic-quarter-cauchy-idempotents-are-not-positive-car-covariances",
        "finding:full-equatorial-checkerboard-free-algebra-fails-fixed-reflection-positivity",
        "finding:genuine-d4-orbifold-branch-has-unique-irreducible-v117-class",
        "finding:wall-weight-additivity-does-not-exclude-stable-v117-parabolic-bundle",
        "finding:recovered-september-c4-triangle-closes-original-a0star-monodromy",
        "finding:actual-a0star-connection-does-not-have-rational-base-inversion-lift",
        "finding:actual-v117-sign-lines-are-negative-weierstrass-triangle-two-torsion",
        "finding:antipodal-and-positive-sign-packets-fail-actual-marked-v117-ramification",
        "finding:common-cyclic-twelve-cover-does-not-trivialize-v117-unramified-sign-lines",
        "finding:negative-sign-packet-has-source-selected-quarter-clock-lift",
        "finding:original-root-and-sign-lines-have-minimal-degree48-common-cover",
        "finding:given-elliptic-flat-connection-family-has-explicit-quillen-norm-and-two-holonomies",
        "finding:bare-large-gauge-quillen-norm-does-not-equal-original-winding-counting-factor",
        "finding:existing-elliptic-half-period-has-canonical-graded-gns-intertwiner",
        "finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law",
        "finding:declared-recursive-machine-baseline-controls-and-recovery-are-finitely-measured",
        "finding:declared-recursive-machine-long-run-retains-motion-at-stable-aggregate-rank",
        "finding:recursive-kohonen-source-investigation-has-source-verified-atlas-handoff",
        "finding:chat-algorithmic-comparison-native-pauli-code-and-scoped-information-loss",
        "finding:chat-20261026-results-consolidated-with-corrected-assumptions",
        "finding:source-inversion-forces-six-line-theta-completion",
        "finding:literal-geometric-quarter-is-not-central-gaussian-quarter-on-labels",
        "finding:source-cubic-and-quarter-select-even-theta-and-spin-half-turn-lift",
        "finding:source-cubic-matches-native-pauli-translations-after-context-target-correction",
        "finding:joint-source-clock-relations-have-one-native-clifford-gauge-class",
        "finding:ordinary-theta-determinant-erases-selected-spin-central-character",
        "finding:marked-negative-point-norm-restores-required-spin-central-character",
        "finding:point-normalized-theta-family-correction-fails-original-cubic-action",
        "finding:source-spin-relative-poincare-normalization-closes-point-norm-family",
        "finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package",
        "finding:tfpt-origin-investigation-full-source-coverage-and-current-frontier",
        "finding:full-clock-norm-power-class-and-canonical-eighth-period",
        "finding:original-unit-winding-selects-one-inverse-norm-in-three-cabled-hardy-pair",
        "finding:original-boundary-audit-and-h1-point-restriction-limit",
        "finding:eta-phase-conventions-do-not-identify-relative-spin-reference-pair",
        "finding:same-spin-unit-shift-gives-native-module-class-with-odd-determinant-line",
        "finding:original-even-odd-operator-split-is-compatible-with-same-spin-seam-reference",
        "finding:elliptic-projector-and-weyl-results-retain-their-source-type-at-cubic-spin-bridge",
        "finding:cubic-spin-cauchy-range-is-three-hardy-with-strong-domain-distinction",
        "finding:original-negative-sea-three-mode-ket-is-dual-to-required-hardy-line",
        "finding:auxiliary-theta-route-needs-no-physical-cubic-bulk-or-eta-selected-dual",
        "finding:primitive-gaussian-theta-frame-constructs-e8-pair-with-retained-spin-action",
        "finding:existing-c12-lift-induces-coherent-two-object-e8-vertex-groupoid",
        "finding:actual-winding-functional-calculus-preserves-ns-ramond-split",
        "finding:single-chiral-cycle-exchange-selects-e8-in-four-extension-class",
        "finding:affine-source-involution-pairs-full-d8-sector-spectra",
        "finding:marked-local-e8-with-unchanged-source-time-fails-euclidean-clustering",
        "finding:original-parity-audit-does-not-supply-local-spinor-gauging",
        "finding:hypergraph-local-update-repaired-with-full-family-clock",
        "finding:petersen-polar-step-has-exact-double-cover-family-intertwiner",
        "finding:petersen-source-current-and-hodge-candidates-fail-physical-identification",
        "finding:a7-clock-direction-identifies-neutral-e7-zero-root",
        "finding:oriented-sewing-cocycle-distinguishes-continuation-and-reversal",
        "finding:calderon-single-face-compression-is-not-perron-projector",
        "finding:hodge-born-magnitudes-and-filtered-petersen-jump-match",
        "finding:five-complement-amplitudes-form-full-petersen-quantum-channel",
        "finding:original-twenty-events-factor-through-hodge-and-conditional-phase-record",
        "finding:actual-e8-mixed-current-response-is-full-clifford-channel",
        "finding:carrier-su5-centralizer-gives-direct-e8-petersen-response",
        "finding:su5-covariance-and-petersen-support-fix-complete-quantum-response",
        "finding:neutral-pair-witness-separates-old-events-and-hodge-response",
        "finding:original-degree-clock-is-not-carrier-slot-cycle-at-fixed-source",
        "finding:full-mark-transport-and-isospectrality-do-not-select-hodge-channel",
        "finding:original-pair-source-fixes-state-but-not-selected-epsilon-process",
        "finding:single-positive-process-saturation-selects-full-hodge-channel",
        "finding:original-five-slot-wedge-is-exact-e8-hodge-coefficient",
        "finding:native-pauli-f20-metric-and-quarter-bridge",
        "finding:two-actual-coherent-events-herald-hodge-at-one-over-twenty-five",
        "finding:original-color-center-removes-only-extra-h8-ground-state",
        "finding:marked-symplectic-functor-fixes-native-hodge-kraus-space",
        "finding:f20-record-repair-removes-chart-induced-three-plus-two",
        "finding:theta-scalar-square-lift-is-distinct-from-symplectic-f20-lift",
        "finding:full-admissibility-vacuum-test-needs-source-image-and-transfer-reduction",
        "finding:canonical-native-spin5-hodge-is-already-one-source-record-subchannel",
        "finding:native-hodge-record-selector-is-image-projector-not-kraus-kernel",
        "finding:irreducible-f20-four-cannot-host-original-independent-native-family-clock",
        "finding:native-hodge-is-exact-collective-five-current-action",
        "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
        "finding:six-hodge-responses-have-exact-full-current-barycenter",
        "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts",
        "finding:spin5-hodge-five-is-plucker-kernel-not-original-quartic-hessian",
        "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
        "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
        "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
        "finding:old-ward-root-generates-exact-charged-fifty-module",
        "finding:tp-charged-bracket-support-forces-entire-carrier-marginal",
        "finding:original-ward-and-p2-grading-select-smaller-creation-thirty",
        "finding:charged-source-quarter-recovers-inverse-internal-glue",
        "finding:state-independent-creation-branch-removes-whole-process-hodge-demand",
        "finding:given-source-current-constructs-half-kink-spinor-transport",
        "finding:neutral-ward-response-needs-no-spinor-observable-membership",
        "finding:actual-source-sector-transport-distinguishes-identical-hodge-marginals",
        "finding:ordinary-weyl-type-obstruction-to-single-chiral-os-anti-anti-reflection",
        "finding:given-two-face-source-derives-opposite-neutral-weyls-and-bounded-time-reflection",
        "finding:verification-recovery-preserves-local-source-chain-and-eight-gate-completeness",
        "finding:positive-spectral-reweighting-does-not-establish-original-source-rp",
        "finding:gapped-quarter-energy-cannot-be-same-borchers-translation",
        "finding:finite-ko6-pairing-does-not-supply-standalone-pfaffian-source",
        "finding:full-free-projector-forces-joint-commuting-source-factorization",
        "finding:actual-neutral-current-source-has-constructive-moebius-standard-pair",
        "finding:continuous-local-current-weyls-cannot-live-in-finite-coordinate-fibers",
        "finding:actual-folded-current-ward-and-state-determine-all-neutral-words",
        "finding:mixed-vector-axial-current-is-existing-full-car-subalgebra",
        "finding:constant-product-time-stable-current-level-is-kernel-index",
        "finding:paired-quarter-source-candidate-needs-original-filter-and-oriented-conjugation",
        "finding:graded-boundary-clifford-typing-transports-full-scalar-and-finite-coupled-source",
        "finding:actual-charge-j-transport-retains-full-dirac-and-distinct-pairings",
        "finding:fixed-graded-chart-transports-normal-dependent-source-and-given-mixed-moments",
        "finding:neutral-many-body-source-time-is-not-finite-summable-geometric-dirac",
        "finding:actual-product-reflection-and-same-time-have-full-positive-clifford-source-intertwiner",
        "finding:actual-v252-positive-grade-has-global-p2-wedge-dictionary",
        "finding:old-quarter-full-source-embeds-locally-exactly-on-decoupled-channel",
        "finding:petersen-population-full-cptp-p5-range-zero-to-ten",
        "finding:marked-sm-phase-p5-exact-range-and-response-collision",
        "finding:shared-epsilon-tp-process-fixes-hodge-marginal-even-for-correlated-inputs",
        "finding:puncture-meridians-have-one-glue-class-and-residue-duality-does-not-select-metric",
        "finding:joint-integral-unimodular-charge-closure-uniquely-selects-complete-invariant-metric",
        "finding:meridian-spinor-joint-source-product-has-actual-family-root-simple-pole",
        "finding:r098-withheld-response-search-has-exact-conditional-affine-certificates",
        "finding:r098-whole-finite-process-segment-preserves-2245-moments"
      ],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ]
    },
    {
      "id": "topic:gravity",
      "titleEN": "Gravity",
      "summaryEN": "The corpus has finite boundary/modular results, free gravitational constructions, source responses, and conditional classical or homogeneous-time bridges. Recent seam checks separate normalization identities from physical coefficient selection and geometric local boosts; universal interacting quantum gravity remains open.",
      "orientation": {
        "role_en": "Connects boundary/entropy readouts, source responses, and candidate classical limits toward the sought gravitational theory.",
        "have_en": "Finite matrix/modular tests, free responses, and classical bridges exist under extra assumptions. The current seam audit separates the variation factor 1/2 from selecting k=c3/2.",
        "seek_en": "Open items are a local geometric horizon-boost action, local geometry, dynamical matter, and universal nonlinear quantum gravity from the same parent.",
        "connection_en": "Entropy, quantum state, spacetime dimension, and physical source rule must fit together; finite covariance alone does not select geometry.",
        "next_bridge_en": "The next decisive bridge is a parent-derived local boost/area rule selecting the area normalization and energy flow."
      },
      "problemIds": [
        "problem:gravity-flow-normalization"
      ],
      "findingIds": [
        "finding:matter-observations-do-not-fix-geometric-response"
      ],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:b8f39b8e95ee0cc35bfb08c8"
      ]
    },
    {
      "id": "topic:cosmology",
      "titleEN": "Cosmology",
      "summaryEN": "Cosmological angles, baryon budgets, inflationary and vacuum readouts connect compiler quantities to large-scale observables under stated branches and calibrations. Shared seeds and known-data freezes do not amount to blind independent predictions.",
      "orientation": {
        "role_en": "Shows how dimensionless compiler budgets and boundary quantities may enter cosmological readouts.",
        "have_en": "Concrete formula/numerical outputs and conditional interpretations exist, some using shared seeds and selected branches.",
        "seek_en": "The open work is internal scale selection, initial state, branch choice, dynamical transfer, and separately tested predictions on independent data.",
        "connection_en": "Metrology supplies unit bridges; the process branch must carry cosmological events and microphysics from one parent process.",
        "next_bridge_en": "A common state/event process must expose the selected cosmological readouts, uncertainties, and any non-blind input."
      },
      "problemIds": [],
      "findingIds": [],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ]
    },
    {
      "id": "topic:rh",
      "titleEN": "External project: Prime Front",
      "summaryEN": "RH and prime-number research moved to the independent Prime Front project on 18 October 2026. Historical mathematical connections do not independently confirm TFPT physics. RH is outside the active TFPT research scope.",
      "orientation": {
        "role_en": "A separate arithmetic research line with possible links to E8/theta/Hecke structures.",
        "have_en": "Exact lattice/theta/Hecke identities and finite tests are documented separately from the open RH target statement.",
        "seek_en": "The target is a complete valid implication to RH; analogies, finite truncations, and measurements do not suffice.",
        "connection_en": "Shared E8 numbers may motivate questions but provide no automatic proof bridge or physical confirmation.",
        "next_bridge_en": "RH work must independently justify the exact arithmetic map, positivity, and every limiting step."
      },
      "problemIds": [],
      "findingIds": [],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ]
    },
    {
      "id": "topic:validation",
      "titleEN": "Tests and predictions",
      "summaryEN": "The ledger is the authority for claim status. Graph edges and model annotations aid navigation, while algebraic identities, computations, external reports, and physical identifications carry different evidential weight; shared inputs correlate readouts.",
      "orientation": {
        "role_en": "Keeps provenance, status, verification scope, and limits traceable across topics.",
        "have_en": "The ledger distinguishes claim status; sources, contracts, and checks document results within their stated scope.",
        "seek_en": "The open work is independent testing, complete premises, holdouts, and correlated-output accounting without status inflation.",
        "connection_en": "Validation reconnects each topic edge to original sources and ledger status; check counts are not independent evidence.",
        "next_bridge_en": "Each new assertion needs an owning claim, original source, exact scope, and a test appropriate to the claim."
      },
      "problemIds": [
        "problem:carrier-pascal-glue-formal-scope"
      ],
      "findingIds": [
        "finding:pascal-carrier-rank-unique-unbounded-source-proof",
        "finding:finite-carrier-glue-elements-orbits-and-halfway"
      ],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:835640f6873d9dcc6e72ea88"
      ]
    },
    {
      "id": "topic:universalraum",
      "titleEN": "Universalraum",
      "summaryEN": "Universalraum keeps two directions separate: operationally complete TFPT as a common parent, and derive TFPT readouts from a deeper shared source. Future equivalence is defined relative to an explicit menu of interventions and records.",
      "orientation": {
        "role_en": "Frames the overall problem as a source/process question and keeps both research directions distinct.",
        "have_en": "Formal future-equivalence criteria, finite filters and parents, and counterexamples to premature correlation removal are available.",
        "seek_en": "The goal is either operational completion of TFPT or a deeper source process that generates TFPT readouts; both require states, interventions, events, and records.",
        "connection_en": "Universalraum→TFPT asks for the deeper source; TFPT→Universalraum asks for complete common implementation. Readout matches answer neither direction automatically.",
        "next_bridge_en": "First, one decisive parent must realize the existing sectors together with a local state, interventions, process law, and records."
      },
      "problemIds": [
        "problem:future-quotient-and-gns-reconstruction",
        "problem:native-charged-seam-selection",
        "problem:constructive-seam-lift-state",
        "problem:fundamental-process-classification"
      ],
      "findingIds": [
        "finding:future-equivalence-minimizes-declared-answer-process",
        "finding:positive-word-kernel-reconstructs-cyclic-gns",
        "finding:native-invariant-response-not-fixed-chiral-twist",
        "finding:native-opposite-charge-response-symmetry",
        "finding:native-chemical-mark-visible-in-charged-corners",
        "finding:fixed-hopping-quarter-phases-retain-antiunitary-discriminator",
        "finding:constructive-phase-class-and-full-winding",
        "finding:constructive-positive-state-extension",
        "finding:constructive-current-group-selects-positive-p-lift",
        "finding:constructive-state-algebra-resolution-and-source-test",
        "finding:constructive-all-phases-fail-unchanged-source",
        "finding:replicated-deterministic-consistency-iff-influence-dag",
        "finding:three-binary-processes-two-copy-reversible-classification",
        "finding:independent-poset-information-composition-consequences",
        "finding:reset-diagnosis-not-global-tfpt-underdetermination",
        "finding:three-inequivalent-repeatable-observation-countermodels",
        "finding:repeatable-reports-do-not-imply-full-state-stability",
        "finding:finite-sequential-data-admit-classical-history-realization"
      ],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ]
    },
    {
      "id": "topic:metrology",
      "titleEN": "Metrology",
      "summaryEN": "Most compiler relations are dimensionless; seconds, GeV, and other units enter through calibration and transfer choices. A dimensional match alone does not derive a physical scale.",
      "orientation": {
        "role_en": "Separates mathematical numerical relations from physically calibrated quantities and measurement units.",
        "have_en": "Dimensionless relations and named v_geo, Planck, and electroweak readout contracts exist, with some external anchors selected.",
        "seek_en": "Open work is a jointly justified internal calibration with uncertainty propagation and physical transfer.",
        "connection_en": "Metrology is the necessary bridge from dimensionless compiler outputs to cosmology, flavor, α, and observable units.",
        "next_bridge_en": "Each scale needs an explicit calibration source, intervention, and uncertainty chain not inferred circularly from the same readout."
      },
      "problemIds": [],
      "findingIds": [],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ]
    },
    {
      "id": "topic:spacetime",
      "titleEN": "Spacetime",
      "summaryEN": "Carrier rank, family indices, field components, gauge symmetries, and spacetime dimensions are different mathematical objects. Physical 3+1D behavior requires a local unitary parent, appropriate actions, and controlled continuum/IR behavior.",
      "orientation": {
        "role_en": "Connects internal discrete structure to the still-sought local spacetime realization.",
        "have_en": "Finite representations, charge/symmetry data, and models with free or classical bridges under extra assumptions exist.",
        "seek_en": "Open items are a local unitary 3+1D parent, interactions, Lorentz symmetry, controlled continuum/IR limit, and explicit action maps.",
        "connection_en": "This bridge is prerequisite to flavor, quantum matter, gravity, and cosmological dynamics; equal ranks do not identify spacetime.",
        "next_bridge_en": "The first gap to close is the local state/geometry parent with physical actions and a controlled limit."
      },
      "problemIds": [],
      "findingIds": [],
      "reviewState": "authored-navigation",
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ]
    },
    {
      "id": "topic:process",
      "titleEN": "Process and compilation",
      "summaryEN": "Single channels, repeated dynamics, measurement events, and continuous embeddings are distinct process laws. A physical parent must jointly specify state, interventions, environment, clock, and records.",
      "orientation": {
        "role_en": "Collects the missing common event and process law across the finite submodels.",
        "have_en": "Finite channels, instruments, discrete and continuous model branches, and checkable records are documented.",
        "seek_en": "The open work is TFPT-derived selection of state, clock, environment, interventions, and a repeatable event rule.",
        "connection_en": "The process parent must carry clock, quantum, spacetime, flavor, and gravity layers together; isolated channels do not close it.",
        "next_bridge_en": "Define one falsifiable parent with a common state and all allowed interventions, then test repetition and record preservation."
      },
      "problemIds": [
        "problem:automated-operator-source-synthesis",
        "problem:automatic-origin-response-decision"
      ],
      "findingIds": [
        "finding:typed-operator-search-calibrated",
        "finding:positive-kernel-construction-with-exact-discriminator",
        "finding:source-typed-kernel-search-controls",
        "finding:collar-car-projection-multifield-ray",
        "finding:known-quarter-source-full-multifield-control",
        "finding:source-reference-amplitude-retained",
        "finding:joint-fermionic-source-schur-functional",
        "finding:quarter-circle-absolute-zeta-green-eta",
        "finding:quarter-sea-absolute-thermal-central-phase",
        "finding:original-operational-seed-and-given-green-pairing",
        "finding:order-one-infinitesimal-bound-inference-fails",
        "finding:joint-ward-two-field-data-miss-fixed-four-field-response",
        "finding:complete-car-kernel-fixes-nongaussian-link-functional",
        "finding:source-covariance-jet-and-mixed-face-interface",
        "finding:e8-grade-two-explicit-spinor-current-action",
        "finding:intrinsic-source-jet-removes-pure-field-frame-motion",
        "finding:unchanged-ns-vector-generators-cannot-create-d5-spinor-fields",
        "finding:two-face-noncommuting-geometric-response-calculus",
        "finding:raw-face-mask-fails-source-kernel-null-descent",
        "finding:action-response-sewing-does-not-select-lf-intervention",
        "finding:faithful-gns-completion-closes-automated-source-query-feedback",
        "finding:whole-quarter-channels-identified-by-exact-internal-kernel",
        "finding:actual-joint-insertion-hull-resolves-eight-coefficient-directions",
        "finding:e8-bare-trilinear-and-single-anchor-weyl-class-insufficient",
        "finding:complete-family-four-cycle-class-separates-native-clock-from-sm-preservation",
        "finding:native-clock-word-transpose-has-static-rank-four-counterexample",
        "finding:whole-constant-coupled-source-is-implementable-despite-isolated-insertion-domain",
        "finding:fixed-quarter-jloc-pfaffian-closure-fails-local-skew-test",
        "finding:same-collar-has-canonical-selfdual-kinetic-pairing-and-charged-determinant",
        "finding:quarter-cover-pairing-does-not-supply-local-normal-or-select-scale-measure",
        "finding:fixed-aps-source-has-whole-inverse-and-finite-boundary-correction",
        "finding:mass-only-deck-relative-heat-action-fails-free-infinite-trace",
        "finding:finite-antiperiodic-scalar-wall-has-no-exact-massless-normal-mode",
        "finding:spectral-heat-covariance-positivity-does-not-imply-time-rp",
        "finding:quaternionic-sm-mass-winding-is-not-normal-determinant-clutch",
        "finding:bounded-relative-trace-obstruction-and-whole-genuine-pair-heat-reader",
        "finding:normal-clutch-orbit-index-equivariantly-recovers-given-weak-module",
        "finding:normal-orbit-spin-family-index-and-signed-charge-balance",
        "finding:fixed-flavor-cartan-sign-cover-and-root-lift-parity",
        "finding:original-family-vector-action-is-not-cartan-rotation-or-spinlift-selection",
        "finding:actual-genus-two-sign-family-closes-common-parallel-k-connection",
        "finding:actual-q-quarter-extends-common-k-connection-and-real-coefficient-lifts",
        "finding:real-source-reflection-is-not-linear-duality-or-compact-clock-inversion",
        "finding:source-selected-spin-and-q-signs-have-three-explicit-global-kernels",
        "finding:source-s0-szego-point-legs-generate-q-kernels-with-typed-products",
        "finding:actual-spin-kernel-determinant-has-inverse-q-norm-character",
        "finding:closed-source-flavor-spin-has-functorial-pfaffline-with-charged-type-limit",
        "finding:original-relative-seam-has-explicit-whole-graph-fredholm-mismatch",
        "finding:whole-constant-coupled-clutch-defects-are-exact-internal-kernels",
        "finding:old-complex-scalar-clutch-separates-c0-and-product-reflection",
        "finding:scalar-defect-circle-character-does-not-select-projector-holonomy",
        "finding:source-spin-is-canonical-ramified-base-spin-pullback",
        "finding:original-v117-has-explicit-algebraic-q-cover-fundamental-frame",
        "finding:double-circle-reflection-does-not-fix-entire-cubic-cable-seam",
        "finding:actual-fuchs-real-map-transports-whole-given-finite-source-state-and-time",
        "finding:actual-e0-compensator-extends-whole-k-e8-with-transported-quarter",
        "finding:actual-v252-entire-real-basis-has-signed-p2-dual-dictionary",
        "finding:chiral-fuchs-source-transport-has-distinct-majorana-phase-and-torus-absorption",
        "finding:native-theta-composition-retains-conjugate-source-and-parity-square",
        "finding:single-graph-range-isometry-does-not-give-local-whole-seed-map",
        "finding:hard-holonomy-selfduality-leg-and-finite-character-phase-separation",
        "finding:original-z6-positive-structural-kernel-does-not-supply-oriented-phase-observable",
        "finding:original-genus-two-hexagonal-rotation-has-concrete-rho-hodge-line",
        "finding:original-mixed-spin-products-realize-positive-u6-cycle",
        "finding:actual-spin-quadratics-reach-original-hexagonal-hodge-line",
        "finding:spin-pair-car-transport-retains-parity-and-whole-source-types",
        "finding:real-total-trace-does-not-exclude-coherent-phase-reader",
        "finding:geometric-six-spin-clock-differs-from-marked-native-clock",
        "finding:whole-q-to-p-pullback-transports-given-source-state-and-time",
        "finding:actual-fixpoint-evaluation-keeps-coefficient-signs-and-source-type",
        "finding:original-source-naturality-needs-no-second-p-image-background",
        "finding:canonical-spin2-lift-carries-whole-annulus-source-with-reversed-time",
        "finding:geometric-spin-collar-map-closes-weighted-image-domain-with-total-deck-action",
        "finding:claude33-annulus-map-is-valid-distinct-type-not-unique-geometric-spin-selection",
        "finding:original-mixed-spin-products-already-have-complete-dual-hom-coefficients",
        "finding:whole-f5-graph-supplies-canonical-reverse-qp-hom-kernel",
        "finding:actual-spin-product-weight-has-canonical-trace-class-form-pairing",
        "finding:fully-descended-covariant-reverse-kernel-removes-rho-form-channel",
        "finding:original-a4-linear-quarter-does-not-supply-proposed-scalar-mu3-repair",
        "finding:offdiagonal-hom-matches-a4-family-six-but-not-two-triplet-e8-product",
        "finding:compact-e8-adjoint-completes-family-six-with-carrier-rank-retained",
        "finding:three-family-cx-recursion-closes-exact-d8-with-minimal-original-escape",
        "finding:original-weak-current-coefficient-has-explicit-finite-oneform-consumer",
        "finding:original-d5-zero-mode-closes-triplet-carrier-and-fixed-glue-is-minimal-escape",
        "finding:mixed-spin-full-deck-has-no-rank-three-projector",
        "finding:actual-reverse-hom-diagonal-supplies-global-q-hodge-response",
        "finding:bare-c3-kernel-diagonal-yukawas-have-common-real-frame",
        "finding:original-primitive-action-is-present-highpass-is-not-finite-selector",
        "finding:atlas-detail-retrieval-recovers-existing-d4-solution",
        "finding:original-poisson-normal-trace-fixes-whole-calderon-graph",
        "finding:induced-original-hardy-defect-gives-finite-whole-source-reader",
        "finding:original-weak-quartic-action-has-nonzero-nonlinear-response",
        "finding:all-common-leading-distance-clutches-fail-original-flavor-lengths",
        "finding:actual-hardy-response-has-weak-clifford-odd-and-ko-real-completion",
        "finding:two-entry-hardy-adjoint-hierarchy-fails-full-ko-and-su2",
        "finding:actual-fuchs-halfpath-has-canonical-g-metric-c6-kernel-map",
        "finding:original-real-delta-jet-reads-same-marked-hardy-open-word",
        "finding:four-actual-fuchs-spine-edges-recover-marked-meridians-and-nonzero-open-word",
        "finding:native-adjoint-quarter-clock-cannot-compensate-hardypair-odd-character",
        "finding:whole-cubic-gram-differential-retains-hardy-phase-and-cross-resonance",
        "finding:complete-original-mu01-hardy-reader-has-two-calibrated-entries",
        "finding:whole-six-original-hardy-inputs-generate-full-family-coefficient-algebra",
        "finding:actual-whole-hardy-alphabet-has-finite-particle-hole-wick-block",
        "finding:bare-unsmeared-mu-crossface-quadratic-fails-vacuum-domain",
        "finding:linear-spectral-centralization-does-not-replace-full-marked-hardy-source",
        "finding:original-admissibility-projector-is-explicit-penalties-do-not-read-retained-amplitudes",
        "finding:actual-original-inner-fluctuation-has-whole-noncommuting-two-face-response",
        "finding:fiber-only-primitive-split-and-frozen-gap-miss-original-action",
        "finding:oriented-resolvent-weights-do-not-identify-original-reflection-producer",
        "finding:current-odd-carrier-reader-is-lossless-on-whole-coupled-source",
        "finding:ap-spectral-formulas-do-not-force-normal-domain-or-complete-source",
        "finding:actual-weak-connection-transmits-family-orientation-to-both-faces",
        "finding:original-higgs-variation-is-not-independent-yukawa-stationarity",
        "finding:actual-weak-cap-converges-on-whole-quarter-circle",
        "finding:canonical-clifford-double-derives-normal-ap-and-typed-deck",
        "finding:universal-graded-source-reducing-images-do-not-fix-carrier-frame",
        "finding:whole-two-face-compression-projector-defect-detects-hidden-source-loss",
        "finding:actual-v252-quark-lepton-split-prevents-weak-grading-uniqueness-inference",
        "finding:actual-graded-hypercharge-trace-rejects-quark-lepton-sign-intertwiner",
        "finding:separable-normal-real-maps-compose-to-given-deck-and-quarter-image",
        "finding:actual-gauge-real-frames-leave-carrier-phase-as-coordinate-freedom",
        "finding:original-higgs-family-has-one-complex-kk-class-but-different-whole-sources",
        "finding:signed-one-particle-modular-weight-is-not-the-positive-even-heat-operator",
        "finding:three-moments-select-one-exponential-exactly-in-positive-laplace-class",
        "finding:existing-ap-positive-source-factor-has-oriented-poisson-heat-bridge",
        "finding:actual-v252-entire-compatibility-family-has-generic31-dimensional-quotient",
        "finding:full-memory-schur-reconstruction-preserves-every-ordered-word-under-nesting",
        "finding:original-return-and-native-j-have-minimal68-dimensional-all-word-memory",
        "finding:original-full-source-regulator-flow-retains-normalized-kernel-and-vacuum-factor",
        "finding:full-reflected-quadratic-regulator-cone-preserves-every-rp-source",
        "finding:original-shared-higgs-source-induces-fixed-yukawa-mixed-matter-words",
        "finding:local-even-yukawa-sewing-preserves-given-joint-graded-rp",
        "finding:whole-original-constant-higgs-orbit-has-reduced-majorana-spectral-response",
        "finding:archived-geometric-higgs-residue-bulk-needs-coefficient-identification-repair",
        "finding:original-local-higgs-residue-linear-coefficients-fail-same-trace-heat-ratio",
        "finding:whole-original-higgs-moments-fix-conditional-local-kinetic-mass-quartic",
        "finding:whole-variable-original-higgs-bound-reference-response-and-forced-clifford-factor",
        "finding:original-symmetric-scale-map-fails-simultaneous-higgs-einstein-repair",
        "finding:whole-original-higgs-inner-scale-and-affine-full-source-transport",
        "finding:normal-higgs-mode-type-and-exact-kernel-metric-require-actual-relative-operator-map",
        "finding:original-superconnection-grades-and-weighted-heat-retain-higgs-kinetic-excursions",
        "finding:whole-normal-reduction-preserves-relative-spectral-reader-and-higgs-jets",
        "finding:original-admissibility-own-spectral-reader-has-no-free-low-mode-residue-repair",
        "finding:whole-total-chiral-positive-spectrum-retains-higgs-kinetics-and-common-half-trace",
        "finding:whole-scale-energy-response-uniquely-reconstructs-normal-profile",
        "finding:original-relative-scale-flow-separates-residue-finite-part-and-local-anomaly",
        "finding:original-whole-green-produces-energy-response-with-correct-orthogonal-trace",
        "finding:whole-mixed-scale-source-reads-bosonic-insertion-before-higgs-average",
        "finding:current-original-spectral-action-triplet-fails-positive-laplace-class-unless-leading-relative-term-cancels",
        "finding:correct-current-argument-weights-link-whole-higgs-threshold-and-same-einstein-response",
        "finding:whole-original-spinor-curvature-a4-has-no-independent-scalaron-r-squared",
        "finding:whole-original-entropic-curvature-corrects-max-symmetric-scalar-scale",
        "finding:given-whole-higgs-source-fixes-radial-curvature-susceptibility-without-extra-scalar",
        "finding:actual-original-four-ghost-complex-preserves-base-selector-with-full-cohomology-and-distinct-traces",
        "finding:whole-original-admissibility-energy-source-recovers-constraints-but-cannot-replace-geometric-operator",
        "finding:original-moving-normal-kernel-fixes-induced-connection-and-full-scale-covariance",
        "finding:fixed-original-o1-source-rejects-nonconstant-normal-multiplier-and-fixes-placement-test",
        "finding:original-master-variation-keeps-spin-weight-and-active-source-route-typed",
        "finding:shared-original-higgs-mixture-has-invariant-color-fourpoint-wick-defect",
        "finding:bounded-fixed-rank-spectral-action-does-not-normalize-noncompact-higgs-volume",
        "finding:whole-original-quarter-source-bounds-higgs-weight-uniformly-through-joint-mode-ir-limits",
        "finding:original-o1-covariance-leaves-full-radial-higgs-law-and-exact-fourier-source-readout",
        "finding:whole-process-reconstruction-priority-and-original-locality-geometry-input-audit",
        "finding:actual-disjoint-local-weyls-acquire-spurious-commutator-under-bare-native-compression",
        "finding:actual-quarter-current-state-excludes-nontrivial-geometric-local-point-time",
        "finding:actual-elliptic-interval-car-source-produces-local-modular-generator",
        "finding:actual-proper-two-face-regions-do-not-contain-pure-local-source-double",
        "finding:actual-elliptic-whole-environment-fixes-regional-car-partner",
        "finding:actual-original-color-triplet-has-spectator-dependent-modular-field-law",
        "finding:actual-color-marginal-has-complete-finite-source-reader-and-mixture-criterion",
        "finding:two-and-four-field-words-do-not-complete-original-color-triplet-source",
        "finding:whole-original-quarter-occupation-tower-uniquely-reconstructs-common-radial-higgs-law",
        "finding:finite-original-tower-reader-and-existing-weak-symmetry-fix-shared-matter-responses",
        "finding:unchanged-free-quarter-source-cannot-be-nontrivial-integrated-higgs-mixture",
        "finding:actual-e8-record-doily-action-is-signed-p-plus-compatible-point-with-typed-sym2-lift",
        "finding:actual-e8-record-words-distinguish-order-and-retain-phase-beyond-fifteen-labels",
        "finding:literal-doily-incidence-output-and-strict-causal-order-on-fifteen-source-labels-excluded",
        "finding:actual-doily-context-record-characters-have-ranks-four-two-two-two",
        "finding:canonical-standard-split-localizes-original-source-record-words-with-full-descendant-companion",
        "finding:unchanged-global-sixty-event-source-fails-local-exterior-current-test",
        "finding:canonical-source-localization-changes-exterior-state-and-does-not-select-event-origin",
        "finding:original-elliptic-fixed-holonomy-insertion-gives-local-operation-on-unchanged-source",
        "finding:original-quarter-pair-fixes-square-charge-law-half-response-and-real-quillen-norm",
        "finding:actual-elliptic-source-determines-all-path-normalized-causal-current-response",
        "finding:original-higgs-quark-source-has-exact-whole-su3-counting-response",
        "finding:single-original-color-parity-separates-free-quillen-from-positive-higgs-integrated-source",
        "finding:whole-original-quarter-graph-color-response-is-relative-and-diagonal-singlet",
        "finding:original-center-selector-requires-typed-state-field-and-face-transport",
        "finding:original-color-center-fixes-whole-e6-a2-source-and-charged-ward-word-action",
        "finding:original-color-neutral-lattice-class-cannot-supply-odd-fields-by-inherited-superlattice-extension",
        "finding:original-color-center-extends-to-folded-ns-but-full-current-action-needs-spin-sector-transport",
        "finding:actual-color-spin-car-mixed-word-has-complete-thermal-source-and-cyclic-sewing",
        "finding:exact-original-ns-ramond-heat-equality-does-not-identify-fixed-color-restricted-source",
        "finding:original-scalar-cover-profile-cannot-implement-fixed-spin-cartan-loop",
        "finding:actual-spin-cartan-composite-source-retains-multi-arc-support-and-fails-additive-even-locality",
        "finding:actual-color-selector-admits-exactly-eighth-periodic-original-density-variations",
        "finding:actual-color-is-internal-exactly-on-eightfold-coordinate-source-regions",
        "finding:original-whole-two-face-multiplier-reduction-is-only-constant-residue-diagonal",
        "finding:original-two-face-local-fock-implementation-and-exact-source-variation-differ-from-reduction",
        "finding:whole-undecorated-transfer-does-not-determine-original-marked-field-source",
        "finding:volume-wise-injective-positive-transfer-does-not-prove-uniform-parent-gap",
        "finding:original-c6-half-power-has-exact-entire-positive-ordered-word-expansion",
        "finding:original-c6-whole-word-sewing-retains-source-amplitude-and-controlled-infinite-tail",
        "finding:historical-parent-and-actual-field-time-bridges-must-be-reused-before-new-source-models",
        "finding:actual-native-v990-full-timed-words-recover-kubo-response-distinct-from-instantaneous-variance",
        "finding:actual-original-higgs-force-has-complete-ordered-fermionic-determinant-source",
        "finding:finite-covariant-higgs-composites-have-no-nontrivial-positive-instantaneous-classical-law",
        "finding:actual-original-collective-mean-has-exact-ball-domain-and-relative-entropy-action",
        "finding:original-uniform-allmode-force-clt-is-nonzero-only-before-fixed-time-smearing",
        "finding:original-unscaled-time-smeared-force-has-selfadjoint-whole-ordered-source",
        "finding:original-local-higgs-force-has-whole-centered-hilbert-schmidt-determinant-source",
        "finding:given-original-circle-force-source-generates-an-exact-causal-local-net",
        "finding:literal-archived-global-rg-kernel-does-not-preserve-finite-measures",
        "finding:native-higgs-marginal-retains-induced-vertex-and-noether-response",
        "finding:isospectral-noether-orbit-does-not-supply-original-metric-higgs-variation",
        "finding:metric-dtn-form-bound-needs-transfer-comparison-for-gap",
        "finding:conditional-higgs-pair-winding-protection-in-common-circle-carrier",
        "finding:natural-five-clock-carrier-excludes-invariant-three-transfer-compression",
        "finding:shared-scalar-shift-whole-retained-higgs-sector-has-index-minus-eighteen",
        "finding:whole-coupled-quark-circle-common-shift-cancels-relative-winding",
        "finding:one-sided-shift-full-higgs-pair-is-hilbert-schmidt-not-trace-class",
        "finding:selective-coupled-higgs-reader-has-well-defined-det2",
        "finding:v311-population-reader-does-not-identify-quantum-channel",
        "finding:declared-charged-pair-relation-leaves-five-word-ambiguity",
        "finding:full-creator-relations-close-fixed-free-two-mode-ambiguity",
        "finding:comoving-diagnostic-clock-exact-response-but-nonlocal-mode-transport",
        "finding:free-quarter-two-face-response-strip-with-relative-zero-mode-defect",
        "finding:e8-hodge-event-perfectly-distinguishable-from-every-unitary",
        "finding:common-five-slot-transfer-preserves-e8-bracket-not-automatic-tp",
        "finding:comoving-clock-dynamic-higgs-connection-and-charged-flow",
        "finding:r064-sixty-record-channel-exact-distance-and-continuous-record-parent",
        "finding:two-syntheses-shared-source-priorities-and-typed-limits",
        "finding:weighted-index-trace-and-selfdual-theta-require-original-selection",
        "finding:ordered-quarter-fourfield-e8-record-and-charge-filters",
        "finding:r091-recovered-native-hodge-sewing-and-full96-quarter-complement",
        "finding:r092-fold-ward-target-neutral-source-and-smaller-creation-branch",
        "finding:r093-original-kink-time-response-distinguishes-quarter-states",
        "finding:r093-ordered-current-kink-and-eight-arc-locality",
        "finding:r094-original-five-excitations-distinct-from-clustering-vacuum",
        "finding:r096-joint-higgs-twoface-source-constraint",
        "finding:r096-positive-twoface-fourword-defect-bound",
        "finding:r096-unnormalized-mixed-source-linear-identity",
        "finding:r096-original-quark-crossing-negative-covariance",
        "finding:r098-withheld-response-search-has-exact-conditional-affine-certificates",
        "finding:r098-whole-finite-process-segment-preserves-2245-moments"
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      "id": "goal:T1",
      "titleEN": "T1 — Origin, markings, and dimension",
      "summaryEN": "Derive why the structural premises, seam/carrier markings, and physical dimension assumptions hold.",
      "status": "open",
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        "topic:spacetime"
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    {
      "id": "goal:T2",
      "titleEN": "T2 — Charged E8 seam and boundary net",
      "summaryEN": "Show the actual microscopic generation of the charged seam, its E8 boundary-net identification, and the scaling limit.",
      "status": "open",
      "topicIds": [
        "topic:e8",
        "topic:quantum",
        "topic:origin"
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      "claimIds": [
        "TFPT.TOE.COMPLETE.01",
        "SEAM.EQUIV.01",
        "SEAM.EQUIV.MMST.01",
        "SEAM.SIMPLECURRENT.GENERATOR.01",
        "SEAM.MMST.TYPEIII.CHARGED.01"
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        "semantic-source:4f98197613fed96709f08c93"
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      "reviewState": "authored-navigation"
    },
    {
      "id": "goal:T3",
      "titleEN": "T3 — Shared local unitary parent",
      "summaryEN": "Construct a concrete local unitary parent process with dynamical gauge fields.",
      "status": "open",
      "topicIds": [
        "topic:process",
        "topic:spacetime",
        "topic:quantum"
      ],
      "claimIds": [
        "TFPT.TOE.COMPLETE.01",
        "QFT4D.LATTICE.FUNDAMENTAL.01",
        "TFPT4D.LATTICE.ACTION.01",
        "DYN.UNITARY.DILATION.01",
        "DYN.MARKOV.EMBED.01"
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      "reviewState": "authored-navigation"
    },
    {
      "id": "goal:T4",
      "titleEN": "T4 — Chiral Standard Model and mirror decoupling",
      "summaryEN": "Derive the chiral Standard Model, controlled measure, and interacting mirror decoupling from the shared parent.",
      "status": "open",
      "topicIds": [
        "topic:e8",
        "topic:spacetime",
        "topic:process"
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      "claimIds": [
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        "CHIRAL4D.NOMIRROR.01"
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      "reviewState": "authored-navigation"
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      "id": "goal:T5",
      "titleEN": "T5 — Correct infrared physics",
      "summaryEN": "Obtain Lorentz symmetry, confinement, clustering, and nontrivial scattering in a controlled infrared/continuum regime.",
      "status": "open",
      "topicIds": [
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        "topic:gravity"
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      "claimIds": [
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        "semantic-source:835640f6873d9dcc6e72ea88"
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      "reviewState": "authored-navigation"
    },
    {
      "id": "goal:T6",
      "titleEN": "T6 — Internal couplings and neutrino texture",
      "summaryEN": "Determine all gauge couplings and the neutrino texture jointly and internally.",
      "status": "open",
      "topicIds": [
        "topic:flavor",
        "topic:alpha",
        "topic:metrology"
      ],
      "claimIds": [
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        "ALPHA.QUILLEN.EXACT.01",
        "GAUGE.DETLINE.FIXPOINT.01",
        "FLAV.NU.TEXTURE.MECHANISM.01",
        "FLAV.NUSCALE.06"
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        "semantic-source:b39e451a05162da745b19d27"
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      "reviewState": "authored-navigation"
    },
    {
      "id": "goal:T7",
      "titleEN": "T7 — Quantum gravity and universal coupling",
      "summaryEN": "Derive a massless quantum spin-2 field, dynamical matter, and universal nonlinear coupling together.",
      "status": "open",
      "topicIds": [
        "topic:gravity",
        "topic:spacetime",
        "topic:process"
      ],
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        "TFPT.TOE.COMPLETE.01",
        "GRAV.SPIN2.EMERGENCE.01",
        "GRAV.NONCIRCULAR.01",
        "GRAV.WEINBERG.WITTEN.01",
        "GRAV.ENTROPY.EQUILIBRIUM.01"
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        "semantic-source:b8f39b8e95ee0cc35bfb08c8"
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      "reviewState": "authored-navigation"
    },
    {
      "id": "goal:T8",
      "titleEN": "T8 — Canonical initial state and event functional",
      "summaryEN": "Justify a unique global state and a shared Schwinger–Keldysh/event functional for all claimed readouts.",
      "status": "open",
      "topicIds": [
        "topic:process",
        "topic:universalraum",
        "topic:cosmology"
      ],
      "claimIds": [
        "TFPT.TOE.COMPLETE.01",
        "FTRANSFER.SK.RHO0.01",
        "FTRANSFER.GENERATING.01",
        "OBS.TRANSDUCTION.01",
        "PRED.JOINTLIKELIHOOD.01"
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      "reviewState": "authored-navigation"
    },
    {
      "id": "goal:universalraum",
      "titleEN": "Universal space — shared operational and physical origin",
      "summaryEN": "Obtain the TFPT readouts from a simple shared information-bearing source that also preserves all allowed future responses. The direction from a deeper origin to TFPT remains distinct from operationally completing TFPT into a predictor.",
      "status": "open",
      "topicIds": [
        "topic:universalraum",
        "topic:origin",
        "topic:process",
        "topic:quantum",
        "topic:clocks"
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      "reviewState": "authored-navigation"
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  ],
  "structures": [
    {
      "id": "structure:p1-p2",
      "titleEN": "P1/P2 origin interface",
      "summaryEN": "Oriented seam/boundary-kernel normalization c3=1/(8π) and five marked carrier slots with a 3+2 split.",
      "epistemic": "declared_inputs; provenance_open",
      "topicIds": [
        "topic:origin",
        "topic:spacetime"
      ],
      "claimIds": [
        "AX.P1.01",
        "AX.P2.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:528b3002ad6d3e8565e949a6"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:anchor",
      "titleEN": "Parabolic anchor and internal number ladder",
      "summaryEN": "a=(1,1,2), (e1,e2,e3)=(4,5,2), and pn=2+2^n connect seam normalization, carrier count, and E8 numbers.",
      "epistemic": "exact_relations_under_named_structure; physical_selection_open",
      "topicIds": [
        "topic:origin",
        "topic:e8",
        "topic:clocks"
      ],
      "claimIds": [
        "ANCHOR.GEN.01",
        "AX.P1.01",
        "AX.P2.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:carrier-family",
      "titleEN": "Carrier modes and family rank",
      "summaryEN": "Five modes and three independent cycles/family rank are connected under the selected Riemann–Roch and marking interpretation.",
      "epistemic": "mathematical_structure_under_mapping; physical_identification_open",
      "topicIds": [
        "topic:e8",
        "topic:flavor",
        "topic:origin"
      ],
      "claimIds": [
        "ANCHOR.GEN.01",
        "E8.GLU.01",
        "E8.DEGREE.JOINT.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:e8-glue",
      "titleEN": "D5+A3 to E8 via Z4 glue",
      "summaryEN": "The discriminant groups Z4 and matching norms permit an index-4 glue into the even unimodular rank-8 E8 lattice.",
      "epistemic": "lattice_certificate; physical_seam_identification_open",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:rh"
      ],
      "claimIds": [
        "E8.GLU.01",
        "TOPO.E8.01",
        "SEAM.EQUIV.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:846edbe1e4e0a19bbe25c851"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:sm-readout",
      "titleEN": "Standard Model representation reading",
      "summaryEN": "Under the chosen group action, the 3+2 marking induces hypercharges and a family representation. This is an algebraic scaffold, not a complete local chiral quantum field theory.",
      "epistemic": "algebraic_readout_under_inputs; physical_dynamics_open",
      "topicIds": [
        "topic:e8",
        "topic:flavor",
        "topic:spacetime"
      ],
      "claimIds": [
        "CAR.SM.ANOM.01",
        "E8.GLU.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:shared-seed",
      "titleEN": "Shared seed φ0/λ",
      "summaryEN": "φ0 and the λ parameters defined from it drive several flavor- and alpha-related outputs; these relations share inputs and are therefore correlated.",
      "epistemic": "formula_relation; physical_origin_and_transfer_open",
      "topicIds": [
        "topic:flavor",
        "topic:alpha",
        "topic:cosmology"
      ],
      "claimIds": [
        "FLAV.SOLAR.01",
        "FLAV.SOLAR.02",
        "EM.FP.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:alpha-root",
      "titleEN": "Alpha equation and positive target root",
      "summaryEN": "The specified function has a unique positive root; the current ledger status of EM.FP.01 is Numerical.",
      "epistemic": "numerical_root_for_fixed_equation; physical_function_selection_open",
      "topicIds": [
        "topic:alpha",
        "topic:origin",
        "topic:flavor"
      ],
      "claimIds": [
        "EM.FP.01",
        "ALPHA.QUILLEN.EXACT.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:55e544ffff08c43dfd9f418e"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:clock-network",
      "titleEN": "Clock network C5/C6/C30/μ4/G31",
      "summaryEN": "Coxeter, Galois, compiler, and family actions form several concrete, related periods and automorphisms.",
      "epistemic": "exact_algebraic_actions_under_representations; physical_clock_open",
      "topicIds": [
        "topic:clocks",
        "topic:e8",
        "topic:origin"
      ],
      "claimIds": [
        "COX.CLOCK.01",
        "E8.G31.CLOCK_ALPHABET.01",
        "COX.COUPLE.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:transfer-attractor",
      "titleEN": "Transfer attractor and relaxation rates",
      "summaryEN": "A selected transfer has a stationary direction and specified damping rates; this characterizes the chosen operator but does not select it from the initial principles.",
      "epistemic": "conditional_on_selected_transfer; physical_selection_open",
      "topicIds": [
        "topic:clocks",
        "topic:process"
      ],
      "claimIds": [
        "DYN.MARKOV.EMBED.01",
        "QFT.MSC.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:msc",
      "titleEN": "Modular Spectral Closure (MSC)",
      "summaryEN": "The assembly certificate combines boundary algebra/state/modular evolution, finite carrier/Dirac data, and relative action into one shared relative object. It remains conditional on explicitly open identification and limit assumptions.",
      "epistemic": "assembly_certificate_with_open_physical_identification",
      "topicIds": [
        "topic:quantum",
        "topic:origin",
        "topic:spacetime",
        "topic:universalraum"
      ],
      "claimIds": [
        "QFT.MSC.01",
        "SEAM.EQUIV.01",
        "SEAM.MMST.TYPEIII.CHARGED.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:2e9aa64c6277b0882b80cac8"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:future-equivalence",
      "titleEN": "Operational future equivalence",
      "summaryEN": "Two histories may coincide in a finite model when all allowed continuations and terminal answers agree. The intervention menu is part of the contract.",
      "epistemic": "exact_criterion_within_declared_operations",
      "topicIds": [
        "topic:universalraum",
        "topic:quantum",
        "topic:process"
      ],
      "claimIds": [
        "OBS.TRANSDUCTION.01",
        "TFPT.TOE.COMPLETE.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:record-closure",
      "titleEN": "Instrument and record closure",
      "summaryEN": "A complete future description must include individual instrument branches, outcome probabilities, and existing memory records—not only the averaged channel.",
      "epistemic": "exact_model_requirement; source_operations_open",
      "topicIds": [
        "topic:universalraum",
        "topic:process",
        "topic:quantum"
      ],
      "claimIds": [
        "OBS.TRANSDUCTION.01",
        "FTRANSFER.GENERATING.01",
        "FTRANSFER.SK.RHO0.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:modular-state",
      "titleEN": "Modular state and admissible compression",
      "summaryEN": "State-preserving conditional expectations and relative entropy constrain physically admissible reductions under named assumptions; they do not select the reference state.",
      "epistemic": "theorem_under_state_and_algebra_conditions; physical_state_open",
      "topicIds": [
        "topic:quantum",
        "topic:universalraum"
      ],
      "claimIds": [
        "QFT.MSC.01",
        "FTRANSFER.SK.RHO0.01",
        "P1.INDEX.KMS.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:finite-parents",
      "titleEN": "Finite parent and source families",
      "summaryEN": "Finite parent, exchange, and encoded-source models instantiate spectra, states, relaxation, records, or repeated single-channel behavior under different contracts. Some couplings, pulse times, preparations, and steps remain inputs.",
      "epistemic": "reported_or_exact_finite_results_in_separate_contracts; not_common_source",
      "topicIds": [
        "topic:process",
        "topic:quantum",
        "topic:clocks",
        "topic:universalraum"
      ],
      "claimIds": [
        "DYN.UNITARY.DILATION.01",
        "DYN.MARKOV.EMBED.01",
        "FTRANSFER.SK.RHO0.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:coupled-sufficiency",
      "titleEN": "Coupling-dependent sufficiency",
      "summaryEN": "A locally sufficient representation can become insufficient after a joint intervention if discarded correlations become observable. The complete contract must carry couplings and records.",
      "epistemic": "exact_counterexamples_in_named_models; full_physical_menu_open",
      "topicIds": [
        "topic:universalraum",
        "topic:quantum",
        "topic:process"
      ],
      "claimIds": [
        "OBS.TRANSDUCTION.01",
        "FTRANSFER.GENERATING.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:gravity-outputs",
      "titleEN": "Gravitational and time readouts",
      "summaryEN": "Free fields, source responses, one specific homogeneous-time contract, and a classical ADM connection are distinct partial results under different premises.",
      "epistemic": "multiple_conditional_results; common_quantum_parent_open",
      "topicIds": [
        "topic:gravity",
        "topic:spacetime",
        "topic:metrology"
      ],
      "claimIds": [
        "GRAV.FREE.CURVATURE.FOCK.01",
        "GRAV.FREE.CURVATURE.COVARIANT.01",
        "GRAV.LINEAR.SOURCE.WARD.01",
        "GRAV.SPIN2.EMERGENCE.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:arithmetic-e8",
      "titleEN": "E8 theta/Hecke arithmetic",
      "summaryEN": "E8 lattice counts have theta-, Hecke-, and Euler-product views and arithmetic addressing; this implies neither RH nor a physical event process.",
      "epistemic": "exact_arithmetic_identities_in_scope; RH_and_physical_bridges_open",
      "topicIds": [
        "topic:rh",
        "topic:e8"
      ],
      "claimIds": [
        "E8.COXETER.EULER.COMPLETION.01",
        "RH.SPLIT.01",
        "RH.BUNDLE.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:T1-T8",
      "titleEN": "Overall closure contracts T1–T8",
      "summaryEN": "T1–T8 name the shared required origin, boundary, parent, chirality, infrared, coupling, gravity, and initial-state results; the ledger keeps the overall contract open.",
      "epistemic": "open_per_current_ledger",
      "topicIds": [
        "topic:origin",
        "topic:e8",
        "topic:spacetime",
        "topic:gravity",
        "topic:flavor",
        "topic:process",
        "topic:universalraum",
        "topic:validation"
      ],
      "claimIds": [
        "TFPT.TOE.COMPLETE.01"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:835640f6873d9dcc6e72ea88"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:gravity-normalization",
      "titleEN": "Gravity normalization: coefficient versus selection",
      "summaryEN": "The v73 calculation inserts c3=1/(8π) and k=c3/2, then checks the variation factor and Gauss–Bonnet normalization for the declared compactified S² seam. v358 inserts η=1/|μ4| and assembles the linearized Einstein equation and thermogeometric coefficients under area/entropy premises. Fixing factors within these contracts is distinct from independently selecting the normalization, microscopic entropy rule, and absolute scale v_geo. The Oct. 13 contract remains PARTIAL; no gate closure or claim promotion.",
      "epistemic": "exact_variation_and_coefficient_identities_given_inputs; physical_origin_of_normalization_and_replica_selection_open",
      "topicIds": [
        "topic:gravity",
        "topic:origin",
        "topic:metrology"
      ],
      "claimIds": [
        "AX.P1.01",
        "GRAV.ENTROPY.EQUILIBRIUM.01",
        "GRAV.NONCIRCULAR.01",
        "GRAV.SPIN2.EMERGENCE.01"
      ],
      "sourceRefIds": [
        "semantic-source:af005b105dde19d95cdea122",
        "semantic-source:ef8c667b2a90db943adda6c7",
        "semantic-source:151d9d719d8ba3f0de9343dd",
        "semantic-source:c6aff0505cc5d4f8c8913119",
        "semantic-source:b8f39b8e95ee0cc35bfb08c8"
      ],
      "reviewState": "authored-navigation"
    },
    {
      "id": "structure:gravity-energy-flow",
      "titleEN": "Gravity flux: local boost versus finite rotation symmetry",
      "summaryEN": "v358 assembles a 3-ball matter boost-flux term using the CHM modular Hamiltonian, conditional on geometric modular flow/Bisognano–Wichmann in an already local 4D QFT. v323 proves finite covariance/commutator facts for its selected covariance, not a local horizon boost: adjacent bilinear phases do not fit one rigid quarter-turn, and the finite helper has no local net or interval inclusion. A conditional Cartan-current result in PROOF.txt gives a relative-entropy/flux identity only on a named localized orbit after assuming the actual (E8)₁ vacuum net and a suitable expectation; it supplies no transverse horizon-area response. The remaining bridge is to construct the actual metric-dependent raw functional, match its conical derivative to microscopic horizon relative entropy with the same state/algebra/normalization/regulator, derive the local geometric modular action, and fix the metric-response/area coefficient. This remains diagnostic/conditional evidence, not promotion or T7 closure.",
      "epistemic": "conditional_local_qft_and_current_subnet_bridge; finite_helper_does_not_establish_geometric_horizon_flow; source_to_area_bridge_open",
      "topicIds": [
        "topic:gravity",
        "topic:quantum",
        "topic:spacetime",
        "topic:process"
      ],
      "claimIds": [
        "GRAV.ENTROPY.EQUILIBRIUM.01",
        "GRAV.NONCIRCULAR.01",
        "QGEO.BW.01",
        "SEAM.KHALF.01",
        "SEAM.THEOREM.01",
        "P1.INDEX.KMS.01",
        "TFPT.TOE.COMPLETE.01"
      ],
      "sourceRefIds": [
        "semantic-source:c942537f41b460fbcfc64a0d",
        "semantic-source:cfa88a2ddace187ef0771fef",
        "semantic-source:656478b60188f0ad22e44e57",
        "semantic-source:360b7d703a948deac6be313a",
        "semantic-source:c6aff0505cc5d4f8c8913119",
        "semantic-source:facd2950a7db5a19f8dea646",
        "semantic-source:b8f39b8e95ee0cc35bfb08c8"
      ],
      "reviewState": "authored-navigation"
    }
  ],
  "problems": [
    {
      "id": "problem:future-quotient-and-gns-reconstruction",
      "titleEN": "Future quotient and positive GNS reconstruction",
      "questionEN": "What is determined by complete future behavior, and what additional positive word-kernel source is needed to reconstruct a cyclic operator realization?",
      "topicIds": [
        "topic:universalraum",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8",
        "goal:universalraum"
      ],
      "acceptedPremiseIds": [
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:future-equivalence-minimizes-declared-answer-process",
        "finding:positive-word-kernel-reconstructs-cyclic-gns"
      ],
      "taskIds": [
        "task:future-quotient-from-complete-r",
        "task:conditional-gns-from-supplied-k",
        "task:select-complete-k-from-original-source"
      ],
      "strategyIds": [
        "strategy:reuse-operational-future-quotient",
        "strategy:reuse-conditional-positive-gns"
      ],
      "connectionIds": [
        "connection:future-kernel-to-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:universalraum-primitive-source-audit-20260915"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:common-source-state-event-selection",
      "titleEN": "Historical: common source, state and event selection",
      "questionEN": "Outside the active mathematical research program since the user's23Oct2026 decision. Historical question: Do the original principles derive a common physical source together with its state, dynamical events, and physically observed fields?",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:declared-p1-p2",
        "premise:quarter-phase-retained",
        "premise:typed-source-structures",
        "premise:original-marked-simplex-positive-polar-rule",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:original-erasure-decoder-and-same-native-quarter-polynomial",
        "premise:unitary-full-branchwise-erasure-clock-lift",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark",
        "premise:original-native-fourth-moment-parent",
        "premise:local-product-code-orbit-geometric-parallel-transport",
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:original-coupled-determinant-event-cover",
        "premise:literal-charged-current-native-register-dictionary",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:compact-inner-e8-zero-mode-operation-class",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:solely-neutral-local-weight-two-zero-mode-class",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:common-unnormalized-positive-return-erasure-test",
        "premise:specified-original-pair-ordered-response-composition",
        "premise:canonical-source-stress-all-mode-history",
        "premise:original-cartan-current-local-smearing-and-weyl-class",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:original-native-event-difference-fields-and-state-controls",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress",
        "premise:charged-car-negative-sea-source",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:original-gap-normalized-primitive-relative-action",
        "premise:positive-scalar-first-order-source-comparison-class",
        "premise:given-original-fixed-one-particle-time-winding-ward",
        "premise:four-starts-fixed-state-versus-whole-datum-comparison",
        "premise:original-stable-pointer-instrument-and-given-context",
        "premise:same-full-positive-energy-separating-local-car-source",
        "premise:complete-lagrangian-dirac-cauchy-car-quantization",
        "premise:given-eightfold-source-odd-refielding-dictionary",
        "premise:sharp-half-flux-original-net-state-contracts",
        "premise:local-register-retained-in-joint-charged-word-limit",
        "premise:conditional-local-parity-gauss-completion-with-common-H",
        "premise:fixed-one-copy-eightfold-connection-charge-dictionary",
        "premise:original-neutral-eightpreimage-parity-pair",
        "premise:complete-vector-phase-word-Ward-comparison",
        "premise:smooth-unitary-pair-return-fixed-compact-source-time",
        "premise:unchanged-full-source-observable-map-and-continuous-time-insertion-limit",
        "premise:retained-local-register-with-one-common-original-vacuum-reference",
        "premise:actual-neutral-pair-heat-filter-and-separate-chiral-Weyl-comparison",
        "premise:given-holomorphic-kms-inclusion-and-local-global-modular-domains",
        "premise:canonical-source-gibbs-and-parity-probe-with-retained-winding",
        "premise:literal-boundary-minimality-and-first-order-domain-statements"
      ],
      "findingIds": [
        "finding:operational-seed-is-input",
        "finding:native-source-common-time-thermal-family",
        "finding:native-grade-carry-and-memory",
        "finding:even-seam-global-operator-factorization",
        "finding:source-generated-marking-classification",
        "finding:source-marking-field-realization-boundary",
        "finding:minimal-defect-uniqueness-not-proved",
        "finding:conditional-seam-field-state-time-reconstruction",
        "finding:continuous-hardy-seam-classification",
        "finding:same-source-seam-energy-selection",
        "finding:master-functional-presupposes-source-selection",
        "finding:geometric-deck-not-calderon-polarization",
        "finding:positive-compression-erases-carrier-minus-sector",
        "finding:higgs-determinant-does-not-discharge-carrier-map",
        "finding:primitive-invariant-does-not-select-rank-three",
        "finding:fixed-background-source-does-not-fix-mixed-vertex",
        "finding:local-quarter-inner-variation-is-connection",
        "finding:calderon-enlargement-does-not-select-higgs",
        "finding:finite-sm-higgs-variation-retains-seed",
        "finding:operator-skeleton-does-not-identify-insertion-algebra",
        "finding:internal-even-car-hodge-is-not-coordinate-algebra",
        "finding:minimum-rank-unique-primitive-channel-does-not-select-32",
        "finding:joint-selfconsistency-presupposes-minimal-algebra-fiber-selection",
        "finding:process-composition-and-cyclicity-do-not-select-algebra",
        "finding:quartic-shape-selects-32-only-with-source-sign",
        "finding:native-symmetric-quartic-erasure-common-object",
        "finding:joint-native-algebra-normalizer-and-response-orbit",
        "finding:native-galois-intertwiner-unique-logical-marked-orbit",
        "finding:native-reflection-full-four-five-generators-rate-injectivity",
        "finding:complete-logical-readout-native-covariant-residual-classification",
        "finding:original-polar-mark-clock-centralizer-orbit",
        "finding:actual-quartic-code-product-stabilizer-quarter-exclusion",
        "finding:original-decoder-versus-native-quarter-polynomial-erasure-test",
        "finding:original-decoder-product-time-and-all-unitary-erasure-lifts",
        "finding:native-clock-compatible-polar-fibre-and-canonical-distance",
        "finding:native-moment-parent-and-product-path-selection-boundary",
        "finding:original-e8-current-response-and-full-quarter-lifts",
        "finding:literal-charged-current-register-dictionary-fails-quarter",
        "finding:native-cartan-code-inner-e8-stabilizer-excludes-marked-quarter",
        "finding:native-code-neutral-weight-two-action-and-global-clock-exclusion",
        "finding:original-neutral-root-mixed-response-derived",
        "finding:actual-mixed-ordered-return-on-native-quartic-code",
        "finding:mixed-return-spectrum-does-not-select-original-polar-mark",
        "finding:actual-mixed-return-fails-native-trimer-erasure-lift",
        "finding:strict-trace-gap-excludes-positive-mixed-return-reweighting",
        "finding:original-source-erasure-ward-terms-derived",
        "finding:uncompressed-original-mixed-return-does-not-preserve-code",
        "finding:original-root-response-sum-also-leaks-from-code",
        "finding:original-full-source-return-exterior-feedback-derived",
        "finding:original-return-requires-memory-in-every-code-direction",
        "finding:native-conformal-primary-multiplicity-source-factorization",
        "finding:canonical-conformal-erasure-forces-primary-twenty-carry",
        "finding:all-canonical-stress-histories-scalar-on-native-code",
        "finding:original-local-current-ope-forces-erasure-and-carry",
        "finding:all-real-local-cartan-profiles-erasure-third-bound",
        "finding:closed-cartan-weyl-histories-only-logical-phase",
        "finding:full-existing-local-e8-hull-of-native-code",
        "finding:full-local-quartic-wick-ladder-and-unprojected-native-actions",
        "finding:unmarked-native-w6-simplex-from-full-quartic-ope",
        "finding:full-e8-current-products-fix-stress-and-exterior-ward-cancellation",
        "finding:full-source-simplex-does-not-select-original-polar-mark",
        "finding:original-full-field-event-gram-reconstructs-relative-polar-mark",
        "finding:raw-event-state-positivity-does-not-execute-polar-normalization",
        "finding:determinant-cover-not-literal-full-cartan-lattice-event",
        "finding:clock-free-quartic-product-spectral-sectors-and-native-five",
        "finding:six-complex-native-simplex-rays-from-holomorphic-product-quadrics",
        "finding:intrinsic-relative-response-covariance-and-state-boundary",
        "finding:intrinsic-event-composition-retains-shared-source-and-correlation-data",
        "finding:clock-free-event-geometry-fixes-clock-class-and-mark-orbit-not-member",
        "finding:original-charged-seam-character-recovers-global-native-event-pair",
        "finding:internal-seam-vacuum-and-original-neutral-tensor-do-not-select-flag-root",
        "finding:actual-quarter-fold-shift-removes-native-symmetry-obstruction-without-flag-selector",
        "finding:fold-shift-equivariance-needs-actual-source-response-map-not-another-symmetry-no-go",
        "finding:original-fold-covariance-current-counterterm-and-quartic-twisted-transport",
        "finding:fold-state-full-quartic-kernel-and-erasure-protected-low-order-response",
        "finding:original-fold-quartic-mean-and-spectral-responses-do-not-match-sixty-flags",
        "finding:original-winding-full-state-response-removes-vacuum-rank-two-shortcut",
        "finding:original-source-global-time-winding-history-factorization",
        "finding:original-local-density-folds-to-correlated-root-current-and-erasure-response",
        "finding:original-current-all-mode-energy-and-geometric-stress-bridge",
        "finding:original-current-geometric-response-pair-has-no-common-polar-sector",
        "finding:original-current-ordered-hall-kernel-and-actual-folded-field-products",
        "finding:original-seam-grades-full-density-geometric-products-and-energy-response",
        "finding:original-seam-complete-density-grading-not-sharp-32-input-sectors",
        "finding:original-density-all-profile-mean-work-scalar-on-native-packet",
        "finding:original-p1-gap-normalized-action-covector-and-scalar-holonomy-class",
        "finding:original-p1-gap-car-component-not-native-sharp-32-event",
        "finding:complete-positive-scalar-first-order-circle-source-normal-form",
        "finding:fixed-source-time-seam-ward-rigidifies-scalar-principal-symbol-with-carry",
        "finding:unit-spectral-flow-gap-and-four-marks-do-not-imply-fixed-source-ward",
        "finding:four-native-starts-have-distinct-original-fold-state-correlations",
        "finding:four-starts-full-joint-kernel-and-charged-covariant-transport",
        "finding:four-native-polar-marks-not-fixed-source-state-gauge-equivalent",
        "finding:original-pointer-template-requires-source-context-identification",
        "finding:four-polar-context-algebra-and-source-crosscoupling",
        "finding:every-native-quartic-has-all-eight-original-car-supports",
        "finding:bounded-proper-local-source-operation-cannot-exactly-prepare-positive-eigenpacket",
        "finding:full-original-erasure20-and-joint25-have-all-eight-source-supports",
        "finding:two-face-collar-fixes-face-current-phase-and-distinguishes-relative-endpoint-lift",
        "finding:full-dirac-cauchy-vector-cocycle-cancels-and-endpoint-domain-distinction",
        "finding:unchanged-qwz-full-finite-energy-spectral-exhaustion",
        "finding:uniform-z4-d8-locality-and-both-spinor-chirality-time-census",
        "finding:odd-spinor-global-refielding-and-unit-source-winding",
        "finding:sharp-half-flux-register-quotient-and-local-normality-exclusion",
        "finding:all-word-register-charged-local-field-limit-obstruction",
        "finding:exact-parity-gauss-locality-completion-of-register-source",
        "finding:cover-half-flux-not-fixed-charge-eightfold-spinor-twist",
        "finding:original-neutral-eightpreimage-parity-pair-has-uniform-cut-action",
        "finding:complete-dirac-vector-phase-pair-has-zero-spinor-Ward-charge",
        "finding:smooth-unitary-endpoint-removal-diverges-at-fixed-source-time",
        "finding:continuous-original-time-nonunitary-limits-stay-in-old-source-folium",
        "finding:common-register-vacuum-reference-uniform-and-local-grade-reduction",
        "finding:actual-heat-filtered-neutral-pair-full-state-time-and-separate-chiral-limit",
        "finding:holomorphic-kms-extension-assumes-charged-net-and-not-microscopic-generator",
        "finding:fixed-interval-rotation-modular-chain-fails-local-state-takesaki-repairs",
        "finding:source-winding-cartan-four-word-and-two-edge-kms-gso-discriminator",
        "finding:p1-parity-gauss-net-selection-undecidable-without-original-localization-map",
        "finding:original-minimality-does-not-reconstruct-operational-source",
        "finding:generic-first-order-relative-bound-zero-counterexample-and-correct-domain-repair"
      ],
      "taskIds": [
        "task:read-operational-inputs",
        "task:derive-physical-source-selector",
        "task:reuse-native-source-common-time-thermal-family",
        "task:reuse-native-grade-carry-and-memory",
        "task:reuse-even-seam-global-operator-factorization",
        "task:reuse-source-generated-marking-classification",
        "task:reuse-conditional-seam-operator-reconstruction",
        "task:reuse-same-source-seam-energy-selection",
        "task:compare-process-first-reconstruction-routes",
        "task:reconstruct-native-joint-operator-object",
        "task:classify-native-source-event-menu-dynamics",
        "task:derive-common-clock-lift-and-original-event-menu",
        "task:reconstruct-polar-mark-and-test-native-quarter-lifts",
        "task:classify-polar-fibre-and-test-native-parent-transport",
        "task:test-original-current-response-and-native-code-dictionary",
        "task:test-original-neutral-quadratic-and-first-mixed-source-response",
        "task:derive-actual-mixed-ordered-code-erasure-return",
        "task:test-full-source-return-code-closure-and-erasure-ward",
        "task:derive-full-source-return-exterior-memory",
        "task:derive-all-mode-canonical-conformal-erasure-bridge",
        "task:derive-full-local-cartan-insertion-and-ordering",
        "task:derive-full-local-source-hull-and-unprojected-returns",
        "task:reconstruct-unmarked-native-simplex-from-local-quartic-ope",
        "task:test-original-seam-state-event-data-on-full-field-tensors",
        "task:classify-intrinsic-event-geometry-and-composition",
        "task:test-original-seam-state-data-on-sixty-native-flags",
        "task:derive-fold-state-quartic-response-and-test-original-winding",
        "task:derive-original-density-geometric-response-and-time-winding-normal-form",
        "task:derive-original-full-current-kernel-field-products-and-seam-grading",
        "task:derive-original-p1-gap-action-differential-and-test-native-spectral-component",
        "task:classify-scalar-first-order-source-fiber-with-actual-seam-time-ward",
        "task:compare-four-native-starts-with-full-original-fold-state-response",
        "task:audit-original-source-minimality-and-domain-theorem"
      ],
      "strategyIds": [
        "strategy:polynomial-degree-selects-source",
        "strategy:source-time-character-closure-search",
        "strategy:internal-character-hit-selects-physical-source",
        "strategy:minimal-defect-value-selects-unique-source",
        "strategy:source-hardy-representative-scan",
        "strategy:same-source-energy-minimization",
        "strategy:master-functional-selects-original-source",
        "strategy:identify-geometric-deck-with-calderon-polarization",
        "strategy:derive-mixed-carrier-from-positive-only-polarization",
        "strategy:primitive-invariant-selects-carrier-rank",
        "strategy:determinant-section-count-selects-internal-rank",
        "strategy:fixed-background-source-selects-mixed-vertex",
        "strategy:quarter-or-given-sm-inner-fluctuation-as-origin",
        "strategy:full-operator-skeleton-selects-insertion-algebra",
        "strategy:full-internal-car-as-spectral-coordinate-algebra",
        "strategy:minimum-rank-unique-primitive-yukawa-selects-32",
        "strategy:downstream-singleton-selfconsistency-selects-upstream-algebra",
        "strategy:clock-symmetry-alone-selects-native-polar-transport",
        "strategy:original-moment-parent-or-local-product-berry-as-quarter",
        "strategy:literal-charged-c4-register-current-clock",
        "strategy:inner-e8-rotation-selects-native-cartan-code-quarter",
        "strategy:neutral-weight-two-source-pulses-as-native-quarter",
        "strategy:positive-adjoint-root-response-reweighting-as-common-clock-lift",
        "strategy:identify-original-positive-return-gram-as-full-code-operation",
        "strategy:closed-five-state-realization-of-original-return-moments",
        "strategy:pure-canonical-stress-history-as-marked-native-clock",
        "strategy:pure-local-erasure-or-cartan-weyl-as-physical-clock",
        "strategy:full-event-gram-positivity-as-physical-polar-selection",
        "strategy:unique-rank-two-mark-from-unmarked-native-event-geometry",
        "strategy:select-native-polar-flag-from-internal-quarter-vacuum-and-neutral-family-data",
        "strategy:select-native-polar-flag-by-fold-shift-fixed-point-condition",
        "strategy:select-native-flag-by-original-fold-quartic-mean-or-spectral-response",
        "strategy:original-source-time-winding-history-normal-form",
        "strategy:original-density-geometric-response-common-spectral-32",
        "strategy:original-current-geometric-seam-graded-full-correlations",
        "strategy:original-seam-full-density-energy-sharp-32-reading",
        "strategy:original-p1-gap-normalized-action-cotangent-to-native-event-selector",
        "strategy:original-gap-projector-canonical-car-sector-response",
        "strategy:classify-full-scalar-first-order-seam-time-operator-fiber",
        "strategy:unit-flow-gap-fourmarks-imply-constant-time-seam-ward",
        "strategy:identify-four-native-starts-as-fixed-fold-state-gauge-redundancy",
        "strategy:compare-four-native-starts-by-full-state-relative-kernels-and-data-transport",
        "strategy:classify-four-polar-pointer-contexts-and-original-multilocal-support",
        "strategy:identify-full-dirac-cauchy-vector-current-with-original-chiral-phase",
        "strategy:squeeze-unitary-neutral-pair-return-at-fixed-compact-time",
        "strategy:nonunitary-endpoint-limit-with-unchanged-full-source-time-and-observables",
        "strategy:holomorphic-kms-uniqueness-as-microscopic-charged-generator",
        "strategy:repair-global-odd-spinor-phi-by-kms-or-global-parity",
        "strategy:derive-existing-parity-gauss-rule-from-original-p1-definitions",
        "strategy:reuse-source-minimality-and-domain-audit"
      ],
      "connectionIds": [
        "connection:common-source-full-collar-reconstruction"
      ],
      "reviewedAttemptIds": [
        "contract:native-mark-memory-20261014",
        "contract:native-source-reconstruction-20261014",
        "contract:seam-joint-ward-state-20261014",
        "contract:source-graded-gns-matter-gate-20260922",
        "contract:seam-constructive-search-20261015",
        "contract:quotient-locality-e8-20261014",
        "contract:seam-source-character-search-20261015",
        "contract:seam-source-operator-reconstruction-20261015",
        "contract:seam-full-collar-reconstruction-20261015",
        "contract:seam-joint-source-origin-audit-20261016",
        "contract:mixed-current-origin-20261014",
        "contract:e-series-source-reconstruction-20261024"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:seam-family-connection-compatibility",
      "titleEN": "Seam connection and family action",
      "questionEN": "Does the joint discrete theorem determine a concrete connection and a family coupling compatible with the determinant seam action?",
      "topicIds": [
        "topic:origin",
        "topic:flavor",
        "topic:e8"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "acceptedPremiseIds": [
        "premise:declared-p1-p2",
        "premise:quarter-phase-retained",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:joint-discrete-data-vs-connection",
        "finding:parallelity-excludes-2plus2-only-conditionally"
      ],
      "taskIds": [
        "task:distinguish-classes-from-connection",
        "task:derive-compatible-joint-connection"
      ],
      "strategyIds": [
        "strategy:parallelity-as-axiom"
      ],
      "connectionIds": [
        "connection:marked-family-transport-to-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:source-boundary-lift-selection-20260922",
        "contract:source-joint-spin-family-lift-20260922"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:physical-time-projector-transfer",
      "titleEN": "Physical time and complete transfer",
      "questionEN": "Do the original reflection/projector structures determine the full physical time generator and required field transfer?",
      "topicIds": [
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:declared-p1-p2",
        "premise:quarter-phase-retained",
        "premise:typed-source-structures",
        "premise:specified-shared-s3-register-channel-family",
        "premise:specified-marked-m4-clifford-channel"
      ],
      "findingIds": [
        "finding:sign-projector-does-not-determine-time-magnitude",
        "finding:full-faithful-kms-or-transfer-recovers-magnitudes",
        "finding:full-two-face-collar-recovers-signed-operator",
        "finding:two-face-graph-state-time-same-datum",
        "finding:shared-register-gkls-embedding-exact-q-interval",
        "finding:marked-m4-channel-all-powers-homogeneous-gksl-excluded"
      ],
      "taskIds": [
        "task:retain-sign-projector-counterexample",
        "task:reuse-conditional-full-transfer-reconstruction",
        "task:derive-physical-full-transfer",
        "task:reuse-full-two-face-collar-reconstruction",
        "task:classify-shared-register-homogeneous-gkls-time",
        "task:decide-fixed-m4-all-branch-homogeneous-time"
      ],
      "strategyIds": [
        "strategy:reuse-sign-only-obstruction",
        "strategy:reuse-full-transfer-kms-reconstruction",
        "strategy:full-two-boundary-calderon-graph-reconstruction",
        "strategy:reuse-shared-register-gkls-q-classification",
        "strategy:exclude-fixed-m4-homogeneous-gksl-logarithm"
      ],
      "connectionIds": [
        "connection:full-time-transfer-to-common-source",
        "connection:full-collar-construction-to-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:seam-state-dynamics-injectivity-20260918",
        "contract:source-current-operator-time-20260921",
        "contract:seam-full-collar-reconstruction-20261015",
        "contract:source-continuous-marked-time-search-20260922"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:flavor-ratio-amplitude-readout",
      "titleEN": "Flavor ratio and absolute amplitude scale",
      "questionEN": "Which flavor quantity is fixed on the derived discrete stratum, and which requires the continuous holonomy anchor?",
      "topicIds": [
        "topic:flavor",
        "topic:e8",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "acceptedPremiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:flavor-ratio-closed-absolute-anchor-open"
      ],
      "taskIds": [
        "task:reuse-derived-flavor-ratio",
        "task:select-absolute-holonomy-anchor"
      ],
      "strategyIds": [
        "strategy:reuse-ratio-not-absolute-anchor"
      ],
      "connectionIds": [
        "connection:absolute-flavor-readout-to-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:source-observation-identifiability-20261013"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:alpha-fixed-input-root",
      "titleEN": "Alpha closure for fixed inputs",
      "questionEN": "Which closure equation follows for a fixed seam projector, and which inputs still need justification?",
      "topicIds": [
        "topic:alpha",
        "topic:origin",
        "topic:e8"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "acceptedPremiseIds": [
        "premise:declared-p1-p2",
        "premise:quarter-phase-retained",
        "premise:fixed-input-models-scoped",
        "premise:marked-e8-regularized-charged-grade-response",
        "premise:fixed-em-seam-function"
      ],
      "findingIds": [
        "finding:alpha-equation-is-fixed-input-closure",
        "finding:alpha-global-positive-root-unique",
        "finding:marked-e8-sector-grade-response-realizes-five-quarters",
        "finding:alpha-exact-coefficients-and-root-retain-specific-physical-ward-obligation",
        "finding:alpha-archive-term-provenance-and-master-functional-scope"
      ],
      "taskIds": [
        "task:separate-root-from-selector",
        "task:derive-alpha-inputs-and-transfer",
        "task:prove-alpha-positive-root-uniqueness"
      ],
      "strategyIds": [
        "strategy:numerical-root-as-origin-proof",
        "strategy:reuse-alpha-convexity-proof"
      ],
      "connectionIds": [
        "connection:alpha-physical-response-to-complete-native-source"
      ],
      "reviewedAttemptIds": [
        "contract:source-flavor-origin-20260920",
        "contract:em-positive-root-convexity-20261013",
        "contract:charged-sector-readout-clock-20261013"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:gravity-flow-normalization",
      "titleEN": "Geometric flow and gravity normalization",
      "questionEN": "Do common matter-only observations derive geometric horizon flow and the area response from the original gravity source?",
      "topicIds": [
        "topic:gravity",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures",
        "premise:fixed-input-models-scoped"
      ],
      "findingIds": [
        "finding:matter-observations-do-not-fix-geometric-response"
      ],
      "taskIds": [
        "task:state-fixed-function-scope",
        "task:derive-geometric-modular-response"
      ],
      "strategyIds": [
        "strategy:add-free-geometric-cocycle"
      ],
      "connectionIds": [
        "connection:gravity-response-to-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:source-observation-identifiability-20261013",
        "contract:seam-gravity-source-bridge-20261013"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:clock-linked-neutral-response-reconstruction",
      "titleEN": "Clocks and complete neutral source response",
      "questionEN": "Which complete quadratic response can the actual clock images reconstruct?",
      "topicIds": [
        "topic:clocks",
        "topic:quantum",
        "topic:alpha"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T6"
      ],
      "acceptedPremiseIds": [
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:four-clock-fields-complete-quadratic-response"
      ],
      "taskIds": [
        "task:reconstruct-full-neutral-quadratic-matrix",
        "task:derive-clock-probe-physical-access"
      ],
      "strategyIds": [
        "strategy:reuse-clock-jordan-response-inverse"
      ],
      "connectionIds": [
        "connection:quadratic-response-constrains-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:clock-jordan-response-reconstruction-20261015",
        "contract:neutral-response-tomography-20261013",
        "contract:native-mark-memory-20261014"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:clock-source-covariant-transport",
      "titleEN": "Clock action on charge, time and quarter transition",
      "questionEN": "How does the actual Gaussian J act on the complete marked source?",
      "topicIds": [
        "topic:clocks",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:typed-source-structures",
        "premise:quarter-phase-retained"
      ],
      "findingIds": [
        "finding:actual-j-covariant-source-transport",
        "finding:fixed-source-affine-j-obstruction"
      ],
      "taskIds": [
        "task:construct-covariant-original-j-lift",
        "task:interpret-clock-source-frames"
      ],
      "strategyIds": [
        "strategy:reuse-j-covariant-source-lift",
        "strategy:fixed-affine-j-as-source-time-symmetry"
      ],
      "connectionIds": [
        "connection:j-transport-constrains-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:clock-source-twist-transport-20261015",
        "contract:seam-joint-ward-state-20261014"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:charged-twist-response-identifiability",
      "titleEN": "Which responses distinguish charged time action?",
      "questionEN": "Which data separate sources with identical complete neutral vacuum response?",
      "topicIds": [
        "topic:quantum",
        "topic:clocks",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:neutral-vacuum-allword-twist-blindness",
        "finding:eight-charged-responses-reconstruct-twist"
      ],
      "taskIds": [
        "task:identify-neutral-response-blind-directions",
        "task:reconstruct-twist-from-charged-data",
        "task:derive-actual-charged-source-probes"
      ],
      "strategyIds": [
        "strategy:more-neutral-vacuum-moments-select-twist",
        "strategy:reuse-eight-charge-twist-inverse"
      ],
      "connectionIds": [
        "connection:charged-identifiability-limits-neutral-tomography",
        "connection:charged-discriminator-constrains-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:clock-source-twist-transport-20261015"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:native-charged-seam-selection",
      "titleEN": "Which seam action distinguishes native opposite charges?",
      "questionEN": "Can existing native charge fields produce the quarter-twist time response of the seam?",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:native-invariant-response-not-fixed-chiral-twist",
        "finding:native-opposite-charge-response-symmetry",
        "finding:native-chemical-mark-visible-in-charged-corners",
        "finding:fixed-hopping-quarter-phases-retain-antiunitary-discriminator"
      ],
      "taskIds": [
        "task:native-field-response-discriminator",
        "task:derive-native-seam-symmetry-breaking"
      ],
      "strategyIds": [
        "strategy:native-invariant-start-matches-single-twist",
        "strategy:fixed-quarter-hopping-phase-selects-chiral-time",
        "strategy:reuse-native-charged-corner-ratio"
      ],
      "connectionIds": [
        "connection:native-symmetry-to-charged-twist",
        "connection:native-selection-to-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:native-charged-conjugation-20261015",
        "contract:local-charge-transport-round20",
        "contract:native-source-reconstruction-20261014",
        "contract:source-ground-response-20260920",
        "contract:source-charged-extension-selection-20260921"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:constructive-seam-lift-state",
      "titleEN": "Constructive seam search: operators, state and source compatibility",
      "questionEN": "What does the complete phase search decide, and which additional state information prevents a false source solution?",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:declared-p1-p2",
        "premise:quarter-phase-retained",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:constructive-phase-class-and-full-winding",
        "finding:constructive-positive-state-extension",
        "finding:constructive-current-group-selects-positive-p-lift",
        "finding:constructive-state-algebra-resolution-and-source-test",
        "finding:constructive-all-phases-fail-unchanged-source"
      ],
      "taskIds": [
        "task:reuse-constructive-seam-1",
        "task:reuse-constructive-seam-2",
        "task:reuse-constructive-seam-3",
        "task:reuse-constructive-seam-4",
        "task:reuse-constructive-seam-5"
      ],
      "strategyIds": [
        "strategy:repeat-closed-seam-phase-search",
        "strategy:shift-functional-selects-physical-state",
        "strategy:crossed-phase-hit-as-unchanged-source"
      ],
      "connectionIds": [
        "connection:constructive-seam-to-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:seam-constructive-search-20261015",
        "contract:quotient-locality-e8-20261014"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:seam-partner-charge-state-time",
      "titleEN": "Which partner actually belongs to the original seam?",
      "questionEN": "Which charge, state type and time action belong to the root partner and original sheet pairing?",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:declared-p1-p2",
        "premise:quarter-phase-retained",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:partner-carrier-charges-and-state-types",
        "finding:partner-fixed-quarter-time-splits-sm-multiplet",
        "finding:partner-original-carrier-cross-sheet-conjugation",
        "finding:partner-chiral-quarter-conjugation-state-time",
        "finding:joint-bilinear-hermitian-correction",
        "finding:joint-quarter-transports-marking",
        "finding:joint-fixed-time-marking-repair-excluded",
        "finding:joint-spinor-not-source-coefficient"
      ],
      "taskIds": [
        "task:reuse-partner-type-1",
        "task:reuse-partner-type-2",
        "task:reuse-partner-type-3",
        "task:reuse-partner-type-4",
        "task:reuse-joint-bilinear-hermitian-correction",
        "task:reuse-joint-quarter-transports-marking",
        "task:reuse-joint-fixed-time-marking-repair-excluded",
        "task:reuse-joint-spinor-not-source-coefficient"
      ],
      "strategyIds": [
        "strategy:root-coordinate-equality-as-physical-partner",
        "strategy:fixed-time-weyl-repair-quarter-conjugation"
      ],
      "connectionIds": [
        "connection:partner-types-to-common-source"
      ],
      "reviewedAttemptIds": [
        "contract:seam-partner-original-action-20261015",
        "contract:seam-joint-conjugation-20261015"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:automated-operator-source-synthesis",
      "titleEN": "Automated construction of operator maps and sources",
      "questionEN": "Which tools generate operator maps, learn counterexamples, and can search for the full positive source?",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:typed-source-structures",
        "premise:actual-diagonal-lepton8-common-insertion-contract",
        "premise:one-e8-bracket-weyl-pairing-with-single-anchor-dressing",
        "premise:fixed-local-quarter-channel-in-constant-odd-source",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:spin10-su4-family-four-cycle-quarter-lift-class",
        "premise:family-four-cycle-lift-commutes-with-original-sm",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:native-third-clock-current-word-pairing-class",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-product-collar-two-face-data",
        "premise:fixed-scalar-quarter-full-jloc-pfaffian-candidate",
        "premise:fixed-quarter-cover-deck-normal-and-convergence-selection-tests",
        "premise:fixed-original-aps-quarter-domain-and-constant-odd-insertion",
        "premise:mass-only-full-deck-relative-and-ordinary-heat-trace",
        "premise:closed-antiperiodic-scalar-wall-with-fixed-hermitian-coefficient",
        "premise:scalar-spectral-heat-covariance-with-geometric-time-reflection",
        "premise:given-global-quaternionic-sm-mass-loop-with-fixed-yukawas",
        "premise:bounded-relative-operator-positive-laplace-and-compact-source-pair",
        "premise:given-normal-spin-clutch-weak-orbit-family-and-u2-linearization",
        "premise:given-normal-orbit-and-four-copy-natural-spin-family",
        "premise:fixed-v117-orthogonal-d3-cartan-identification",
        "premise:given-original-su3-to-su4-family-vector-action",
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:same-spin-hardy-shift-against-identity-with-grading-retained",
        "premise:given-relative-unit-seam-on-specified-collar-faces",
        "premise:whole-constant-odd-coefficient-on-scalar-unit-clutch-domain",
        "premise:declared-q-column-to-v252-generation-slot-comparison",
        "premise:declared-q-column-to-v252-chiral-slot-comparison",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract",
        "premise:oriented-p2-exterior-carrier",
        "premise:given-original-e8-cx-current-cocycle-and-compact-adjoint",
        "premise:original-d5-base-current-action-on-given-p2-e8-source",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:original-gap-normalized-primitive-relative-action",
        "premise:original-closed-real-delta-transport-action",
        "premise:four-original-diagonal-paths-and-regularized-endpoints",
        "premise:native-clock-adjoint-compensation-for-hardypair",
        "premise:declared-positive-cubic-hardy-direction-for-gram-differential",
        "premise:whole-same-mu01-induced-ns-halfmode-reader",
        "premise:whole-six-original-induced-inputs-at-fixed-kinetic-ns-reader",
        "premise:canonical-finite-particle-hole-corner-of-given-kinetic-graph",
        "premise:bare-unsmoothed-crossface-quadratic-on-given-graph-vacuum",
        "premise:given-original-two-stage-admissibility-complex-and-blocked-weight-caller",
        "premise:local-geometric-dirac-deck-lift",
        "premise:original-admissibility-and-graded-source-interfaces",
        "premise:whole-product-dirac-with-standard-normal-clifford-double",
        "premise:full-independent-even-odd-matrix-coefficient-class",
        "premise:whole-fermi-two-face-projection-and-diagonal-isometric-compression",
        "premise:actual-v252-sm-coefficients-and-internal-ko6-without-extra-mixing",
        "premise:separable-normal-real-map-with-actual-jodd-gauge-and-typed-quarter-image",
        "premise:actual-p2-six-multiplet-gauge-real-coordinate-frame-class",
        "premise:original-higgs-radial-family-on-common-compact-product-domain",
        "premise:positive-laplace-profile-finite-three-moment-comparison",
        "premise:existing-ap-positive-source-factor-and-declared-squared-energy-comparison",
        "premise:actual-v252-entire-yukawa-majorana-family-with-compatibility-only",
        "premise:original-invariant-word-domain-with-nested-readouts",
        "premise:original-single-beta-return-with-native-cartan-j-word-alphabet",
        "premise:original-regulated-full-source-with-actual-measure-and-legs",
        "premise:finite-reflected-positive-quadratic-ir-regulator-class",
        "premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber",
        "premise:original-graded-rp-reference-and-even-local-reflected-half-action",
        "premise:original-constant-higgs-fiber-and-symmetric-majorana-spectral-consumer",
        "premise:literal-archived-geometric-residue-and-common-higgs-field-comparison",
        "premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer",
        "premise:whole-variable-higgs-bound-reference-and-conformal-dirac-map",
        "premise:original-inner-higgs-central-scale-and-finite-affine-source-map",
        "premise:given-normal-higgs-mode-realization-and-distinct-module-types",
        "premise:given-product-clifford-grades-parallel-projection-and-complete-relative-block-reader",
        "premise:original-positive-admissibility-reader-and-given-total-chiral-product",
        "premise:whole-original-scale-congruence-and-specified-normal-energy-data",
        "premise:given-whole-green-energy-source-and-conditional-scale-response",
        "premise:current-original-spectral-action-and-fixed-ordinary-moment-dictionary",
        "premise:original-whole-spinor-and-entropic-curvature-consumers-with-given-higgs-response",
        "premise:actual-original-four-ghost-commuting-projection-admissibility-complex",
        "premise:actual-smooth-normal-family-with-supplied-unitary-horizontal-connection",
        "premise:fixed-original-o1-section-consumer-and-actual-normal-first-order-placement",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:fixed-rank-bounded-cutoff-with-ordinary-noncompact-higgs-volume",
        "premise:whole-constant-original-quarter-source-positive-traceclass-profile-and-flat-higgs-volume",
        "premise:given-o1-mode-isometry-and-weak-invariant-positive-higgs-covariance-marginal",
        "premise:literal-whole-source-localization-and-geometric-readout-contracts",
        "premise:actual-proper-local-current-weyls-and-bare-native-code-compression",
        "premise:actual-elliptic-quarter-supported-current-and-interval-car-modular-test",
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:actual-elliptic-two-face-projection-with-genuine-regional-support",
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source",
        "premise:original-common-positive-constant-higgs-law-over-whole-quarter-tower",
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:actual-single-source-event-coherent-stinespring-record",
        "premise:given-e8-current-vacuum-net-and-original-grade-two-descendant-with-standard-split",
        "premise:local-e8-current-response-realization",
        "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion",
        "premise:original-quark-particle-color-group-counting-on-whole-constant-quarter-source",
        "premise:given-whole-quarter-graph-and-canonical-diagonal-original-color-lift",
        "premise:stipulated-e8-h8-with-original-color-center-selector",
        "premise:original-marked-color-center-on-whole-e8-lattice-current-source",
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:original-fixed-color-and-folded-ns-cartan-interface",
        "premise:actual-thermal-quarter-source-and-retained-spin-parent-mixed-word",
        "premise:actual-eightfold-arc-residue-source-and-fixed-spin-cartan-insertion",
        "premise:actual-original-ns-color-center-continuous-density-and-coordinate-net",
        "premise:actual-original-full-two-face-graph-and-local-matrix-operations",
        "premise:original-blocked-transfer-algebra-and-marked-source-uniformity-audit",
        "premise:original-bare-c6-fixed-analytic-half-power-and-literal-word-alphabet",
        "premise:actual-original-finite-v990-source-and-historical-parent-recovery",
        "premise:actual-original-finite-car-higgs-force-and-faithful-collective-source",
        "premise:actual-whole-circle-product-car-force-and-original-time-smearing",
        "premise:original-constant-circle-local-higgs-force-and-hilbert-schmidt-time-source",
        "premise:literal-archived-global-positive-kernel-finite-measure-map",
        "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction"
      ],
      "findingIds": [
        "finding:typed-operator-search-calibrated",
        "finding:positive-kernel-construction-with-exact-discriminator",
        "finding:source-typed-kernel-search-controls",
        "finding:collar-car-projection-multifield-ray",
        "finding:known-quarter-source-full-multifield-control",
        "finding:source-reference-amplitude-retained",
        "finding:joint-fermionic-source-schur-functional",
        "finding:quarter-circle-absolute-zeta-green-eta",
        "finding:quarter-sea-absolute-thermal-central-phase",
        "finding:original-operational-seed-and-given-green-pairing",
        "finding:order-one-infinitesimal-bound-inference-fails",
        "finding:joint-ward-two-field-data-miss-fixed-four-field-response",
        "finding:complete-car-kernel-fixes-nongaussian-link-functional",
        "finding:source-covariance-jet-and-mixed-face-interface",
        "finding:e8-grade-two-explicit-spinor-current-action",
        "finding:intrinsic-source-jet-removes-pure-field-frame-motion",
        "finding:unchanged-ns-vector-generators-cannot-create-d5-spinor-fields",
        "finding:two-face-noncommuting-geometric-response-calculus",
        "finding:raw-face-mask-fails-source-kernel-null-descent",
        "finding:action-response-sewing-does-not-select-lf-intervention",
        "finding:faithful-gns-completion-closes-automated-source-query-feedback",
        "finding:whole-quarter-channels-identified-by-exact-internal-kernel",
        "finding:actual-joint-insertion-hull-resolves-eight-coefficient-directions",
        "finding:e8-bare-trilinear-and-single-anchor-weyl-class-insufficient",
        "finding:complete-family-four-cycle-class-separates-native-clock-from-sm-preservation",
        "finding:native-clock-word-transpose-has-static-rank-four-counterexample",
        "finding:whole-constant-coupled-source-is-implementable-despite-isolated-insertion-domain",
        "finding:fixed-quarter-jloc-pfaffian-closure-fails-local-skew-test",
        "finding:same-collar-has-canonical-selfdual-kinetic-pairing-and-charged-determinant",
        "finding:quarter-cover-pairing-does-not-supply-local-normal-or-select-scale-measure",
        "finding:fixed-aps-source-has-whole-inverse-and-finite-boundary-correction",
        "finding:mass-only-deck-relative-heat-action-fails-free-infinite-trace",
        "finding:finite-antiperiodic-scalar-wall-has-no-exact-massless-normal-mode",
        "finding:spectral-heat-covariance-positivity-does-not-imply-time-rp",
        "finding:quaternionic-sm-mass-winding-is-not-normal-determinant-clutch",
        "finding:bounded-relative-trace-obstruction-and-whole-genuine-pair-heat-reader",
        "finding:normal-clutch-orbit-index-equivariantly-recovers-given-weak-module",
        "finding:normal-orbit-spin-family-index-and-signed-charge-balance",
        "finding:fixed-flavor-cartan-sign-cover-and-root-lift-parity",
        "finding:original-family-vector-action-is-not-cartan-rotation-or-spinlift-selection",
        "finding:actual-genus-two-sign-family-closes-common-parallel-k-connection",
        "finding:actual-q-quarter-extends-common-k-connection-and-real-coefficient-lifts",
        "finding:real-source-reflection-is-not-linear-duality-or-compact-clock-inversion",
        "finding:source-selected-spin-and-q-signs-have-three-explicit-global-kernels",
        "finding:source-s0-szego-point-legs-generate-q-kernels-with-typed-products",
        "finding:actual-spin-kernel-determinant-has-inverse-q-norm-character",
        "finding:closed-source-flavor-spin-has-functorial-pfaffline-with-charged-type-limit",
        "finding:original-relative-seam-has-explicit-whole-graph-fredholm-mismatch",
        "finding:whole-constant-coupled-clutch-defects-are-exact-internal-kernels",
        "finding:old-complex-scalar-clutch-separates-c0-and-product-reflection",
        "finding:scalar-defect-circle-character-does-not-select-projector-holonomy",
        "finding:source-spin-is-canonical-ramified-base-spin-pullback",
        "finding:original-v117-has-explicit-algebraic-q-cover-fundamental-frame",
        "finding:double-circle-reflection-does-not-fix-entire-cubic-cable-seam",
        "finding:actual-fuchs-real-map-transports-whole-given-finite-source-state-and-time",
        "finding:actual-e0-compensator-extends-whole-k-e8-with-transported-quarter",
        "finding:actual-v252-entire-real-basis-has-signed-p2-dual-dictionary",
        "finding:chiral-fuchs-source-transport-has-distinct-majorana-phase-and-torus-absorption",
        "finding:native-theta-composition-retains-conjugate-source-and-parity-square",
        "finding:single-graph-range-isometry-does-not-give-local-whole-seed-map",
        "finding:hard-holonomy-selfduality-leg-and-finite-character-phase-separation",
        "finding:original-z6-positive-structural-kernel-does-not-supply-oriented-phase-observable",
        "finding:original-genus-two-hexagonal-rotation-has-concrete-rho-hodge-line",
        "finding:original-mixed-spin-products-realize-positive-u6-cycle",
        "finding:actual-spin-quadratics-reach-original-hexagonal-hodge-line",
        "finding:spin-pair-car-transport-retains-parity-and-whole-source-types",
        "finding:real-total-trace-does-not-exclude-coherent-phase-reader",
        "finding:geometric-six-spin-clock-differs-from-marked-native-clock",
        "finding:whole-q-to-p-pullback-transports-given-source-state-and-time",
        "finding:actual-fixpoint-evaluation-keeps-coefficient-signs-and-source-type",
        "finding:original-source-naturality-needs-no-second-p-image-background",
        "finding:canonical-spin2-lift-carries-whole-annulus-source-with-reversed-time",
        "finding:geometric-spin-collar-map-closes-weighted-image-domain-with-total-deck-action",
        "finding:claude33-annulus-map-is-valid-distinct-type-not-unique-geometric-spin-selection",
        "finding:original-mixed-spin-products-already-have-complete-dual-hom-coefficients",
        "finding:whole-f5-graph-supplies-canonical-reverse-qp-hom-kernel",
        "finding:actual-spin-product-weight-has-canonical-trace-class-form-pairing",
        "finding:fully-descended-covariant-reverse-kernel-removes-rho-form-channel",
        "finding:original-a4-linear-quarter-does-not-supply-proposed-scalar-mu3-repair",
        "finding:offdiagonal-hom-matches-a4-family-six-but-not-two-triplet-e8-product",
        "finding:compact-e8-adjoint-completes-family-six-with-carrier-rank-retained",
        "finding:three-family-cx-recursion-closes-exact-d8-with-minimal-original-escape",
        "finding:original-weak-current-coefficient-has-explicit-finite-oneform-consumer",
        "finding:original-d5-zero-mode-closes-triplet-carrier-and-fixed-glue-is-minimal-escape",
        "finding:mixed-spin-full-deck-has-no-rank-three-projector",
        "finding:actual-reverse-hom-diagonal-supplies-global-q-hodge-response",
        "finding:bare-c3-kernel-diagonal-yukawas-have-common-real-frame",
        "finding:original-primitive-action-is-present-highpass-is-not-finite-selector",
        "finding:atlas-detail-retrieval-recovers-existing-d4-solution",
        "finding:original-poisson-normal-trace-fixes-whole-calderon-graph",
        "finding:induced-original-hardy-defect-gives-finite-whole-source-reader",
        "finding:original-weak-quartic-action-has-nonzero-nonlinear-response",
        "finding:all-common-leading-distance-clutches-fail-original-flavor-lengths",
        "finding:actual-hardy-response-has-weak-clifford-odd-and-ko-real-completion",
        "finding:two-entry-hardy-adjoint-hierarchy-fails-full-ko-and-su2",
        "finding:actual-fuchs-halfpath-has-canonical-g-metric-c6-kernel-map",
        "finding:original-real-delta-jet-reads-same-marked-hardy-open-word",
        "finding:four-actual-fuchs-spine-edges-recover-marked-meridians-and-nonzero-open-word",
        "finding:native-adjoint-quarter-clock-cannot-compensate-hardypair-odd-character",
        "finding:whole-cubic-gram-differential-retains-hardy-phase-and-cross-resonance",
        "finding:complete-original-mu01-hardy-reader-has-two-calibrated-entries",
        "finding:whole-six-original-hardy-inputs-generate-full-family-coefficient-algebra",
        "finding:actual-whole-hardy-alphabet-has-finite-particle-hole-wick-block",
        "finding:bare-unsmeared-mu-crossface-quadratic-fails-vacuum-domain",
        "finding:linear-spectral-centralization-does-not-replace-full-marked-hardy-source",
        "finding:original-admissibility-projector-is-explicit-penalties-do-not-read-retained-amplitudes",
        "finding:actual-original-inner-fluctuation-has-whole-noncommuting-two-face-response",
        "finding:fiber-only-primitive-split-and-frozen-gap-miss-original-action",
        "finding:oriented-resolvent-weights-do-not-identify-original-reflection-producer",
        "finding:current-odd-carrier-reader-is-lossless-on-whole-coupled-source",
        "finding:ap-spectral-formulas-do-not-force-normal-domain-or-complete-source",
        "finding:actual-weak-connection-transmits-family-orientation-to-both-faces",
        "finding:original-higgs-variation-is-not-independent-yukawa-stationarity",
        "finding:actual-weak-cap-converges-on-whole-quarter-circle",
        "finding:canonical-clifford-double-derives-normal-ap-and-typed-deck",
        "finding:universal-graded-source-reducing-images-do-not-fix-carrier-frame",
        "finding:whole-two-face-compression-projector-defect-detects-hidden-source-loss",
        "finding:actual-v252-quark-lepton-split-prevents-weak-grading-uniqueness-inference",
        "finding:actual-graded-hypercharge-trace-rejects-quark-lepton-sign-intertwiner",
        "finding:separable-normal-real-maps-compose-to-given-deck-and-quarter-image",
        "finding:actual-gauge-real-frames-leave-carrier-phase-as-coordinate-freedom",
        "finding:original-higgs-family-has-one-complex-kk-class-but-different-whole-sources",
        "finding:signed-one-particle-modular-weight-is-not-the-positive-even-heat-operator",
        "finding:three-moments-select-one-exponential-exactly-in-positive-laplace-class",
        "finding:existing-ap-positive-source-factor-has-oriented-poisson-heat-bridge",
        "finding:actual-v252-entire-compatibility-family-has-generic31-dimensional-quotient",
        "finding:full-memory-schur-reconstruction-preserves-every-ordered-word-under-nesting",
        "finding:original-return-and-native-j-have-minimal68-dimensional-all-word-memory",
        "finding:original-full-source-regulator-flow-retains-normalized-kernel-and-vacuum-factor",
        "finding:full-reflected-quadratic-regulator-cone-preserves-every-rp-source",
        "finding:original-shared-higgs-source-induces-fixed-yukawa-mixed-matter-words",
        "finding:local-even-yukawa-sewing-preserves-given-joint-graded-rp",
        "finding:whole-original-constant-higgs-orbit-has-reduced-majorana-spectral-response",
        "finding:archived-geometric-higgs-residue-bulk-needs-coefficient-identification-repair",
        "finding:original-local-higgs-residue-linear-coefficients-fail-same-trace-heat-ratio",
        "finding:whole-original-higgs-moments-fix-conditional-local-kinetic-mass-quartic",
        "finding:whole-variable-original-higgs-bound-reference-response-and-forced-clifford-factor",
        "finding:original-symmetric-scale-map-fails-simultaneous-higgs-einstein-repair",
        "finding:whole-original-higgs-inner-scale-and-affine-full-source-transport",
        "finding:normal-higgs-mode-type-and-exact-kernel-metric-require-actual-relative-operator-map",
        "finding:original-superconnection-grades-and-weighted-heat-retain-higgs-kinetic-excursions",
        "finding:whole-normal-reduction-preserves-relative-spectral-reader-and-higgs-jets",
        "finding:original-admissibility-own-spectral-reader-has-no-free-low-mode-residue-repair",
        "finding:whole-total-chiral-positive-spectrum-retains-higgs-kinetics-and-common-half-trace",
        "finding:whole-scale-energy-response-uniquely-reconstructs-normal-profile",
        "finding:original-relative-scale-flow-separates-residue-finite-part-and-local-anomaly",
        "finding:original-whole-green-produces-energy-response-with-correct-orthogonal-trace",
        "finding:whole-mixed-scale-source-reads-bosonic-insertion-before-higgs-average",
        "finding:current-original-spectral-action-triplet-fails-positive-laplace-class-unless-leading-relative-term-cancels",
        "finding:correct-current-argument-weights-link-whole-higgs-threshold-and-same-einstein-response",
        "finding:whole-original-spinor-curvature-a4-has-no-independent-scalaron-r-squared",
        "finding:whole-original-entropic-curvature-corrects-max-symmetric-scalar-scale",
        "finding:given-whole-higgs-source-fixes-radial-curvature-susceptibility-without-extra-scalar",
        "finding:actual-original-four-ghost-complex-preserves-base-selector-with-full-cohomology-and-distinct-traces",
        "finding:whole-original-admissibility-energy-source-recovers-constraints-but-cannot-replace-geometric-operator",
        "finding:original-moving-normal-kernel-fixes-induced-connection-and-full-scale-covariance",
        "finding:fixed-original-o1-source-rejects-nonconstant-normal-multiplier-and-fixes-placement-test",
        "finding:original-master-variation-keeps-spin-weight-and-active-source-route-typed",
        "finding:shared-original-higgs-mixture-has-invariant-color-fourpoint-wick-defect",
        "finding:bounded-fixed-rank-spectral-action-does-not-normalize-noncompact-higgs-volume",
        "finding:whole-original-quarter-source-bounds-higgs-weight-uniformly-through-joint-mode-ir-limits",
        "finding:original-o1-covariance-leaves-full-radial-higgs-law-and-exact-fourier-source-readout",
        "finding:whole-process-reconstruction-priority-and-original-locality-geometry-input-audit",
        "finding:actual-disjoint-local-weyls-acquire-spurious-commutator-under-bare-native-compression",
        "finding:actual-quarter-current-state-excludes-nontrivial-geometric-local-point-time",
        "finding:actual-elliptic-interval-car-source-produces-local-modular-generator",
        "finding:actual-proper-two-face-regions-do-not-contain-pure-local-source-double",
        "finding:actual-elliptic-whole-environment-fixes-regional-car-partner",
        "finding:actual-original-color-triplet-has-spectator-dependent-modular-field-law",
        "finding:actual-color-marginal-has-complete-finite-source-reader-and-mixture-criterion",
        "finding:two-and-four-field-words-do-not-complete-original-color-triplet-source",
        "finding:whole-original-quarter-occupation-tower-uniquely-reconstructs-common-radial-higgs-law",
        "finding:finite-original-tower-reader-and-existing-weak-symmetry-fix-shared-matter-responses",
        "finding:unchanged-free-quarter-source-cannot-be-nontrivial-integrated-higgs-mixture",
        "finding:actual-e8-record-doily-action-is-signed-p-plus-compatible-point-with-typed-sym2-lift",
        "finding:actual-e8-record-words-distinguish-order-and-retain-phase-beyond-fifteen-labels",
        "finding:literal-doily-incidence-output-and-strict-causal-order-on-fifteen-source-labels-excluded",
        "finding:actual-doily-context-record-characters-have-ranks-four-two-two-two",
        "finding:canonical-standard-split-localizes-original-source-record-words-with-full-descendant-companion",
        "finding:unchanged-global-sixty-event-source-fails-local-exterior-current-test",
        "finding:canonical-source-localization-changes-exterior-state-and-does-not-select-event-origin",
        "finding:original-elliptic-fixed-holonomy-insertion-gives-local-operation-on-unchanged-source",
        "finding:original-quarter-pair-fixes-square-charge-law-half-response-and-real-quillen-norm",
        "finding:actual-elliptic-source-determines-all-path-normalized-causal-current-response",
        "finding:original-higgs-quark-source-has-exact-whole-su3-counting-response",
        "finding:single-original-color-parity-separates-free-quillen-from-positive-higgs-integrated-source",
        "finding:whole-original-quarter-graph-color-response-is-relative-and-diagonal-singlet",
        "finding:original-center-selector-requires-typed-state-field-and-face-transport",
        "finding:original-color-center-fixes-whole-e6-a2-source-and-charged-ward-word-action",
        "finding:original-color-neutral-lattice-class-cannot-supply-odd-fields-by-inherited-superlattice-extension",
        "finding:original-color-center-extends-to-folded-ns-but-full-current-action-needs-spin-sector-transport",
        "finding:actual-color-spin-car-mixed-word-has-complete-thermal-source-and-cyclic-sewing",
        "finding:exact-original-ns-ramond-heat-equality-does-not-identify-fixed-color-restricted-source",
        "finding:original-scalar-cover-profile-cannot-implement-fixed-spin-cartan-loop",
        "finding:actual-spin-cartan-composite-source-retains-multi-arc-support-and-fails-additive-even-locality",
        "finding:actual-color-selector-admits-exactly-eighth-periodic-original-density-variations",
        "finding:actual-color-is-internal-exactly-on-eightfold-coordinate-source-regions",
        "finding:original-whole-two-face-multiplier-reduction-is-only-constant-residue-diagonal",
        "finding:original-two-face-local-fock-implementation-and-exact-source-variation-differ-from-reduction",
        "finding:whole-undecorated-transfer-does-not-determine-original-marked-field-source",
        "finding:volume-wise-injective-positive-transfer-does-not-prove-uniform-parent-gap",
        "finding:original-c6-half-power-has-exact-entire-positive-ordered-word-expansion",
        "finding:original-c6-whole-word-sewing-retains-source-amplitude-and-controlled-infinite-tail",
        "finding:historical-parent-and-actual-field-time-bridges-must-be-reused-before-new-source-models",
        "finding:actual-native-v990-full-timed-words-recover-kubo-response-distinct-from-instantaneous-variance",
        "finding:actual-original-higgs-force-has-complete-ordered-fermionic-determinant-source",
        "finding:finite-covariant-higgs-composites-have-no-nontrivial-positive-instantaneous-classical-law",
        "finding:actual-original-collective-mean-has-exact-ball-domain-and-relative-entropy-action",
        "finding:original-uniform-allmode-force-clt-is-nonzero-only-before-fixed-time-smearing",
        "finding:original-unscaled-time-smeared-force-has-selfadjoint-whole-ordered-source",
        "finding:original-local-higgs-force-has-whole-centered-hilbert-schmidt-determinant-source",
        "finding:given-original-circle-force-source-generates-an-exact-causal-local-net",
        "finding:literal-archived-global-rg-kernel-does-not-preserve-finite-measures",
        "finding:native-higgs-marginal-retains-induced-vertex-and-noether-response",
        "finding:isospectral-noether-orbit-does-not-supply-original-metric-higgs-variation",
        "finding:metric-dtn-form-bound-needs-transfer-comparison-for-gap",
        "finding:conditional-higgs-pair-winding-protection-in-common-circle-carrier",
        "finding:natural-five-clock-carrier-excludes-invariant-three-transfer-compression",
        "finding:shared-scalar-shift-whole-retained-higgs-sector-has-index-minus-eighteen",
        "finding:whole-coupled-quark-circle-common-shift-cancels-relative-winding",
        "finding:one-sided-shift-full-higgs-pair-is-hilbert-schmidt-not-trace-class",
        "finding:selective-coupled-higgs-reader-has-well-defined-det2",
        "finding:v311-population-reader-does-not-identify-quantum-channel",
        "finding:declared-charged-pair-relation-leaves-five-word-ambiguity",
        "finding:full-creator-relations-close-fixed-free-two-mode-ambiguity",
        "finding:comoving-diagnostic-clock-exact-response-but-nonlocal-mode-transport",
        "finding:free-quarter-two-face-response-strip-with-relative-zero-mode-defect",
        "finding:e8-hodge-event-perfectly-distinguishable-from-every-unitary",
        "finding:common-five-slot-transfer-preserves-e8-bracket-not-automatic-tp",
        "finding:comoving-clock-dynamic-higgs-connection-and-charged-flow",
        "finding:r064-sixty-record-channel-exact-distance-and-continuous-record-parent",
        "finding:two-syntheses-shared-source-priorities-and-typed-limits",
        "finding:weighted-index-trace-and-selfdual-theta-require-original-selection",
        "finding:ordered-quarter-fourfield-e8-record-and-charge-filters",
        "finding:r091-recovered-native-hodge-sewing-and-full96-quarter-complement",
        "finding:r092-fold-ward-target-neutral-source-and-smaller-creation-branch",
        "finding:r093-original-kink-time-response-distinguishes-quarter-states",
        "finding:r093-ordered-current-kink-and-eight-arc-locality",
        "finding:r094-original-five-excitations-distinct-from-clustering-vacuum",
        "finding:r096-joint-higgs-twoface-source-constraint",
        "finding:r096-positive-twoface-fourword-defect-bound",
        "finding:r096-unnormalized-mixed-source-linear-identity",
        "finding:r096-original-quark-crossing-negative-covariance"
      ],
      "taskIds": [
        "task:calibrate-typed-operator-synthesis",
        "task:synthesize-joint-source-operator-dictionary",
        "task:implement-positive-source-kernel-synthesis",
        "task:construct-certify-discriminate-finite-kernels",
        "task:repair-and-pass-collar-source-control",
        "task:reconstruct-canonical-collar-multifield-ray",
        "task:retain-source-reference-amplitude",
        "task:integrate-given-free-source-jointly",
        "task:reconstruct-complete-nongaussian-car-link",
        "task:close-original-recursive-word-memory",
        "task:retain-full-original-source-through-regulator-and-readout",
        "task:execute-original-shared-higgs-source-and-local-rp-sewing",
        "task:reduce-whole-constant-original-higgs-spectral-fiber",
        "task:resolve-original-geometric-higgs-residue-sign-and-field-map",
        "task:evaluate-original-local-higgs-heat-coefficient-compatibility",
        "task:evaluate-whole-variable-bound-higgs-reference-and-scale-map",
        "task:execute-original-inner-higgs-scale-and-normal-kernel-map",
        "task:execute-given-superconnection-grades-and-whole-normal-spectral-reader",
        "task:evaluate-own-admissibility-and-whole-total-chiral-spectral-readers",
        "task:derive-whole-scale-energy-profile-and-relative-flow",
        "task:execute-original-green-energy-producer-and-mixed-scale-readout",
        "task:resolve-current-spectral-action-argument-and-common-higgs-gravity-weights",
        "task:execute-whole-original-curvature-consumers-and-higgs-radial-source",
        "task:execute-original-four-ghost-admissibility-source-and-geometric-type-test",
        "task:execute-original-moving-normal-kernel-derivative-and-source-response",
        "task:test-original-fixed-o1-source-and-normal-operator-placement",
        "task:test-whole-higgs-mixture-against-covariance-only-modular-reader",
        "task:test-exact-bounded-cutoff-higgs-normalization-at-fixed-rank",
        "task:test-whole-original-circle-joint-mode-ir-higgs-normalization",
        "task:classify-original-o1-mode-covariance-versus-whole-higgs-law",
        "task:reconstruct-original-whole-process-localization-before-geometric-readout",
        "task:test-bare-native-code-word-compression-for-original-locality",
        "task:decide-original-quarter-geometric-local-time-and-interval-source-reader",
        "task:derive-actual-regional-two-face-partner-and-supported-charged-word",
        "task:derive-original-color-marginal-modular-law-and-complete-source-reader",
        "task:reconstruct-common-higgs-law-from-whole-original-quarter-source",
        "task:execute-original-record-action-on-doily-and-ordered-source-response",
        "task:localize-original-record-process-and-test-unchanged-source-exterior",
        "task:execute-original-elliptic-supported-insertion-and-causal-source-test",
        "task:execute-original-mixed-higgs-color-group-response",
        "task:execute-whole-original-graph-color-selector-and-relative-reader",
        "task:execute-original-color-fixed-field-source-and-first-graded-matter-test",
        "task:execute-original-color-spin-mixed-four-word-and-full-sector-sewing",
        "task:execute-original-color-density-and-coordinate-region-descent",
        "task:execute-original-calderon-operation-and-full-source-response",
        "task:execute-original-c6-entire-word-expansion-and-source-amplitude",
        "task:execute-original-collective-higgs-force-source-and-mean-dual",
        "task:execute-original-allmode-force-with-actual-time-and-whole-source",
        "task:execute-original-local-spacetime-force-source-and-causal-lift"
      ],
      "strategyIds": [
        "strategy:repeat-known-car-synthesis-calibration",
        "strategy:repeat-finite-positive-kernel-calibration",
        "strategy:trace-and-joint-ward-select-fixed-fields",
        "strategy:complete-kernel-to-nongaussian-functional",
        "strategy:repair-ns-vector-matter-by-local-composites",
        "strategy:repeat-given-quarter-gns-feedback-control",
        "strategy:exact-kernel-and-common-insertion-identification",
        "strategy:repeat-e8-single-anchor-weyl-polynomial-search",
        "strategy:repeat-sm-preserving-family-four-cycle-native-clock-search",
        "strategy:reuse-whole-coupled-source-and-test-first-original-oneform",
        "strategy:identify-fixed-scalar-quarter-beta-with-original-pfaffian-source",
        "strategy:rescan-constant-whole-clutch-for-selected-protected-three-modes",
        "strategy:rescan-common-leading-distance-clutch-for-original-flavor",
        "strategy:d5-zero-mode-commutator-as-odd-hardy-background-generator",
        "strategy:infer-yukawa-hierarchy-and-ckm-from-two-directed-hardy-entries",
        "strategy:compensate-hardypair-quarter-character-with-native-clock-adjoint",
        "strategy:replace-whole-marked-hardy-reader-by-linear-spectral-centralization",
        "strategy:enumerate-finite-compatibility-as-unique-physical-source-selector",
        "strategy:infer-original-locality-from-bare-native-code-weyl-commutators",
        "strategy:identify-actual-quarter-local-modular-time-with-geometric-current-point-flow",
        "strategy:identify-proper-opposite-face-alone-as-canonical-local-purification-partner",
        "strategy:complete-original-higgs-color-source-from-two-and-four-words-only",
        "strategy:reconstruct-common-radial-higgs-law-from-entire-original-quarter-occupation-tower",
        "strategy:identify-unchanged-primitive-free-quarter-covariance-with-integrated-nontrivial-higgs-source",
        "strategy:derive-original-record-action-on-doily-and-ordered-source-response",
        "strategy:identify-doily-compatible-point-with-unitary-record-output-and-causal-event",
        "strategy:canonical-split-localization-of-original-source-records-with-state-and-region-audit",
        "strategy:actual-elliptic-source-equilibrium-versus-causal-current-response",
        "strategy:original-coupled-higgs-color-holonomy-response-versus-free-quillen",
        "strategy:whole-source-color-selection-versus-one-face-postselection",
        "strategy:original-color-center-fixed-source-and-charged-ward-words",
        "strategy:identify-unchanged-folded-ns-source-as-whole-original-color-current-net",
        "strategy:identify-full-marked-spin-source-from-unmarked-heat-partition-alone",
        "strategy:replace-actual-spin-cartan-insertion-with-original-scalar-cover-phase",
        "strategy:execute-original-color-density-and-coordinate-region-descent",
        "strategy:execute-original-calderon-operation-and-full-source-response",
        "strategy:close-original-marked-source-from-undecorated-transfer-and-finite-injectivity",
        "strategy:reuse-original-c6-entire-word-expansion-before-marked-field-coupling",
        "strategy:reuse-recovered-historical-source-and-native-timed-consumer-before-primitive-matching",
        "strategy:original-collective-higgs-force-source-before-any-new-classical-measure",
        "strategy:whole-original-circle-force-actual-time-before-classical-higgs-identification",
        "strategy:original-supported-force-source-before-new-geometric-measure",
        "strategy:einstein-noether-four-origin-hypotheses-first-structural-tests"
      ],
      "connectionIds": [
        "connection:operator-synthesis-to-positive-kernel",
        "connection:multifield-collar-to-original-time",
        "connection:joint-source-functional-to-origin-selection",
        "connection:actual-whole-source-to-universalraum-futures",
        "connection:source-q-spin-kernels-to-native-theta-clock-insertion"
      ],
      "reviewedAttemptIds": [
        "contract:seam-operator-synthesis-20261015",
        "contract:seam-positive-kernel-search-20261015",
        "contract:seam-collar-multifield-20261016"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:reverse-bootstrap-physical-field-dictionary",
      "titleEN": "Origin reverse selection, field dictionary and original P1 kernel",
      "questionEN": "What does reverse selection of P1/P2 give for concrete local fields and multi-field responses, and which identification with the original P1 kernel has actually been proved?",
      "topicIds": [
        "topic:origin",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:reverse-bootstrap-e8-closure-framework",
        "premise:local-e8-current-response-realization",
        "premise:quarter-phase-retained",
        "premise:typed-source-structures",
        "premise:literal-microscopic-charged-scaling-and-v988-slater-data",
        "premise:original-v988-periodic-zero-mode-state-comparison"
      ],
      "findingIds": [
        "finding:known-fourmark-system-has-three-and-five-canonical-views",
        "finding:reverse-bootstrap-retained-operator-scope",
        "finding:e8-current-dictionary-all-separated-responses",
        "finding:charged-scaling-microscopic-map-still-unspecified",
        "finding:original-slater-proxy-fitted-bound-fails-actual-norm",
        "finding:periodic-microscopic-zero-modes-distinguish-source-state",
        "finding:r097-original-q-twins-are-integrally-conjugate-before-fixed-source-form"
      ],
      "taskIds": [
        "task:explicit-e8-all-current-response-reader",
        "task:audit-actual-charged-scaling-source-reproduction"
      ],
      "strategyIds": [
        "strategy:reuse-e8-complete-separated-current-response",
        "strategy:replace-microscopic-charged-map-by-abstract-fock-refinement",
        "strategy:reuse-proved-fourmark-three-five-views"
      ],
      "connectionIds": [
        "connection:reverse-bootstrap-field-response-to-automated-operator-source-synthesis",
        "connection:reverse-bootstrap-field-response-to-common-source-state-event-selection"
      ],
      "reviewedAttemptIds": [
        "contract:seam-collar-multifield-20261016",
        "contract:seam-joint-ward-state-20261014",
        "contract:e-series-source-reconstruction-20261024"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:fundamental-process-classification",
      "titleEN": "Observable reality: minimal conditions and counterworlds",
      "questionEN": "Which operational conditions are independently required, which inequivalent models satisfy them, and which observable distinctions remain for selection?",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T8",
        "goal:universalraum"
      ],
      "acceptedPremiseIds": [
        "premise:foundational-reset-no-target-input",
        "premise:finite-event-poset",
        "premise:finite-deterministic-joint-replication-control",
        "premise:finite-update-observation-errors",
        "premise:finite-operational-composition-action",
        "premise:repeatable-distinction-benchmark",
        "premise:three-explicit-observability-countermodels",
        "premise:finite-prefix-consistent-sequential-data"
      ],
      "findingIds": [
        "finding:replicated-deterministic-consistency-iff-influence-dag",
        "finding:three-binary-processes-two-copy-reversible-classification",
        "finding:independent-poset-information-composition-consequences",
        "finding:reset-diagnosis-not-global-tfpt-underdetermination",
        "finding:three-inequivalent-repeatable-observation-countermodels",
        "finding:repeatable-reports-do-not-imply-full-state-stability",
        "finding:finite-sequential-data-admit-classical-history-realization"
      ],
      "taskIds": [
        "task:compare-four-independent-foundations",
        "task:assess-record-preserving-composition-principle",
        "task:compare-minimal-observable-counterworlds",
        "task:ground-observable-discriminator-constraints"
      ],
      "strategyIds": [],
      "connectionIds": [],
      "reviewedAttemptIds": [
        "contract:foundational-process-classification-20261016"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:carrier-pascal-glue-formal-scope",
      "titleEN": "Formal carrier core: unbounded Pascal uniqueness and finite glue",
      "questionEN": "Which carrier and glue statements are already present in the papers and Lean sources, and which physical selection does not follow?",
      "topicIds": [
        "topic:e8",
        "topic:origin",
        "topic:validation"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "acceptedPremiseIds": [
        "premise:pascal-carrier-exhaustion-equation",
        "premise:specified-finite-carrier-discriminant-form",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:pascal-carrier-rank-unique-unbounded-source-proof",
        "finding:finite-carrier-glue-elements-orbits-and-halfway"
      ],
      "taskIds": [
        "task:review-unbounded-pascal-source",
        "task:review-finite-glue-source-scope"
      ],
      "strategyIds": [
        "strategy:reuse-unbounded-pascal-carrier-proof",
        "strategy:reuse-explicit-finite-glue-classification"
      ],
      "connectionIds": [],
      "reviewedAttemptIds": [],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Active mathematical program: marked seam monodromies and lattice lifts",
      "questionEN": "Which marked seam/lattice transport geometries, lift classes and local-coefficient invariants arise from existing clock/reflection/quartic data? First complete case: sign lifts of fourJ representation on CP1 minusμ4.",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "acceptedPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:existing-marked-cyclic-cover-and-burau-model",
        "premise:joint-native-compiler-cover-covariance-category",
        "premise:marked-c4-unitary-local-extension-reconstruction-class",
        "premise:connected-local-same-conformal-compiler-extension-with-generator",
        "premise:fixed-native-reflection-rotation-character-markings",
        "premise:ordered-quarter-clock-pure-hurwitz-equivalence",
        "premise:standard-e8-root-cut-full-flag-incidence-category",
        "premise:scalar-eight-channel-twist-and-explicit-compiler-charge-chart",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:four-d8-sectors-with-fixed-affine-source-time"
      ],
      "findingIds": [
        "finding:marked-seam-category-and-character-valued-full-lift-factor",
        "finding:quarter-clock-sign-lift-complete-four-puncture-classification",
        "finding:quarter-lift-central-quotient-class-and-all-subgroup-restrictions",
        "finding:native-clock-reflection-full-factor-cocycle-trivialization",
        "finding:native-quartic-exterior-local-cohomology-distinguishes-clock-monodromies",
        "finding:orbifold-lift-criterion-and-determinant-eight-divisibility",
        "finding:original-g31-reflection-census-and-all-integral-cohomology",
        "finding:all62-original-clock-obstructions-and-central-variants",
        "finding:actual-sign-lift-g31-group-comparison",
        "finding:complete-g31-lift-invariants-and-explicit-collisions",
        "finding:e7-quarter-pairs-literal-native-g31-reflections",
        "finding:e6-root-subsystem-quarter-clock-discriminant-obstruction",
        "finding:e-series-square-cover-family-and-quarter-descent",
        "finding:e-series-integral-glue-and-normalization-nonidentifiability",
        "finding:global-original-g31-character-lift-nonsplitting",
        "finding:all62-original-character-clock-lifts-complete",
        "finding:all17-original-character-monodromy-lifts-complete",
        "finding:e7-pair-full-lattice-field-character-torsor",
        "finding:e-series-complete-native-compiler-cut-dictionary",
        "finding:common-cover-clock-and-maximal-integral-phi12-intertwiner",
        "finding:native-four-cut-projectors-unify48-fourthirds-fivequarters",
        "finding:complete-covariant-compiler-voa-source-and-weyl-closure",
        "finding:complete-fixed-jhat-cyclic-field-lift-and-associated-clock",
        "finding:relative-native-burau-clock-hom-faithful12-transport",
        "finding:e6-vertex-nonselection-survives-full-field-clock-phases",
        "finding:marked-c4-glue-unique-local-e8-vacuum-source",
        "finding:canonical-vacuum-clock-preserves-e6-nonselection",
        "finding:marked-generator-forces-e8-without-support-multiplicity-or-minimality-input",
        "finding:native-reflection-rotation-lift-classes-and-forgetful-images",
        "finding:quarter-clock-pure-mapping-class-complete-quotient",
        "finding:e8-cut-five-orbital-incidence-algebra-complete",
        "finding:compiler-d8-frame-requires-full-d5-a3-flag",
        "finding:tetrahedron-incidence-lossless-e6-reconstruction",
        "finding:restricted-clock-lift-and-global-cover-audit-reconciled",
        "finding:double-scalar-quarter-is-marked-glue-with-two-step-index",
        "finding:scalar-quarter-two-involutive-e8-extensions",
        "finding:native-quarter-glue-inner-conjugacy-and-oriented-tetrahedron-flags",
        "finding:native-cyclic-compiler-inner-conjugacy",
        "finding:recovered-e6-closed-81-current-module-and-unique-source-cubic",
        "finding:e-series-operational-role-review-and-source-time-centralizer"
      ],
      "taskIds": [
        "task:define-marked-seam-transport-category",
        "task:classify-quarter-clock-four-puncture-sign-lifts",
        "task:compute-quarter-central-quotient-restrictions",
        "task:compute-native-g0-full-factor-class",
        "task:compute-native-456-local-cohomology",
        "task:classify-unrestricted-g31-reflection-monodromy",
        "task:compute-lift-class-beyond-native-g0",
        "task:classify-reflection-equivariant-and-mapping-class-seam-lifts",
        "task:completed-equivariant-study-0",
        "task:completed-equivariant-study-2",
        "task:completed-equivariant-study-3",
        "task:completed-equivariant-study-4",
        "task:e-series-slices-under-actual-quarter-clock",
        "task:completed-original-g31-character-monodromy-lifts",
        "task:complete-e7-pair-all-field-dictionary",
        "task:complete-native-compiler-e-series-cut-dictionary",
        "task:complete-cover-clock-actual-carrier-dictionary",
        "task:complete-shared48-fourthirds-fivequarters-consequence",
        "task:complete-joint-native-compiler-cover-covariance",
        "task:reconstruct-canonical-compiler-field-source-from-c4",
        "task:eliminate-redundant-c4-support-and-multiplicity-inputs",
        "task:native-quarter-equivariant-markings",
        "task:pure-quarter-clock-mapping-class-quotient",
        "task:complete-e6-incidence-and-lossless-tetrahedron-transform",
        "task:identify-scalar-glue-and-native-cyclic-clock-class"
      ],
      "strategyIds": [
        "strategy:reuse-complete-quarter-clock-monodromy-normal-forms",
        "strategy:reuse-original62-clock-obstruction-classification",
        "strategy:reuse-global-g31-character-lift-decision",
        "strategy:reuse-complete-e-series-compiler-closure",
        "strategy:reuse-complete-covariant-compiler-cover-source",
        "strategy:reuse-marked-c4-vacuum-source-reconstruction",
        "strategy:reuse-generator-forced-local-e8-completion",
        "strategy:reuse-lossless-e6-tetrahedron-incidence",
        "strategy:reuse-native-glue-cyclic-inner-conjugacy",
        "strategy:identify-uniform-scalar-quarter-with-native-clock-over-fixed-d8",
        "strategy:reuse-reviewed-e-series-field-roles-and-completed-e6-cubic"
      ],
      "connectionIds": [],
      "reviewedAttemptIds": [
        "contract:marked-seam-monodromy-20261023",
        "contract:equivariant-monodromy-20261023",
        "contract:e-series-quarter-clock-20261023",
        "contract:global-g31-lattice-lift-20261023",
        "contract:e-series-compiler-closure-20261023",
        "contract:e-series-joint-source-20261023",
        "contract:e-series-source-reconstruction-20261024",
        "contract:seam-equivariant-active-search-20261024",
        "contract:e-series-incidence-algebra-20261024"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Common clock sectors, quartic geometry and operational reconstruction",
      "questionEN": "Which previously separate data of the original TFPT core follow from a common clock and representation geometry, and which complete finite measurement classification follows without asserting physical source selection?",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "acceptedPremiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:marked-c4-unitary-local-extension-reconstruction-class",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:original-six-ovoid-covariant-instrument-category",
        "premise:relational-native-quartic-tensor-sector-without-state-selection",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:declared-p1-p2",
        "premise:native-tensor-povm-and-coherent-source-category",
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-microscopic-qwz-integer-car-edge-limit",
        "premise:full-graded-car-with-original-positive-time",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:original-seam-pair-and-full-moment-os-statements",
        "premise:strong-seam-covariance-and-same-pair-index",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:given-quarter-circle-full-heat-transfer-comparison",
        "premise:original-a4-same-moebius-order-four-pin-lift",
        "premise:fixed-marked-glue-and-retained-source-d8-frame",
        "premise:standard-four-d8-module-parent-with-retained-subtheories",
        "premise:same-original-circle-trace-class-covariance",
        "premise:existing-finite-orthogonal-carrier-on-same-source",
        "premise:original-admissibility-and-graded-source-interfaces",
        "premise:typed-source-structures",
        "premise:trace-class-polarization-pair-with-restricted-unitary",
        "premise:smooth-matrix-clutch-on-original-negative-fourier-sea",
        "premise:actual-finite-ns-kernel-and-sampled-original-winding",
        "premise:given-normal-spin-line-and-genuine-circle-product",
        "premise:given-exact-reducing-indexline-with-horizontal-connection",
        "premise:positive-determinant-response-of-transverse-product-channels",
        "premise:closed-normal-fredholm-with-retained-complex-kernel-representation",
        "premise:smooth-matrix-circle-source-and-moving-projector-with-fixed-scalar-symbol",
        "premise:oriented-d3-tetrahedron-in-bloch-chart-versus-original-quarter-marks",
        "premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images",
        "premise:natural-joint-spin-family-lift-with-given-split-connection",
        "premise:fixed-kappa-toral-third-centralizing-split-carrier",
        "premise:same-angle-evaluation-of-primitive-determinant-clutch-as-native-clock",
        "premise:native-cartan-four-in-full-clock-conjugate-source",
        "premise:primitive-normal-sphere-joint-k-bundle-class-two",
        "premise:given-same-normal-base-degree-pullback",
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:existing-elliptic-curve-with-specified-normal-spin-factor",
        "premise:existing-cut-cover-car-with-actual-winding-and-sea",
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover",
        "premise:declared-recursive-native-som-update",
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:given-pin-source-conformal-normal-geometry-probes",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:theta-square-modular-transport-with-distinct-geometric-clock",
        "premise:fixed-three-slot-permutation-and-original-compiler-comparison",
        "premise:same-marked-elliptic-annulus-massless-conformal-metric-family",
        "premise:positive-joint-car-source-tested-against-full-geometric-projector",
        "premise:actual-elliptic-half-form-l2-trace-on-full-marked-equator",
        "premise:genuine-d4-unitary-stable-parabolic-orbifold-descent",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:normal-even-sea-car-source-and-canonical-graded-hs-double",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:ordinary-rigidified-genus-two-theta-determinant-functor",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:same-spin-hardy-shift-against-identity-with-grading-retained",
        "premise:standard-chiral-spin-trace-on-original-cubic-disk-pullback",
        "premise:conditional-three-sheet-negative-sea-car-source",
        "premise:marked-theta-frame-with-explicit-primitive-gaussian-root-normalization",
        "premise:two-theta-lattice-voas-with-given-geometric-faithful-c12-lift",
        "premise:connected-local-same-conformal-compiler-extension-unselected-support",
        "premise:four-d8-sectors-with-fixed-affine-source-time",
        "premise:marked-local-e8-completion-with-original-source-time-and-euclidean-clustering",
        "premise:specified-petersen-shell-and-full-family-finite-recursions",
        "premise:marked-oriented-quarter-spin-and-two-object-vertex-transport",
        "premise:natural-single-face-inclusion-in-given-family-calderon-graph",
        "premise:oriented-five-slot-hodge-candidate-with-explicit-basis-readout",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:given-full-e8-current-source-with-fixed-carrier-su5",
        "premise:specified-inclusive-current-response-with-invariant-metric",
        "premise:specified-old-j20-instrument-in-fixed-six-mark-duad-chart",
        "premise:specified-conjugate-su5-covariant-petersen-channel",
        "premise:fixed-three-plus-two-mark-and-typed-original-degree-clock",
        "premise:specified-cptp-source-process-with-p5-saturation",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:two-actual-source-events-with-coherent-record-access",
        "premise:stipulated-e8-h8-with-original-color-center-selector",
        "premise:actual-single-source-event-coherent-stinespring-record",
        "premise:native-pauli-clock-family-with-marked-f20-inclusion",
        "premise:given-e8-fold-matrix-with-retained-source-charge-and-p2-grading",
        "premise:given-eightfold-even-car-quotient-with-marked-charge-and-source-time",
        "premise:ordinary-weyl-product-and-explicit-reflection-type-comparison",
        "premise:existing-normal-thermal-source-with-bounded-neutral-insertions",
        "premise:finite-reflected-spectral-weight-preservation-test",
        "premise:original-v252-real-finite-block-and-selfdual-field-test",
        "premise:full-projector-car-marginal-and-commuting-joint-algebra",
        "premise:actual-quarter-neutral-vacuum-current-core",
        "premise:actual-local-weyls-and-finite-fiber-coordinate-target",
        "premise:neutral-current-recognition-with-actual-time-state-and-local-image",
        "premise:actual-product-collar-two-face-data",
        "premise:charged-car-pure-two-face-cauchy-graph-state",
        "premise:constant-finite-dirac-product-mixed-current-test",
        "premise:given-finite-sm-triple-yukawa-inputs",
        "premise:paired-quarter-external-lowest-block-candidate",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:fixed-frame-graded-normal-dependent-source-family",
        "premise:given-quarter-many-body-source-and-compact-dirac-comparison",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:fixed-local-quarter-channel-in-constant-odd-source",
        "premise:fixed-puncture-spinor-extension-with-integral-selfdual-pairing"
      ],
      "findingIds": [
        "finding:actual-clock-doily-ovoid-kernel-is-native-quartic-five",
        "finding:glue-clock-twisted-sectors-share-marked-quadratic-module",
        "finding:complete-native-six-effect-covariant-instrument-classification",
        "finding:native-six-effect-readout-on-existing-erasure-output",
        "finding:relational-quartic-singlet-and-invariant-density-separation",
        "finding:new-clock-feedback-origin-input-audit",
        "finding:native-event-channel-cone-intersection-is-tenth-to-half",
        "finding:native-six-ovoid-observation-first-occurs-at-tensor-degree-three",
        "finding:original-quartic-erasure-and-hamming-octic-share-marked-ovoid-response",
        "finding:native-octic-field-ray-is-explicit-but-retained-clock-stress-preparation-fails",
        "finding:actual-quarter-fold-stress-has-nonzero-octic-eighth-jet",
        "finding:native-octic-is-an-original-even-car-current-composite",
        "finding:original-geometric-source-jet-and-partial-p1-seed-closure",
        "finding:full-root-ope-has-normalized-native-octic-component",
        "finding:paper-microscopic-car-composes-with-native-octic-ward",
        "finding:microscopic-neutral-octic-has-controlled-smeared-limit",
        "finding:paper-seed-source-needs-local-image-not-global-equivalence",
        "finding:full-car-positive-time-forces-source-vacuum",
        "finding:original-winding-theorem-does-not-select-seam-ray",
        "finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel",
        "finding:original-os-step-needs-full-moments-not-connected-cumulants",
        "finding:graded-field-image-precedes-physical-observable-restriction",
        "finding:older-original-circle-representative-already-realizes-ward-and-index",
        "finding:old-quarter-heat-transfer-has-controlled-rank-one-limit-and-odd-product",
        "finding:historical-em-rank-one-and-full-heat-traces-have-different-contracts",
        "finding:older-frg-functional-already-supplies-formal-full-moment-parent",
        "finding:earliest-c3-route-quantizes-level-but-needs-physical-kinetic-normalization",
        "finding:canonical-positive-circle-half-selects-the-toeplitz-line-and-sixth-order-correction",
        "finding:old-seam-shift-canonically-gives-relative-car-line-and-fredholm-factor",
        "finding:old-index-coupling-removes-heat-map-and-has-sharp-residual-ward-test",
        "finding:original-admissibility-requires-image-membership-not-positive-half-or-commutation",
        "finding:old-closure-already-assumes-car-but-does-not-map-the-geometric-circle",
        "finding:historical-uv-map-infinite-mass-exclusion-already-proved-and-recovered",
        "finding:a4-spin-lift-fixes-local-ns-and-unordered-quarter-pair",
        "finding:cover-winding-exchanges-quarter-sectors-before-its-square",
        "finding:retained-winding-preserves-local-support-and-neutral-time",
        "finding:marked-glue-square-is-the-e8-fermionization-character",
        "finding:fixed-canonical-d8-is-not-transported-source-d8",
        "finding:actual-winding-has-four-module-e8-defect-extension",
        "finding:ramond-lift-sign-is-common-intertwiner-basis-gauge",
        "finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class",
        "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor",
        "finding:schur-carrier-plus-complement-preserves-original-relative-determinant",
        "finding:v258-forward-source-gap-is-reused-not-solved-by-inversion",
        "finding:one-sided-source-and-real-em-norm-need-response-map-not-chiral-phase",
        "finding:trace-class-pair-index-fixes-relative-factor-without-primitive-ray",
        "finding:matrix-clutch-degree-connects-weak-determinant-class-without-ray-selector",
        "finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index",
        "finding:inner-carrier-is-infinite-spacetime-module-not-finite-circle-cut",
        "finding:normal-spin-determinant-line-exactly-transports-whole-circle-in-given-product",
        "finding:normal-index-line-source-match-is-holonomy-condition-not-vertical-degree",
        "finding:full-normal-product-polarization-change-is-not-trace-class",
        "finding:massive-transverse-zero-index-retains-positive-determinant-response",
        "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel",
        "finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection",
        "finding:tetrahedral-quarter-face-phase-does-not-identify-original-quarter-marked-curve",
        "finding:existing-elliptic-cover-correspondence-has-exact-c6-image-and-retained-mixed-clock",
        "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
        "finding:global-split-joint-carrier-admits-parallel-native-c12-clock",
        "finding:pure-weak-clutch-clock-identification-fails-despite-quarter-matches",
        "finding:same-chern-clutch-native-compiler-does-not-select-physical-connection",
        "finding:native-gaussian-four-is-cartan-subspace-in-whole-sixtyfour",
        "finding:native-family-factor-is-not-gaussian-four-despite-symmetric-coincidences",
        "finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice",
        "finding:even-degree-pullback-removes-cartan-topology-without-selecting-clock-cover",
        "finding:global-cartan-choice-is-optional-for-original-scalar-source-fields",
        "finding:bare-native-octic-is-not-whole-e8-zero-mode-singlet",
        "finding:explicit-primary-e8-invariant-octic-completes-same-neutral-car-source",
        "finding:completed-octic-has-exact-old-root-ope-component-and-quarter-source-value",
        "finding:elliptic-normal-spin-pullback-doubles-index-and-deck-quarter-lifts-anticommute",
        "finding:exact-separated-w8-twopoint-in-original-quarter-current-source",
        "finding:unshifted-vacuum-fails-same-w8-source-state-time-dictionary",
        "finding:local-current-phase-and-conditional-cyclic-p1-w8-image",
        "finding:all-neutral-w8-correlations-identify-the-two-original-quarter-charges",
        "finding:original-w8-response-has-infinite-same-time-spectral-support",
        "finding:older-seam-equivalence-verifications-do-not-supply-marked-local-p1-map",
        "finding:full-original-c1-stress-cycle-reconstructs-neutral-w8-response",
        "finding:folded-c8-cycle-misses-intrinsic-w8-tangent-without-obstructing-original-stress",
        "finding:native-source-first-nonuniform-moment-is-four-with-literal-five",
        "finding:native-whole-five-ground-space-needs-four-register-interaction",
        "finding:old-cover-winding-reconstructs-local-quarter-current-net",
        "finding:untransported-independent-quarter-stress-pair-is-not-current",
        "finding:current-public-paper-bytes-and-binding-source-gaps-recovered",
        "finding:winding-charge-conjugation-descends-fixed-pin-domain-but-not-full-dirac-sea",
        "finding:native-fourth-root-frame-has-signed-collective-sixty-mode-dual",
        "finding:native-root-gram-spectrum-is-not-canonical-source-energy-selection",
        "finding:identical-overlapping-native-five-codes-have-no-common-state",
        "finding:horizontal-e8-invariant-octic-cannot-isolate-native-five-ground-space",
        "finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea",
        "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity",
        "finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp",
        "finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum",
        "finding:declared-recursive-native-som-is-u35-equivariant",
        "finding:declared-recursive-native-som-clocks-depend-on-chosen-rates",
        "finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower",
        "finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent",
        "finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms",
        "finding:finite-crosscap-cauchy-state-is-not-original-quarter-vacuum-by-normal-filtering",
        "finding:native-quartic-relative-arc-charge-excludes-additive-density-stress-insertion",
        "finding:retained-quarter-sea-finite-modular-transfer-preserves-integrated-native-cartan",
        "finding:original-neutral-interarc-fields-have-exact-connected-current-vertex-reconstruction",
        "finding:actual-pin-zero-branch-retains-quarter-car-state-time-but-no-uniform-scale-return",
        "finding:conformal-pin-source-geometry-fixes-exterior-return-and-unitary-memory",
        "finding:geometric-exterior-schur-response-transfers-proper-native-arc-charge-but-is-compact",
        "finding:actual-ns-half-cover-cauchy-graph-purifies-green-state-with-neutral-ground-time-obstruction",
        "finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots",
        "finding:full-marked-equatorial-pullback-is-ramified-graph-not-smooth-seam-circle",
        "finding:same-elliptic-szego-green-functional-has-all-word-free-rp-and-calderon-marginal",
        "finding:elliptic-scalar-spin-pushforward-has-original-holomorphic-p2-anchor",
        "finding:natural-elliptic-anchor-connection-is-not-original-p2-cusp-connection",
        "finding:actual-elliptic-gaussian-source-determines-full-quarter-current-functional",
        "finding:elliptic-current-state-differs-from-hardy-on-every-proper-current-interval",
        "finding:primitive-geometric-force-retains-coupled-reference-and-parity-variation",
        "finding:equal-finite-positive-heat-channel-values-do-not-fix-geometric-force",
        "finding:elliptic-ns-spin-trace-has-complete-global-quarter-kernel",
        "finding:source-induced-ramified-resolutions-do-not-select-quarter-circle-domain",
        "finding:fixed-native-and-fermat-c3-carriers-do-not-identify-marked-v117-pair",
        "finding:theta-square-modular-pair-reconstructs-v117-with-distinct-geometric-q",
        "finding:archived-d4-puncture-formula-fails-and-existing-v117-repairs-existence",
        "finding:geometric-square-clock-is-not-theta-v117-quarter-generator",
        "finding:canonical-conformal-boundary-trace-fixes-existing-elliptic-cauchy-state",
        "finding:conformal-factor-averaging-preserves-given-free-boundary-wick-words",
        "finding:retained-seam-defect-has-derived-causal-geometric-response-with-contact",
        "finding:same-final-pin-geometry-retains-history-while-relative-index-factor-is-fixed",
        "finding:full-projector-covariance-and-positivity-force-all-car-words",
        "finding:actual-two-face-projector-reduces-free-source-test-to-cross-coherence",
        "finding:retained-marked-quarter-compiler-has-no-local-geometric-wick-correction",
        "finding:changed-elliptic-modulus-has-derived-cauchy-response-and-neutral-fourfield-variance",
        "finding:actual-equatorial-half-form-trace-fixes-orthogonal-hardy-range",
        "finding:actual-holomorphic-quarter-cauchy-idempotents-are-not-positive-car-covariances",
        "finding:full-equatorial-checkerboard-free-algebra-fails-fixed-reflection-positivity",
        "finding:genuine-d4-orbifold-branch-has-unique-irreducible-v117-class",
        "finding:wall-weight-additivity-does-not-exclude-stable-v117-parabolic-bundle",
        "finding:recovered-september-c4-triangle-closes-original-a0star-monodromy",
        "finding:actual-a0star-connection-does-not-have-rational-base-inversion-lift",
        "finding:actual-v117-sign-lines-are-negative-weierstrass-triangle-two-torsion",
        "finding:antipodal-and-positive-sign-packets-fail-actual-marked-v117-ramification",
        "finding:common-cyclic-twelve-cover-does-not-trivialize-v117-unramified-sign-lines",
        "finding:negative-sign-packet-has-source-selected-quarter-clock-lift",
        "finding:original-root-and-sign-lines-have-minimal-degree48-common-cover",
        "finding:given-elliptic-flat-connection-family-has-explicit-quillen-norm-and-two-holonomies",
        "finding:bare-large-gauge-quillen-norm-does-not-equal-original-winding-counting-factor",
        "finding:existing-elliptic-half-period-has-canonical-graded-gns-intertwiner",
        "finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law",
        "finding:declared-recursive-machine-baseline-controls-and-recovery-are-finitely-measured",
        "finding:declared-recursive-machine-long-run-retains-motion-at-stable-aggregate-rank",
        "finding:recursive-kohonen-source-investigation-has-source-verified-atlas-handoff",
        "finding:chat-algorithmic-comparison-native-pauli-code-and-scoped-information-loss",
        "finding:chat-20261026-results-consolidated-with-corrected-assumptions",
        "finding:source-inversion-forces-six-line-theta-completion",
        "finding:literal-geometric-quarter-is-not-central-gaussian-quarter-on-labels",
        "finding:source-cubic-and-quarter-select-even-theta-and-spin-half-turn-lift",
        "finding:source-cubic-matches-native-pauli-translations-after-context-target-correction",
        "finding:joint-source-clock-relations-have-one-native-clifford-gauge-class",
        "finding:ordinary-theta-determinant-erases-selected-spin-central-character",
        "finding:marked-negative-point-norm-restores-required-spin-central-character",
        "finding:point-normalized-theta-family-correction-fails-original-cubic-action",
        "finding:source-spin-relative-poincare-normalization-closes-point-norm-family",
        "finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package",
        "finding:tfpt-origin-investigation-full-source-coverage-and-current-frontier",
        "finding:full-clock-norm-power-class-and-canonical-eighth-period",
        "finding:original-unit-winding-selects-one-inverse-norm-in-three-cabled-hardy-pair",
        "finding:original-boundary-audit-and-h1-point-restriction-limit",
        "finding:eta-phase-conventions-do-not-identify-relative-spin-reference-pair",
        "finding:same-spin-unit-shift-gives-native-module-class-with-odd-determinant-line",
        "finding:original-even-odd-operator-split-is-compatible-with-same-spin-seam-reference",
        "finding:elliptic-projector-and-weyl-results-retain-their-source-type-at-cubic-spin-bridge",
        "finding:cubic-spin-cauchy-range-is-three-hardy-with-strong-domain-distinction",
        "finding:original-negative-sea-three-mode-ket-is-dual-to-required-hardy-line",
        "finding:auxiliary-theta-route-needs-no-physical-cubic-bulk-or-eta-selected-dual",
        "finding:primitive-gaussian-theta-frame-constructs-e8-pair-with-retained-spin-action",
        "finding:existing-c12-lift-induces-coherent-two-object-e8-vertex-groupoid",
        "finding:actual-winding-functional-calculus-preserves-ns-ramond-split",
        "finding:single-chiral-cycle-exchange-selects-e8-in-four-extension-class",
        "finding:affine-source-involution-pairs-full-d8-sector-spectra",
        "finding:marked-local-e8-with-unchanged-source-time-fails-euclidean-clustering",
        "finding:original-parity-audit-does-not-supply-local-spinor-gauging",
        "finding:hypergraph-local-update-repaired-with-full-family-clock",
        "finding:petersen-polar-step-has-exact-double-cover-family-intertwiner",
        "finding:petersen-source-current-and-hodge-candidates-fail-physical-identification",
        "finding:a7-clock-direction-identifies-neutral-e7-zero-root",
        "finding:oriented-sewing-cocycle-distinguishes-continuation-and-reversal",
        "finding:calderon-single-face-compression-is-not-perron-projector",
        "finding:hodge-born-magnitudes-and-filtered-petersen-jump-match",
        "finding:five-complement-amplitudes-form-full-petersen-quantum-channel",
        "finding:original-twenty-events-factor-through-hodge-and-conditional-phase-record",
        "finding:actual-e8-mixed-current-response-is-full-clifford-channel",
        "finding:carrier-su5-centralizer-gives-direct-e8-petersen-response",
        "finding:su5-covariance-and-petersen-support-fix-complete-quantum-response",
        "finding:neutral-pair-witness-separates-old-events-and-hodge-response",
        "finding:original-degree-clock-is-not-carrier-slot-cycle-at-fixed-source",
        "finding:full-mark-transport-and-isospectrality-do-not-select-hodge-channel",
        "finding:original-pair-source-fixes-state-but-not-selected-epsilon-process",
        "finding:single-positive-process-saturation-selects-full-hodge-channel",
        "finding:original-five-slot-wedge-is-exact-e8-hodge-coefficient",
        "finding:native-pauli-f20-metric-and-quarter-bridge",
        "finding:two-actual-coherent-events-herald-hodge-at-one-over-twenty-five",
        "finding:original-color-center-removes-only-extra-h8-ground-state",
        "finding:marked-symplectic-functor-fixes-native-hodge-kraus-space",
        "finding:f20-record-repair-removes-chart-induced-three-plus-two",
        "finding:theta-scalar-square-lift-is-distinct-from-symplectic-f20-lift",
        "finding:full-admissibility-vacuum-test-needs-source-image-and-transfer-reduction",
        "finding:canonical-native-spin5-hodge-is-already-one-source-record-subchannel",
        "finding:native-hodge-record-selector-is-image-projector-not-kraus-kernel",
        "finding:irreducible-f20-four-cannot-host-original-independent-native-family-clock",
        "finding:native-hodge-is-exact-collective-five-current-action",
        "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
        "finding:six-hodge-responses-have-exact-full-current-barycenter",
        "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts",
        "finding:spin5-hodge-five-is-plucker-kernel-not-original-quartic-hessian",
        "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
        "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
        "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
        "finding:old-ward-root-generates-exact-charged-fifty-module",
        "finding:tp-charged-bracket-support-forces-entire-carrier-marginal",
        "finding:original-ward-and-p2-grading-select-smaller-creation-thirty",
        "finding:charged-source-quarter-recovers-inverse-internal-glue",
        "finding:state-independent-creation-branch-removes-whole-process-hodge-demand",
        "finding:given-source-current-constructs-half-kink-spinor-transport",
        "finding:neutral-ward-response-needs-no-spinor-observable-membership",
        "finding:actual-source-sector-transport-distinguishes-identical-hodge-marginals",
        "finding:ordinary-weyl-type-obstruction-to-single-chiral-os-anti-anti-reflection",
        "finding:given-two-face-source-derives-opposite-neutral-weyls-and-bounded-time-reflection",
        "finding:verification-recovery-preserves-local-source-chain-and-eight-gate-completeness",
        "finding:positive-spectral-reweighting-does-not-establish-original-source-rp",
        "finding:gapped-quarter-energy-cannot-be-same-borchers-translation",
        "finding:finite-ko6-pairing-does-not-supply-standalone-pfaffian-source",
        "finding:full-free-projector-forces-joint-commuting-source-factorization",
        "finding:actual-neutral-current-source-has-constructive-moebius-standard-pair",
        "finding:continuous-local-current-weyls-cannot-live-in-finite-coordinate-fibers",
        "finding:actual-folded-current-ward-and-state-determine-all-neutral-words",
        "finding:mixed-vector-axial-current-is-existing-full-car-subalgebra",
        "finding:constant-product-time-stable-current-level-is-kernel-index",
        "finding:paired-quarter-source-candidate-needs-original-filter-and-oriented-conjugation",
        "finding:graded-boundary-clifford-typing-transports-full-scalar-and-finite-coupled-source",
        "finding:actual-charge-j-transport-retains-full-dirac-and-distinct-pairings",
        "finding:fixed-graded-chart-transports-normal-dependent-source-and-given-mixed-moments",
        "finding:neutral-many-body-source-time-is-not-finite-summable-geometric-dirac",
        "finding:actual-product-reflection-and-same-time-have-full-positive-clifford-source-intertwiner",
        "finding:actual-v252-positive-grade-has-global-p2-wedge-dictionary",
        "finding:old-quarter-full-source-embeds-locally-exactly-on-decoupled-channel",
        "finding:petersen-population-full-cptp-p5-range-zero-to-ten",
        "finding:marked-sm-phase-p5-exact-range-and-response-collision",
        "finding:shared-epsilon-tp-process-fixes-hodge-marginal-even-for-correlated-inputs",
        "finding:puncture-meridians-have-one-glue-class-and-residue-duality-does-not-select-metric",
        "finding:joint-integral-unimodular-charge-closure-uniquely-selects-complete-invariant-metric",
        "finding:meridian-spinor-joint-source-product-has-actual-family-root-simple-pole"
      ],
      "taskIds": [
        "task:reconstruct-actual-clock-doily-quartic",
        "task:unify-clock-glue-and-twisted-branches",
        "task:classify-native-six-effect-instruments",
        "task:connect-new-observable-to-existing-erasure-consumer",
        "task:separate-singlet-ray-from-physical-state-selection",
        "task:audit-feedback-loop-origin-premises",
        "task:compare-classified-channels-with-original-native-events",
        "task:derive-original-seam-selection-of-native-observable-process",
        "task:classify-minimum-native-ovoid-observation-stage",
        "task:close-original-quartic-erasure-derivative-dictionary",
        "task:identify-original-octic-field-and-test-clock-preparation",
        "task:derive-actual-quarter-fold-octic-stress-response",
        "task:reconstruct-octic-directly-in-original-car-and-geometric-jet",
        "task:recover-paper-microscopic-neutral-octic-chain",
        "task:correct-paper-source-identification-criterion",
        "task:repair-original-seam-ray-and-os-moment-identifications",
        "task:recover-older-circle-source-and-controlled-heat-closure",
        "task:close-direct-original-seam-defect-and-reweighting-interface",
        "task:close-original-spin-and-retained-source-defect-dictionary",
        "task:transport-original-seam-factor-through-faithful-kms-and-carrier",
        "task:close-pair-index-original-clutch-and-ns-limit-interface",
        "task:resolve-normal-index-line-and-full-source-pushforward-criterion",
        "task:compare-normal-connection-and-tetrahedral-cover-transport",
        "task:close-joint-lift-split-connection-and-native-clock-compatibility",
        "task:identify-native-cartan-four-and-global-joint-mark-transport",
        "task:complete-native-octic-under-existing-source-zero-mode-symmetry",
        "task:compute-source-w8-twopoint-and-assess-original-local-p1-map",
        "task:audit-older-seam-results-and-reconstruct-full-original-stress-cycle",
        "task:recover-original-winding-comparison-and-local-quarter-current-net",
        "task:assess-fixed-pin-descent-of-original-winding-conjugation",
        "task:resolve-full-pin-reflection-and-ns-cover-green-positivity",
        "task:realize-existing-quarter-source-on-concrete-elliptic-moebius-cut",
        "task:complete-full-elliptic-real-slots-and-test-marked-seam-and-p2-pushforward",
        "task:close-global-spin-kernel-and-test-modular-three-source-dictionary",
        "task:derive-real-equatorial-trace-and-recover-original-c4-monodromy-proof",
        "task:derive-entire-charge-metric-from-joint-completion"
      ],
      "strategyIds": [
        "strategy:reuse-primitive-b-u-reconstruction-and-full-os-repair",
        "strategy:reuse-recovered-original-circle-and-controlled-heat-ir",
        "strategy:reuse-direct-old-seam-defect-and-relative-weight",
        "strategy:reuse-historical-uv-profile-map-exclusion",
        "strategy:reuse-original-pin-and-actual-four-sector-defect",
        "strategy:identify-fixed-canonical-and-source-d8-by-identity",
        "strategy:extend-original-seam-relative-determinant-through-faithful-kms-and-actual-carrier-compression",
        "strategy:replace-full-thermal-winding-response-by-naive-finite-compression",
        "strategy:derive-seam-source-by-inverting-given-v258-dirac",
        "strategy:replace-rank-one-ray-selection-by-trace-class-pair-index-relative-determinant",
        "strategy:obtain-infinite-winding-factor-as-ordinary-finite-ns-determinant-limit",
        "strategy:normal-dirac-index-pushforward-to-original-circle-source",
        "strategy:extend-one-dimensional-ordinary-fredholm-factor-to-full-normal-product",
        "strategy:use-bosonic-callias-doublet-count-as-rank-one-source-index",
        "strategy:identify-tetrahedral-bloch-quartet-with-original-quarter-by-mobius",
        "strategy:reuse-existing-elliptic-cover-correspondence-with-full-c4-data",
        "strategy:reuse-global-joint-lift-with-native-clock-in-split-connection-centralizer",
        "strategy:identify-pure-weak-primitive-clutch-angle-with-native-full-compiler",
        "strategy:reuse-native-cartan-subspace-as-whole-source-little-weyl-dictionary",
        "strategy:identify-native-gaussian-four-directly-with-family-factor",
        "strategy:global-smooth-cartan-selection-on-primitive-normal-sphere",
        "strategy:identify-bare-native-octic-with-full-e8-invariant-operator",
        "strategy:reuse-screened-primary-octic-in-same-original-car-source",
        "strategy:replace-original-quarter-w8-source-by-unshifted-e8-vacuum",
        "strategy:use-local-cyclic-current-image-for-original-p1-w8",
        "strategy:use-only-folded-c8-stress-cycle-for-complete-w8-response",
        "strategy:reuse-full-original-c1-stress-cycle-for-neutral-w8-states",
        "strategy:reuse-actual-cover-winding-for-local-quarter-current",
        "strategy:subtract-independent-quarter-stress-factors-without-winding",
        "strategy:use-winding-charge-conjugation-as-reflection-of-full-flat-dirac-sea",
        "strategy:use-fixed-pin-green-covariance-as-original-positive-p1-kernel",
        "strategy:retain-full-original-ns-cover-for-free-dirac-green-positivity",
        "strategy:reuse-concrete-elliptic-moebius-quarter-source-bridge",
        "strategy:replace-quarter-hardy-source-by-finite-normal-crosscap-preparation",
        "strategy:reconstruct-neutral-native-transfers-in-connected-original-current-net",
        "strategy:derive-original-half-cover-cauchy-projection-and-source-response",
        "strategy:identify-full-marked-equator-pullback-with-single-smooth-quarter-circle",
        "strategy:reuse-same-elliptic-free-gaussian-rp-and-labelled-calderon-state",
        "strategy:derive-original-p2-connection-from-natural-c2-scalar-spin-pushforward",
        "strategy:reuse-full-current-functional-of-existing-elliptic-gaussian-source",
        "strategy:derive-coupled-primitive-geometric-response",
        "strategy:reuse-complete-elliptic-spin-quarter-kernel",
        "strategy:automatic-ramified-flat-transport-selects-single-quarter-circle",
        "strategy:identify-fixed-native-three-cycle-with-v117-at-fixed-compiler",
        "strategy:derive-v117-from-theta-family-with-unchanged-geometric-q",
        "strategy:derive-conformal-boundary-trace-before-geometric-fourpoint-mixture",
        "strategy:derive-retarded-geometric-response-of-retained-seam-defect",
        "strategy:derive-positive-full-projector-source-before-independent-fourpoint-fit",
        "strategy:generate-fermion-fourfield-by-retained-quarter-geometric-averaging",
        "strategy:derive-real-elliptic-modulus-boundary-and-fourfield-response",
        "strategy:reuse-recovered-original-c4-triangle-monodromy-proof",
        "strategy:use-oblique-quarter-cauchy-idempotent-as-positive-car-state",
        "strategy:identify-actual-a0star-c4-connection-with-genuine-d4-base-inversion",
        "strategy:reuse-actual-negative-triangle-sign-line-cover",
        "strategy:complete-sign-fields-by-bare-common-cyclic-twelve-root-cover",
        "strategy:construct-given-elliptic-flat-quillen-family-before-physical-insertion-comparison",
        "strategy:identify-bare-flat-large-gauge-quotient-with-minimal-em-counting-transfer",
        "strategy:derive-actual-half-period-graded-gns-and-source-saturation",
        "strategy:reuse-source-selected-spin-and-correct-pauli-translation-target",
        "strategy:derive-native-central-quarter-from-ordinary-theta-determinant",
        "strategy:promote-fixed-point-spin-phase-via-direct-theta-evaluation-family",
        "strategy:reuse-complete-tfpt-origin-investigation-state",
        "strategy:reuse-original-winding-relative-three-cable-hardy-norm",
        "strategy:reuse-same-spin-seam-reference-and-retain-fermionic-grading",
        "strategy:reuse-cubic-cauchy-range-and-oriented-car-dual-before-physical-source-map",
        "strategy:construct-theta-frame-e8-lattice-pair-with-retained-odd-spin-lift",
        "strategy:generate-source-spinor-by-winding-functional-calculus",
        "strategy:select-local-e8-extension-by-chiral-vacuum-cycle-exchange",
        "strategy:identify-full-local-marked-e8-with-unchanged-clustering-source-time",
        "strategy:reuse-affine-source-spectrum-and-local-operator-discriminator",
        "strategy:reuse-original-parity-before-local-spinor-extension",
        "strategy:reuse-full-recursion-and-signed-petersen-double-cover",
        "strategy:replace-hodge-amplitude-by-positive-petersen-via-phase-gauge",
        "strategy:identify-calderon-and-perron-by-natural-face-compression",
        "strategy:reuse-e8-a4-hodge-and-record-resolved-petersen-response",
        "strategy:reuse-full-covariant-quantum-rigidity",
        "strategy:exclude-central-clock-and-mark-transport-as-complete-phase-selector",
        "strategy:derive-single-source-epsilon-process-saturation",
        "strategy:recover-native-f20-spin5-carrier-before-event-selection",
        "strategy:coherent-two-event-record-search-exact-support-and-loewner",
        "strategy:test-original-color-selector-before-repeating-e8-ground-no-go",
        "strategy:replace-fixed-clock-four-by-full-native-six-ovoid-bundle",
        "strategy:derive-source-selected-charged-e8-sewing-line",
        "strategy:use-charge-compensated-quarter-and-smaller-original-ward-component",
        "strategy:derive-neutral-observable-source-through-half-kink-transport",
        "strategy:transfer-os-word-anti-anti-type-to-single-chiral-ordinary-weyl-reflection",
        "strategy:use-original-schottky-time-and-graded-opposite-weyls-for-joint-source",
        "strategy:reuse-audited-local-source-chain-and-test-actual-p1-joint-functional",
        "strategy:infer-joint-p1-source-by-pointwise-positive-spectral-reweighting-alone",
        "strategy:identify-gapped-quarter-source-time-with-borchers-translation",
        "strategy:repair-standalone-finite-pfaffian-by-changing-only-internal-J",
        "strategy:derive-neutral-cayley-standard-pair-from-original-currents",
        "strategy:embed-full-local-current-net-directly-in-finite-spectral-coordinate-algebra",
        "strategy:recognize-original-neutral-current-sector-from-actual-ward-and-state",
        "strategy:use-mixed-currents-and-test-complete-constant-product-time-reduction",
        "strategy:test-paired-quarter-source-at-original-filter-and-full-graph",
        "strategy:use-canonical-graded-boundary-clifford-functor",
        "strategy:reuse-full-charge-dirac-transport-in-graded-chart",
        "strategy:reuse-fixed-chart-for-normal-dependent-and-mixed-source",
        "strategy:identify-full-os-time-with-finite-rank-geometric-dirac",
        "strategy:reuse-actual-p2-and-decoupled-quarter-source-dictionary"
      ],
      "connectionIds": [
        "connection:clock-defect-operational-core-to-original-source",
        "connection:parallel-native-clock-to-joint-family-connection",
        "connection:cartan-source-globalization-to-family-connection",
        "connection:invariant-quantum-octic-glues-without-global-cartan-choice",
        "connection:old-winding-current-net-to-quarter-partner",
        "connection:full-cover-green-reflection-to-original-quarter-source",
        "connection:elliptic-moebius-boundary-to-marked-compiler-source"
      ],
      "reviewedAttemptIds": [
        "contract:atlas-defect-synthesis-20261024",
        "contract:native-observation-arity-20261025",
        "contract:native-octic-seam-origin-20261025",
        "contract:paper-source-reconstruction-20261025",
        "contract:microscopic-charged-car-limit",
        "contract:primitive-seam-operator-reconstruction-20261025",
        "contract:older-paper-source-recovery-20261025",
        "contract:canonical-seam-fermionization-20261025",
        "contract:collective-native-marginal-origin-20261026",
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "problem:automatic-origin-response-decision",
      "titleEN": "Automatic response search with original-source decision",
      "questionEN": "Which additional joint response actually follows from original source equations, and which entire finite process family remains undecided without it?",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "acceptedPremiseIds": [
        "premise:typed-source-structures",
        "premise:finite-positive-kernel-search-class"
      ],
      "findingIds": [
        "finding:r098-withheld-response-search-has-exact-conditional-affine-certificates",
        "finding:r098-whole-finite-process-segment-preserves-2245-moments"
      ],
      "taskIds": [],
      "strategyIds": [
        "strategy:r098-test-whole-response-families-before-more-enumeration"
      ],
      "connectionIds": [
        "connection:r098-response-search-to-physical-source-dictionary"
      ],
      "reviewedAttemptIds": [
        "contract:seam-positive-kernel-search-20261015"
      ],
      "reviewState": "reviewed-authored"
    }
  ],
  "findings": [
    {
      "id": "finding:future-equivalence-minimizes-declared-answer-process",
      "titleEN": "Complete answers determine the minimal process quotient",
      "statementEN": "For a fixed experiment alphabet and complete answer functional r, u~v exactly when r(uw)=r(vw) for every allowed continuation w. The quotient is the minimal distinguishable process state relative to those answers; by itself it yields neither complex amplitudes, the Born rule, continuous time, a metric, nor E8.",
      "scopeEN": "Applies exactly relative to the declared experiment alphabet and complete answer functional; no absolute ontology or physical TFPT source claim.",
      "status": "established_scoped",
      "problemId": "problem:future-quotient-and-gns-reconstruction",
      "topicIds": [
        "topic:universalraum",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8",
        "goal:universalraum"
      ],
      "premiseIds": [
        "premise:future-answer-functional"
      ],
      "attemptIds": [
        "contract:universalraum-primitive-source-audit-20260915"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4d1cad18bd2f6e1ea54ec909"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:positive-word-kernel-reconstructs-cyclic-gns",
      "titleEN": "Positive null-stable word kernel reconstructs cyclic representation",
      "statementEN": "Given a positive Gram kernel K with normalized reference, compatible composition/adjunction, and null-stable continuation, quotienting by null vectors and completing constructs H_K and the well-defined word action. Cyclic realizations of the same complete K values are unitarily equivalent on the common word domain; for unbounded operators, closures and self-adjointness remain additional requirements.",
      "scopeEN": "Construction applies only with complete coherent K values and stated domain conditions; K from the original TFPT source has not been derived.",
      "status": "conditional",
      "problemId": "problem:future-quotient-and-gns-reconstruction",
      "topicIds": [
        "topic:universalraum",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8",
        "goal:universalraum"
      ],
      "premiseIds": [
        "premise:positive-word-kernel-null-stability"
      ],
      "attemptIds": [
        "contract:universalraum-primitive-source-audit-20260915"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6c4bf91ed3e3e25f68d1913f",
        "source:d14d8eba68cd7040a6e9ee3d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:operational-seed-is-input",
      "titleEN": "The operational seed category takes the central data as an input object",
      "statementEN": "The original definition already assumes (A_loc, tau_t, Theta, omega, [u_Sigma], D_coll); its collar-completion theorem derives B_Sigma and spectral data from them, but does not select those inputs.",
      "scopeEN": "Applies to the cited operational seed category and its collar completion; it does not claim that no other original selector exists.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:source-graded-gns-matter-gate-20260922"
      ],
      "historical": true,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a9e0479abeec3c6a6739d295"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-source-common-time-thermal-family",
      "titleEN": "The same source supplies Hamiltonian, time and thermal state",
      "statementEN": "The original H is positive self-adjoint and has a faithful Gibbs state for every prescribed beta. The actual transfer reconstructs Hδ=−log Qδ/δ; removing the temporal regulator makes its unitary dynamics converge to the same H. Spatial lattice, couplings and beta remain declared inputs.",
      "scopeEN": "Finite spatial volume and original neutral scalar/charge source; no spatial continuum or P1/P2 selection claim.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-native-round20-source"
      ],
      "attemptIds": [
        "contract:native-source-reconstruction-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f229447932498ddeff1f3dda"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-grade-carry-and-memory",
      "titleEN": "Marking and necessary memory are connected within the given source",
      "statementEN": "Original grade and transport generate M4(C(S1)) with integer carry. Full H couples grade and carry. The GNS projection has K(t)=B*exp(itLQ)B with rank K(0)=3; its minimal temporal realization may be infinite-dimensional. No external memory is appended.",
      "scopeEN": "Given source, grade and J>0; the two-time kernel is neither a physical measuring instrument nor a universal three-dimensional memory realization.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-native-round20-source"
      ],
      "attemptIds": [
        "contract:native-mark-memory-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e0ee6607c2146261c68ef1be"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:even-seam-global-operator-factorization",
      "titleEN": "A common global seam-operator factorization exists",
      "statementEN": "On the even D8 Fock sector W4=Us Rc holds with the actual ordered CAR/E8 cocycle, Klein signs, all oscillators and current central term; Rc preserves Q,K and the quarter transition. The E8 extension and lift convention are explicitly given.",
      "scopeEN": "Global charge transports in the stipulated even completion; not local vertex insertions, an ordinary-local odd CAR/E8 inclusion or event dynamics.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:stipulated-even-e8-seam-lift"
      ],
      "attemptIds": [
        "contract:seam-joint-ward-state-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1a8db88614570db5aa2d1c62"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-generated-marking-classification",
      "titleEN": "Four internal markings completely classified from time and charge",
      "statementEN": "Full lattice saturation reduces the continuous source torus to sixteen four-torsion characters, twelve primitive and exactly four D5+A3 markings. P5 is reconstructed from neutral root moments; a control without M or a target projector finds the same four. W=exp(4πiK)exp(-iπαQ/2) realizes one while preserving quarter time; sheet transport gives W Zq. Compensation was previously known; complete classification and control are added here.",
      "scopeEN": "Given chiral source, fold, full normalized charge and stipulated E8 completion. Algebraic construction and Lean lattice theorem; no physical selection of W or source from P1/P2.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:full-normalized-charge-time-character-family",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:actual-chiral-opposite-quarter-domains"
      ],
      "attemptIds": [
        "contract:seam-source-character-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f864a1c437b82d7af5312b24"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-marking-field-realization-boundary",
      "titleEN": "A matching E8 marking is not yet an elementary P2 carrier",
      "statementEN": "Each of the four candidates acts on the eight original complex fields with two copies of every quarter phase. Their neutral bilinears form A3+4A1 with twenty roots and rank seven, rather than D5+A3 with fifty-two roots. The latter uses the stipulated spinor completion. The new marking changes neither K nor the known ground-state comparison and supplies no event instrument.",
      "scopeEN": "Exact field-type comparison in the same given source. No universal exclusion of E8 or future source/sector extensions.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:full-normalized-charge-time-character-family",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:actual-chiral-opposite-quarter-domains"
      ],
      "attemptIds": [
        "contract:seam-source-character-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:fe82b84dadf6c9e88dbb0ef6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:minimal-defect-uniqueness-not-proved",
      "titleEN": "A minimal defect value does not yet select a unique source",
      "statementEN": "The original argument first states that uniqueness needs classification of the minimal stratum, then asserts it without that classification. Well-ordering N4 yields a minimal value, not a unique operator fiber. Nonzero spectral flow alone also does not prove attainability of one.",
      "scopeEN": "Audit of the cited proof only; not a general impossibility theorem for P1/P2 or a revocation of declared unit winding.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-source-operator-reconstruction-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7ea86fac672df5557d1c5f55",
        "source:658548913675f0bb16f766e6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:conditional-seam-field-state-time-reconstruction",
      "titleEN": "Joint seam, field, sea and time action reconstructed",
      "statementEN": "Under the operator hypotheses, Wold supplies a complete mode basis U^n w and B=N+alpha. With the CAR/sea premise, R c_n R*=c_(n+1), R*QR=Q+1 and R*H_alpha R=H_alpha+Q+alpha. R Omega is a new charge-one state; exp(2pi iH_alpha)=exp(2pi ialpha Q) retains the quarter phase.",
      "scopeEN": "Conditional analytic reconstruction on a common core; Lean verifies the algebraic identity and mode recurrence, not physical derivation of inputs. One channel is not the five-slot P2 carrier; no event law.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-wold-source-operator-hypotheses",
        "premise:charged-car-negative-sea-source"
      ],
      "attemptIds": [
        "contract:seam-source-operator-reconstruction-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d7d559d773cf2c69223c3e98",
        "source:0cc47d877fdae3fd408fc783"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:continuous-hardy-seam-classification",
      "titleEN": "The scalar isometry family is completely classified",
      "statementEN": "Every continuous scalar unimodular winding-one symbol with isometric Hardy compression is a single Blaschke factor modulo phase. With B_alpha fixed, only the centered factor z has constant shift covariance. The strictly oriented control z²/b_(1/4) has leakage 15/4096.",
      "scopeEN": "Complete analytic theorem in the supplied scalar Hardy class. Leakage excludes only the pure-isometry route, not general physical sources. Not a P1 classification.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-scalar-quarter-hardy-source"
      ],
      "attemptIds": [
        "contract:seam-source-operator-reconstruction-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:10843ef87f7062e60e223846",
        "source:def48efd06595636cfc12fa3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:same-source-seam-energy-selection",
      "titleEN": "Original time energy minimizes at the uniform scalar winding",
      "statementEN": "With B_alpha and the reference sea fixed, every unimodular H1 symbol u=exp(i phi) of winding one has E(R_u Omega)=alpha+½⟨(phi prime−1)²⟩. The unique scalar-multiplier minimum is u=exp(i chi)z. Both b_(1/4) and z²/b_(1/4) have excess 1/15. The produced state changes, not the reference sea.",
      "scopeEN": "Global variational theorem in a given scalar CAR source; no change to B and no finite-search proof. General unitary vacuum symmetries may yield the same minimal state energy. The least-excitation selection rule and origin of fields, state and time are not derived from P1/P2.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:charged-car-negative-sea-source"
      ],
      "attemptIds": [
        "contract:seam-source-operator-reconstruction-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4d31a1915a888adf4e1db873"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:master-functional-presupposes-source-selection",
      "titleEN": "The master functional already presupposes its minimal source",
      "statementEN": "The definition fixes d*_disc and P_adm first. Its barrier is zero for B≅B_min and infinity otherwise. M therefore optimizes continuous xi on the already selected branch; this definition neither classifies B_min nor derives the least charge-one excitation rule.",
      "scopeEN": "Audit of this definition, not a disproof of all other selection theorems. Its electromagnetic alpha is not automatically the quarter-phase parameter in the CAR energy test.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-source-operator-reconstruction-20261015"
      ],
      "historical": true,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b1f42b48aede12a331992117"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:geometric-deck-not-calderon-polarization",
      "titleEN": "Geometric deck reflection is not generally boundary polarization",
      "statementEN": "The original source identifies R_tau=2P_C−I from reflection regularity. A compact product-Dirac counterexample with B=diag(A_1/4,−A_1/4) and local R=σx disproves that general inference: the deck lift on the two fixed boundary faces changes G, whereas 2G−I commutes with G. The principal-symbol comparison confirms the type distinction. R_alg=J_n(2C−I) is a reconstructed, generally nonlocal involution; its algebraic quarter turn does not derive charged quarter holonomy.",
      "scopeEN": "Correction of the general geometric identification in the archived source, not rejection of P1/P2 or all seam realizations. A nonlocal R:=2C−I can be defined but thereby has no demonstrated geometric origin.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-geometric-dirac-deck-lift"
      ],
      "attemptIds": [
        "contract:seam-full-collar-reconstruction-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7af7894ef3e81fd54f22b386",
        "source:6b67a85030211d469cf49044"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:positive-compression-erases-carrier-minus-sector",
      "titleEN": "Positive-only compression removes the required negative carrier sector",
      "statementEN": "Pprim=C Pgap implies Ran(Pprim)⊂Ran(C). Thus (2C−I)|H_car=I for a carrier embedded there, and E_−=0. Every isometric pullback W into Ran(C) also yields W*(2C−I)W=I. The later 3+2 polarization does not follow this way. The general lemma CQ=Q ⇒ (2C−I)Q=Q is kernel-checked. A different carrier factor needs an explicit different map.",
      "scopeEN": "Literal source interface of the archived definition; not a refutation of the algebraic 3+2 statement for a supplied P2 carrier. Likewise (2G−I)|Ran(G)=I: full boundary data alone do not create an internal marking.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:literal-carrier-after-positive-compression"
      ],
      "attemptIds": [
        "contract:seam-full-collar-reconstruction-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:cf7337f72906cd78af4ce6e4",
        "source:c1565366722f99a531f2beb6",
        "source:52fe3040988f27f15347181f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:higgs-determinant-does-not-discharge-carrier-map",
      "titleEN": "Higgs determinant argument does not supply the upstream carrier map",
      "statementEN": "The archived determinant argument uses X=-2P3+3P2 and an explicitly rank-two weak block before the later rank-two conclusion. H0(O(1))=C² alone determines neither rank E+ nor its operator kernel; the same determinant line occurs at different ranks and different h0. The Lean Higgs theorem explicitly assumes its linear identification with binary forms.",
      "scopeEN": "Audit of the specified archived origin chain and elementary bundle controls; no refutation of an actually supplied equivariant bosonic operator, P2 postulate, or conditional Lean theorem.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3acf62a86d119d723e073692"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:primitive-invariant-does-not-select-rank-three",
      "titleEN": "Invariant-ring primitiveness alone does not select rank three",
      "statementEN": "For V=C5,W=C2, (V⊗W)⊗Λ4V⊗W→detV⊗detW is a nonzero S(U5×U2)-invariant tensor with even fermion degrees2/4. Centers and U1 charge force positive invariant total degrees(5m,2m); thus the tensor is primitive at carrier degree7. It refutes the local inference that r≥4 must factor in the invariant ring. The stronger Lean premise E≃(Λ²E)* remains valid and needs its own source derivation.",
      "scopeEN": "Excludes only the local invariant-theoretic inference under the stated polynomial interpretation. No P1/P2 countermodel or refutation of additionally justified global minimality or actual branch-tensor support; no new Lean build.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:carrier-covariant-invariant-ring",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:02475417ecd31cfaaa97d0aa"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-background-source-does-not-fix-mixed-vertex",
      "titleEN": "Complete fixed-background fermion source does not fix the Higgs derivative",
      "statementEN": "The existing direct Grassmann path yields the same complete unnormalized source polynomial and Z0=69649/65536 for both supplied extensions at Φ=0. The mixed derivative is zero or offdiagonal -65536/69649; -K0(∂Φ K^-1)K0 reconstructs the supplied derivative K′. A joint source derivation therefore still needs the actual original field dependence and correctly equivariantly typed coupling.",
      "scopeEN": "Exact zero-jet identifiability test on the given free source path. No no-go for a complete Φ-dependent functional or later original selector; no general interacting Yukawa theorem.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-background-quarter-fermion-source",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7b1dd6d6937506140efae602"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:local-quarter-inner-variation-is-connection",
      "titleEN": "Local quarter-source fluctuation yields connections, not a new carrier",
      "statementEN": "From [Bα,Mb]=−iMb′ and U*[Bα,U]=I one obtains exactly Ω¹_B(C∞(S¹))={Mv}. Selfadjoint perturbations are real smooth v. With mean vbar, Bα,v=e^(−iλ)Bα+vbar e^(iλ), λ′=v−vbar; the same quarter holonomy requires vbar∈Z. Fluctuation preserves the represented algebra and line module and thus creates no new SU2 fundamental or3+2 selection in this realization.",
      "scopeEN": "Complete one-form/one-particle holonomy theorem only for this explicit coordinate algebra. No P1/P2 no-go, identification with the full physical net, fixed Fock-vacuum equivalence or anomaly cancellation. Real completion depends on actual J and sign.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:quarter-circle-coordinate-local-algebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:73c63e13f7c4f9c521185f54"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:calderon-enlargement-does-not-select-higgs",
      "titleEN": "Cauchy enlargement supplies arbitrary finite matrix directions, not a selector",
      "statementEN": "P0=C−UCU* and Emn=U^m P0 U^(−n) supply all finite matrix units. The represented generated algebra has scalar commutant and center. Since I is a one-form, every element a=aU*[B,U] is a one-form. The enlargement permits arbitrary finite-rank matrix perturbations but selects neither a Higgs coupling nor3+2 and cannot silently replace the original local algebra with smooth center.",
      "scopeEN": "Concrete algebraic/smooth enlargement, not the entire bounded-operator algebra. Does not exclude an independently derived noncommutative local field algebra.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:quarter-circle-nonlocal-cauchy-enlargement",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ad808b045fe2a4afa1c6a725"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:finite-sm-higgs-variation-retains-seed",
      "titleEN": "Finite SM Higgs fluctuation retains the supplied Yukawa seed",
      "statementEN": "For M=diag(Yup,Ydown), every particle LR one-form obeys q_a(Mr_b−q_bM)=q_a(r_b−q_b)M. The factor is quaternionic and b=eR spans all qM. Including the seed yields M(H)=HM with H=[[φ1,φ2],[-barφ2,barφ1]]. The four Yukawa matrices and color/weak modules remain inputs; D_F=0 gives no finite fluctuation. The linear identity was checked exactly against unchanged existing code with a complete coefficient basis, without choosing physical couplings.",
      "scopeEN": "Exact conditional classification of the particle LR block of the given representation, not a complete real-triple classification or P1/P2-derived coupling. Already encoded3+2 structure is not newly selected.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-finite-sm-triple-yukawa-inputs",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:20ba7d005ffba64df6121ea0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:operator-skeleton-does-not-identify-insertion-algebra",
      "titleEN": "Full operator skeleton does not select local insertion algebra",
      "statementEN": "On the same product skeleton A0=C∞(M)I and A1=C∞(M,Mn) acting on the left differ, with the same scalar center, identical D,J,Γ,B,R and fixed relative spectral/eta responses. Both obey order zero/one: JL_(b*)J^-1=R_b, [[D,L_a],R_b]=0. A1 mixes internal left indices, A0 does not. For n=2: fiber-span dimensions1/4, commutant dimensions16/4 and16 exactly vanishing left/right basis commutators. These operator/center/order conditions therefore do not reconstruct the multiplication algebra.",
      "scopeEN": "Excludes only unique algebra reconstruction from these data in the declared product/domain setting. Not identical complete original tuples, full OS/P1/P2/minimality countermodels or a universal TFPT no-go. Additional algebra hypotheses need their own origin.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-domain-product-dirac-skeleton",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ee46166597a824b7ce9b0d9a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:internal-even-car-hodge-is-not-coordinate-algebra",
      "titleEN": "Internal Hodge structure exists, full even CAR is not the coordinate algebra",
      "statementEN": "For the given E=C5, J_H²=1, J_HΓ=-ΓJ_H and (ΓJ_H)²=-1 hold on ΛE. Internal CAR is End(ΛE), its even part End(S+)⊕End(S-). J_H swaps both blocks and maps this full algebra onto itself; order zero would require commutativity. An explicit matrix-unit commutator has rank2. The full internal algebra is thus not a spectral coordinate algebra with this J_H. A selected left/right bimodule subalgebra remains missing. Reuse the existing SU5 no-selector: unmarked exterior algebra and trace balance select no3+2 projector.",
      "scopeEN": "Excludes only full even internal CAR as coordinate algebra with J_H; positive Hodge signs conditional on rank/metric/volume. No physical CAR, J, KO6, spacetime or E=C5 origin derivation. Proper compatible subalgebras and originally derived symmetry breaking remain possible. Whole-space antiunitarity is not automatically the quaternionic W factor of a different triple.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:unmarked-hermitian-rank-five-exterior-carrier",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:14b79976c0cdc4a86896b795"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:minimum-rank-unique-primitive-channel-does-not-select-32",
      "titleEN": "Minimum rank and unique primitive channel do not select3+2",
      "statementEN": "Rank5 is the first possible rank in the stated class: even ranks fail total parity, and at rank3 total degree5 is not a multiple of3. The same canonical volume tensor supplies nonzero primitive trilinears on E=C5 for1+4,2+3,3+2,4+1. Minimal covariant degree5 channel spaces modulo fermion exchange have dimensions1,2,1,1. Thus even unique primitive channel leaves1+4,3+2,4+1; with b>s,3+2 and4+1 remain. All four16-dimensional packets have Tr X=Tr X³=0 for X=(-s)I_V+bI_W.2652 integer group-action coefficients were checked exactly; no suitable coupling was fitted.",
      "scopeEN": "Excludes the finite rank/primitivity/channel-uniqueness implication in the stated covariant exterior class, stronger than the earlier nonminimal5+2 test. Does not establish multiple global original minimizers, equal S1 defect vectors, all anomalies or complete P1/P2 worlds. An original bosonic index and actual sector/vertex map could distinguish them but are not derived here.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:minimum-rank-holomorphic-even-even-fundamental-class",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5eff217dfbf84613642dbf11"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-selfconsistency-presupposes-minimal-algebra-fiber-selection",
      "titleEN": "Joint self-consistency presupposes minimal algebra selection",
      "statementEN": "Original minimization does not classify the minimal algebra/bimodule fiber. The joint discrete theorem imports Higgs rank2 and branch-Yukawa rank3; the master functional fixes d_disc*,P_adm and B_min before varying only ξ=(α,χ_geo,δ_ph,ρ_vac). The singleton fiber product presupposes discrete uniqueness with E3⊕E2,Y in the shared invariant tuple. Two exact conditional decoders exist: independent occupancy balance at g5 gives {b,s}={2,3}; independent Bγ=g/(g−1) with Y roots−1/b,+1/s gives s²=g−1, hence s2,b3. Their cited original proofs evaluate these equalities only on the fixed3+2 branch. Using them as upstream selectors adds a premise.",
      "scopeEN": "Source and logical dependency audit of the cited chain, not a universal impossibility theorem. An independent original derivation of the cross-identification or unique minimal algebra/bimodule classification could close the gap. E8 glue rank selection and fixed state for given transport are retained and not equated with local algebra selection.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:eb1d0f76c9eb499a0c5919dc",
        "source:46175cb67814f7e6c2d9f168"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:process-composition-and-cyclicity-do-not-select-algebra",
      "titleEN": "Composition and a cyclic faithful state do not yet select the algebra",
      "statementEN": "The existing operational context-quotient/GNS result remains conditional on the original operation alphabet. Classical and quantum models obey general composition, causality and local tomography. C4 and L(M2) additionally share HS(M2), J and Omega, cyclic/separating faithfulness and order zero, yet only the latter is noncommutative; their centers differ. A coherent two-channel operation separates a restricted population protocol (double pulse:1 versus1/2), but source availability must first be derived.",
      "scopeEN": "Only excludes these general composition/cyclicity conditions as sufficient algebra selectors. The new pair is not a same-center counterexample or full physical TFPT countermodel. Additional principles such as purification remain conditional, not P1-derived.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:process-composition-finite-controls",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5071933310a0491ab858d581",
        "source:16452f3332cf251606ce7ce8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:quartic-shape-selects-32-only-with-source-sign",
      "titleEN": "Positive quartic shape conditionally selects3+2; boundedness alone does not fix its sign",
      "statementEN": "For every traceless Hermitian rank-five endomorphism with trX²=1, globally7/30≤trX⁴≤13/20. Exhaustive stationary-spectrum classification gives equality below only at2+3 and above at1+4. The even conjugation-invariant bounded-below controls -t+t²±trX⁴ therefore favor different splits, without an inserted preferred direction. The primitive spectral functional differentiates a supplied deformation; a positive profile does not imply a positive fourth-order shape term. Original X, trace constraint, deformation and sign remain to be derived.",
      "scopeEN": "Exact conditional internal shape selector and scoped control. No P1-derived field/potential, complete TFPT dynamical uniqueness, physical Higgs/gauge identification or T1–T8 closure.",
      "status": "conditional",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:unmarked-five-traceless-hermitian-quartic",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-joint-source-origin-audit-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4e83650102b031f401d38984",
        "source:325594481f50c3ab3e4b5f31",
        "source:748b7940e88d21a0f908d8c7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-symmetric-quartic-erasure-common-object",
      "titleEN": "One native representation forces the actual quartic code and erasure action",
      "statementEN": "P64 is characteristic as O2(G31). Fix_P64(Sym^4 V4) is exactly the actual five-code; the original codeword sums give its real intertwiner rather than a fitted embedding. The existing erasure intertwiner forces rho20(g)=rho5(g) tensor bar(rho4(g)) for the same words. The full fourth tensor power has Pauli fixed rank16, whereas the symmetric fourth power has rank5.",
      "scopeEN": "Shared mathematical cause within the given core. The physical symmetric rule, origin of the core data, and an E8-current/fermion identification are not derived.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:319bc0f7a7a5db692a18f6fe",
        "source:d54ab75eaa1320f0d41907b1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-native-algebra-normalizer-and-response-orbit",
      "titleEN": "Joint block algebra, normalizer and intrinsic2+3 orbit",
      "statementEN": "The actual4-,5-,20-representations are distinct irreducibles. Their group algebra is M4+M5+M20 with commutant C^3 and group normalizer U(1)^3 rho(G31). The algebra quotient preserves these word representations but is not tensor-closed by itself. The15 original matching involutions yield a canonical transitive family of rank2 projectors with rank3 complements. Joint group-invariant states retain free positive block weights. The decisive exact comparison nevertheless gives P2 != Q_t for ALL15 projectors of the native response orbit: color-S3 commutation excludes this identification structurally.",
      "scopeEN": "No unique physical3+2 marking, no spacetime dimension29 and no physical5/4 normalization derived from dimension ratios. The associative-algebra normalizer is larger than the group normalizer. The existing physical mark is therefore not simply an as-yet-unselected member of those15 responses.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b35b33d12d71c4b5bfb98a67",
        "source:b5679d9ec5cced65fcc43cbe"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-galois-intertwiner-unique-logical-marked-orbit",
      "titleEN": "Actual native-four Galois clock and one marked representation orbit",
      "statementEN": "For each of the six remaining F20 representatives actual native C,G satisfy C^5=G^4=I and GCG^-1=C^2. Simultaneous intertwiners to the original v419 carrier have solution dimension1 and rank4. The six representatives form ONE orbit of the existing logical stabilizer, already S2×C3 acts regularly. R5 is not a native group word by an exact centralizer test; the compiler clock instead maps to an order3 operator on the quartic code. The canonical cyclotomic trace metric is carried isometrically into the native four-metric by normalized intertwiners, leaving an overall phase.",
      "scopeEN": "Explicit operator identification and one logical equivalence class, not six independent physical options. A common native-four/P1 clock continuation and the twenty-lift of a specified coherent R polynomial are not thereby derived.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bfcb7f5b7fc4fc9ef6df239f",
        "source:62f7fdedfb6be0f366b10437",
        "source:d56c47bd0f63f6e19f7b0cc8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-reflection-full-four-five-generators-rate-injectivity",
      "titleEN": "Complete four/five generators determine the60 native rates",
      "statementEN": "The native rate map has rank55 on the four and15 on the five, jointly rank60 with60 columns. Its joint nullity is0: fixing complete generators excludes a hidden twenty-rate twin inside the60-reflection Poisson menu. The old coherent S3 sign twin belongs to a different event menu and additionally violates the actual branchwise erasure contract, with trace distance1/4 for an explicit input.",
      "scopeEN": "Unique continuation within exactly this menu, not selection of that menu, complete generators or their physical time scale from P1. A few populations or a single finite-time channel are weaker inputs.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:fixed-complete-four-five-primitive-reflection-generators"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7c6d7af400f74a33e2efb5a4",
        "source:39067a0de1982abeee09eafe"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:complete-logical-readout-native-covariant-residual-classification",
      "titleEN": "Complete logical nondisturbance classifies the covariant residual channel",
      "statementEN": "CPTP and Tr4 Phi(X)=Tr4 X for all joint X force Phi=id5 tensor D by the multiplicative domain; factorization is not a fitted ansatz. Native G31 covariance forces D=Dq with -1/15<=q<=1. Continuous semigroups have q(t)=exp(-gamma t), gamma>=0. The original central J-character projector and Paulis realize this in the coherent block-algebra menu with common normalized branchwise erasure records; the gauge correlator is q(t).",
      "scopeEN": "Classification of this explicit residual class, not all sources. No original physical permission for the coherent Kraus events or selection of gamma.16-record equivariance is sectorwise/on the block algebra, not on extra End(H29) coherences. G31 covariance does not prove covariance under arbitrary coherent clock polynomials.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:complete-logical-nondisturbance-native-covariance",
        "premise:coherent-block-source-algebra-operation-menu"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3ae8f67c730c7344b42acfae"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-polar-mark-clock-centralizer-orbit",
      "titleEN": "Actual polar mark reconstructed from simplex and clock",
      "statementEN": "In consistent original N coordinates P2(q)=F_sigma-c_q c_q*, c_q=[n2+n3+n4-3(sqrt(6)-1)n_q/5]/sqrt(3). For q=5 this is the actual existing mark without SM charges. All three clock-fixed points form one mark orbit under actual native reflection lifts commuting with sigma4. N=O C^T, O=-rho_C(reverse), transports all labels together.",
      "scopeEN": "Positive polar rule and physical interpretation remain inputs. One mark orbit does not prove every anisotropic source invariant or select a physical state. The mark remains distinct from all15 matching-response projectors.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:original-marked-simplex-positive-polar-rule"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:282d62bf436a998787bc4bd0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-quartic-code-product-stabilizer-quarter-exclusion",
      "titleEN": "All product-unitary lifts of the quarter clock excluded",
      "statementEN": "All six actual code-projector pair marginals are (I+Swap)/4. Every code-preserving U1 tensor U2 tensor U3 tensor U4 therefore has projectively equal factors. The identical local stabilizer is K=U(1)G31 by leakage Gram32I15, a finite determinant slice and NRS6.5. R5 lies projectively outside logical S6, excluding every such product lift. Rank-one Choi also excludes convex native-word-channel mixtures reproducing Ad_R5 on all inputs.",
      "scopeEN": "Classification of code-preserving product unitaries and stated classical mixtures. Collective operations, ancillas, general LOCC, postselection and protocols leaving the code temporarily are not excluded.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:53e2a86bf96738d9810109c6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-decoder-versus-native-quarter-polynomial-erasure-test",
      "titleEN": "Decoder and same native clock polynomial act differently",
      "statementEN": "The existing three-register decoder derives encoded R5 tensor I4. Substituting actual sigma20 and all four native tau20 into the same R polynomial with original decoder marking gives unitarity and the correct square but fails common erasure action. The pure input rho=(I-F_sigma5)(I+s23)/2 yields output-difference eigenvalues +1/4,+1/4,-1/4,-1/4 and16 zeros: trace distance1/2 for all four lifts.",
      "scopeEN": "This excludes exactly the stated native polynomial continuation with the fixed decoder P220, not every coherent common-clock lift. The logical decoder does not prove original physical permission for the collective intervention.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:original-marked-simplex-positive-polar-rule",
        "premise:original-erasure-decoder-and-same-native-quarter-polynomial"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:19b2612a4f6eeca233ec850a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-decoder-product-time-and-all-unitary-erasure-lifts",
      "titleEN": "Decoder forces product and temporal composition; all unitary erasure lifts classified",
      "statementEN": "The actual decoder D(A)=W(A tensor I4)W* is an injective corner *-homomorphism. Thus D(A)D(B)=D(AB), product preservation of unitary complement extensions and exp(-itD(H))=D(exp(-itH))+I-Pi follow without a new composition rule for given H. Every unitary lift with full branchwise erasure compatibility is necessarily and sufficiently R tensor V4, forced by the commutant rather than fitted. On C64 an arbitrary unitary44-complement block remains.",
      "scopeEN": "Given original code/decoder and logical operation. No selection of H, logarithm branch, physical time normalization or actual intervention permission. Unitary class, not all CPTP instruments. Native group action differs from the decoder by an explicit gauge factor whose physical compensation remains open.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:original-erasure-decoder-and-same-native-quarter-polynomial",
        "premise:unitary-full-branchwise-erasure-clock-lift"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:36c2f5f8da2e151c28ac1a51"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-clock-compatible-polar-fibre-and-canonical-distance",
      "titleEN": "Clock-compatible marking fibre and canonical polar distance",
      "statementEN": "The entire stated native mark class is P=F-cc*, [c] in CP1(E+), or RP1 for real projectors. Every point gives the same quarter spectrum and square; q families are natively S3fix-equivariant. The native q/sigma stabilizer cannot remove the parameter. Original cpol=-sqrt(3/5)e0+sqrt(2/5)e1 and c=e0 differ exactly: HS squared4/5, marked-ray responses2/5 versus0. Uq is also the uniquely nearest isometry to actual orthonormalized Dq, with Frobenius cost7-2sqrt6.",
      "scopeEN": "Completeness only for the stated operator-compatibility class. Countermarks are not full P1 sources and need not obey the original polar rule. Unique distance minimization does not prove a physical law minimizing that distance or matrix positivity from reflection positivity.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2e26454bda2d4c5cd60c3038"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-moment-parent-and-product-path-selection-boundary",
      "titleEN": "Moment parent and local code holonomy do not select the quarter clock",
      "statementEN": "The existing Hnat obeys Hnat V=0, hence exp(-itHnat)V=V for every t; every marking direction has equal ground energy. Alg(Hnat|Code,sigma,tau) is scalar on E+. Reusing the existing Berry theorem and one-register erasure gives V*X_jV=tr(X)I5/4 at each site. All local-product code paths have scalar connection; for a closed code path the previously classified full product stabilizer forces phase-S6 holonomy, outside which R5 lies.",
      "scopeEN": "Excludes the specified moment parent, its code algebra with sigma/tau and this geometric product-path parallel transport. Not a general exclusion of combined local drives plus parent, collective code paths, extra dynamics, ancillas or every physical adiabatic protocol.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:original-native-fourth-moment-parent",
        "premise:local-product-code-orbit-geometric-parallel-transport"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:df45b0e6d2ba8d3e37266ff7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-e8-current-response-and-full-quarter-lifts",
      "titleEN": "Original E8 current response and full quarter lifts",
      "statementEN": "Actual mixed Chevalley brackets give Q(H)|F20=H tensor I4, Q(H)|C4=trH/3 and kappa=trHK-trH trK/9. Noncommuting E+ responses exist. Separated Ward responses distinguish original polar and countermarks. Clock-current norm25/18 is constant throughout CP1 and selects no point. Three gl5 lifts of given R5 have full orders12,4,12; a genuine order4 source clock exists. All60 actual finite event charts match the native erasure twenty-action on the coupled determinant cover.",
      "scopeEN": "Given original E8_1 vacuum source and coupled finite lift; no P1 source selection, physical time, instrument, polar minimization or physical field identification.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark",
        "premise:original-coupled-determinant-event-cover"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a16d54a9201cf1b5a63761fb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:literal-charged-current-register-dictionary-fails-quarter",
      "titleEN": "Charged four-current fails the common tensor-register dictionary",
      "statementEN": "Under literal C4/register identification all three source clock branches act as -I20 on three C currents but as R5 tensor I4 on F20. The actual W intertwiner has squared HS residual48. Every traceless Q(H) already acts0 on C and its products but nontrivially on F. Thus finite cover agreement is not a full field-algebra map.",
      "scopeEN": "Excludes this literal charged four-current identification with unchanged tensor intertwiner, not the actual Cartan four-space or every derived composite field map.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:original-coupled-determinant-event-cover",
        "premise:literal-charged-current-native-register-dictionary"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e2b3d5d46fe02dff10f71155"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-cartan-code-inner-e8-stabilizer-excludes-marked-quarter",
      "titleEN": "Full inner E8 stabilizer of native Cartan code excludes marked quarter",
      "statementEN": "The original lattice vertex law gives root PBW component f(b)alpha(-3)ealpha/3. The actual five quartics have no common projective zero; all240 root zero modes therefore leak from the neutral code. Distinct charge sectors prevent cancellation. The stabilizer has Lie algebra Cartan8 and H0=T8; its components normalize T8 and preserve the actual H+ four-plane. The full native U4 code-stabilizer theorem restricts its logical action to phase-G31, outside which R5 lies. Arbitrary inner-group sequences returning to code are included in the exclusion. L0 acts as4I5; conformal time and Casimir shift do not enlarge the logical action.",
      "scopeEN": "Actual J-positive canonical Cartan Fock embedding in given lattice vacuum and compact inner E8 zero-mode operations. Not an exclusion of higher modes, nonlinear mode products, other derived field maps, non-automorphism interventions or all P1 physics; no physical preparation or selection of the embedding proved.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:compact-inner-e8-zero-mode-operation-class"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:149adc3f438c019710647381"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-code-neutral-weight-two-action-and-global-clock-exclusion",
      "titleEN": "Neutral weight-two source action on actual code completely determined",
      "statementEN": "The full lattice-neutral weight-two space is8 derivatives plus36 symmetric quadratic fields. On original quartic code o(T_A)=dGamma(A), compression=(trA)/2 I5. Exact leakage sum is4||Ac-trA I8/8||²+(5/2)||Aa||²; real Gram relative to matrix HS metric has spectrum0^1,4^15,(5/2)^20 and kernel only A=aI. Original R_neut compresses0 with universal leakage bounds240..384, B48 compresses48I and B64 acts64I. Any sequence solely of these neutral zero modes acts by U8 on mode1; a code-preserving endpoint forces the U4 stabilizer and logical phase-G31 action, excluding marked R5.",
      "scopeEN": "Complete exclusion of this neutral local weight-two zero-mode class including temporary code exits. Do not unite with separate inner E8 exclusion: mixed root/quadratic histories, individual mode roundtrips and higher fields remain outside. R_neut itself is not zero as a field.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:solely-neutral-local-weight-two-zero-mode-class"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:004d30aa548e470c0013882d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-neutral-root-mixed-response-derived",
      "titleEN": "First mixed response of original R and root currents derived",
      "statementEN": "Original vertex formula gives E_beta,0 T_AR=(v_beta.h(-1))e_beta with v_beta=-AR beta+(beta^T AR beta)beta/2 and beta.v_beta=0. All240 original Chevalley roots have exact norm distribution0:46,14:96,30:32,32:60,64:6, hence194 nonzero source responses without fitted coefficients. Their weight-two zero mode on quartic f has PBW component [f(b)v_beta(-3)-(D_c f)(b)beta(-3)/3]e_beta. Basepoint freedom and transversality prove leakage of each individual nonzero direction; compression vanishes by lattice charge. Four original family omissions have R-sum0, without deriving a physical averaging rule.",
      "scopeEN": "Actual first algebraic source variation in given E8_1 vacuum;194 complex root responses are not particle counts or selected events. Leakage existence is orthogonally covariant; numerical code matrices require actual source isometry. Second responses, joint return histories, physical history, P1 source and marking selection remain undetermined.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:926e641f31d54b9d051cf0c4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-mixed-ordered-return-on-native-quartic-code",
      "titleEN": "Actual ordered mixed return on native code",
      "statementEN": "With existing isometry O and full vertex-mode action, all194 nonzero original W_beta give positive definite nonscalar rank5 returns on actual code. Unchanged sum over original root-current input basis is diag(3581,4191,3419,3419,3790), identical for all4 original family omissions. No intermediate projection or fitted coupling is inserted.",
      "scopeEN": "Existing E8_1 vacuum, original code embedding and given R_neut branch. Return amplitudes are not selected physical channels.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f32af3a628626f3b4bf49b5a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:mixed-return-spectrum-does-not-select-original-polar-mark",
      "titleEN": "Mixed return spectrum does not select original mark",
      "statementEN": "None of194 nonzero individual returns commutes with original P2. Sum spectrum is3581,4191,3419²,3790 and commutes with tau but not sigma or P2. Exact witnesses [Ksum,sigma]12=772 and [Ksum,P2]01=(488sqrt2-61sqrt3)/5. Its spectral functions therefore do not give original P2; all4 supplied family variants leave sum unchanged.",
      "scopeEN": "Excludes direct or spectral identification of these concrete kernels with existing mark, not every joint source history or mixed operator algebra.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e03f500b0c90d73d6a50e8e7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-mixed-return-fails-native-trimer-erasure-lift",
      "titleEN": "Actual return fails original trimer erasure lift",
      "statementEN": "Original W20 has Fock columns g_(i,a)=partial_a f_i, all20 orthonormal. Same source channel for doubled root(0,0,0,0,0,0,-2,-2) has K5 rank5, actual trimer K20 rank13 and operator-Schmidt rank4. HS² residual from decoder lift is124096/3. It kills g00=x0³/sqrt6 while decoder lift gives188/3 there. This positive unrenormalized paired response is not a common complete branchwise erasure lift.",
      "scopeEN": "Actual neutral Sym3 trimer, not charged E8 F20 block. Specific response branch, not classification of all combined histories or instruments.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:common-unnormalized-positive-return-erasure-test"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f10c047561901ee024f7809f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:strict-trace-gap-excludes-positive-mixed-return-reweighting",
      "titleEN": "Strict trace gap excludes positive return reweighting",
      "statementEN": "For every original root and real transverse v,4trK5-trK20=(43/12)||v_parallel_Jbeta||²+(25/4)||v_orth||²>0 for v!=0. Full7x7 trace forms and actual native240-root transitivity prove the theorem; all240 computed code traces agree. Original aggregates:trK5=18400,trK20=46848,gap26752. Charge orthogonality gives Kd(a)=sum|a_beta|² Kd,beta for every coherent profile of original W_beta. Thus no nontrivial positive reweighting repairs common unrenormalized erasure continuation.",
      "scopeEN": "Common original normalization, positive adjoint two-insertion returns with original real v_beta. Nonadjoint return fields, new complex transverse fields, independent relative20/5 calibration, longer histories and general physical channels are outside.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:common-unnormalized-positive-return-erasure-test"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bfcc2a4f63b2b13ce7645d61"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-source-erasure-ward-terms-derived",
      "titleEN": "Original source-erasure Ward terms derived",
      "statementEN": "For actual erasure a_a=bar(u_a)(1) and original W_beta=(v.h(-1))e_beta, exactly [a_a,W_beta,1]=bar(c_a)E_beta,1+bar(b_a)W_beta,2 with b_a=u_a.beta,c_a=u_a.v. All20 identities on5 original code states and4 erasures agree exactly. Original witness b2=-i,c3=4-4i has zero a0/a1 terms; a2 gives iW2 and a3 gives(4+4i)E1. No coupling was chosen.",
      "scopeEN": "Algebraic Ward identity in given E8_1 source with original Fock/erasure map. No physical contact, measurement, reset or P1 time law; physical source selection remains open.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:58a5708d94440eda16633c5f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:uncompressed-original-mixed-return-does-not-preserve-code",
      "titleEN": "Full original mixed return does not preserve code",
      "statementEN": "Earlier positive rank5 matrix is Pi L Pi, not full operation L=S_beta* S_beta. Original doubled root(0,0,0,0,0,0,-2,-2) has S_beta h=0 for h=x0^4/sqrt24. Normalized code-orthogonal q=(2/sqrt3)(h-f0/2) gives <q,L f0>=-188/(3sqrt3) and ||(I-Pi)L f0||²>=35344/27. Thus full operation is not code preserving. a0 commutes with S_beta and its adjoint; no omitted Ward term repairs this erasure branch.",
      "scopeEN": "Specific full adjoint two-insertion return in original code embedding. Rank5 Gram stays correct; no global E8/P1 or all-history impossibility claim.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1d01f2ff35f42c2238281e46"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-root-response-sum-also-leaks-from-code",
      "titleEN": "Original root-response sum also leaks from code",
      "statementEN": "For unchanged original unrenormalized root-input basis, Lsum=sum_beta S_beta* S_beta and <q,Lsum f0>=-2092/sqrt3 with leakage norm²>=4376464/3. All4 original family omissions give same exact witness. Independent targeted original-data check confirms35736-343776/4=-50208 for unnormalized witness. Full coherent S* S sum has additional charged cross terms, which vanish exactly in neutral q/f0 matrix element. Thus coherent profiles with |a_beta|=1 also fail code closure regardless of phases.",
      "scopeEN": "Original sum and coherent profiles with unchanged moduli; no physically selected execution or code-closure theorem for arbitrary new weights. Prior complete positive-profile erasure trace gap remains separately valid. Other higher source histories are not excluded.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:64a2291b4a7949a5ac65ed99"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-full-source-return-exterior-feedback-derived",
      "titleEN": "Full original source exterior feedback derived",
      "statementEN": "Original vertex formula gives complete192x726 single-beta S from neutral grade4 to charged grade4, with original Fock adjoint L=S* S. K=Pi L Pi,B=Q L Pi,D=Q L Q give exactly x_(n+1)=Kx_n+sum_(j=0)^(n-1)B*D^(n-1-j)Bx_j for code input. No projection is executed. Actual four-insertion response H=Pi L² Pi equals K²+B*B, not K². Example H00=81152/3 versus(K²)00=40144/9. Next memory term B*DB and Pi L³ Pi are also checked exactly from full source; all H entries independently reproduced in active Laurent/Heisenberg blocks.",
      "scopeEN": "Fixed specified algebraic original single-pair response family. Given source functional is evaluable, but P1 physical event/time selection remains open. Neutral726 space is not complete for coherent multiroot cross terms.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:specified-original-pair-ordered-response-composition"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:13154d801766701a92f47d9a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-return-requires-memory-in-every-code-direction",
      "titleEN": "Original return requires memory in every code direction",
      "statementEN": "Complete exact feedback Gram Delta=B*B satisfies Delta>=5120I5 and has rank5. Every nonzero code input obeys sharp ||Pi Lpsi||²/||Lpsi||²<=9/44, equality exactly span(f2,f3); at least35/44 of squared response norm is exterior. Hankel/Gram block[[I,K],[K,H]] has exact rank10. Hence any fixed linear realization M_n=C A^n E for n>=0 with time-independent input/output maps needs at least10state dimensions. Closed5D continuation of these moments is excluded even after fixed input/output changes.",
      "scopeEN": "Same specified single-beta response family only. Norm fraction is not an instrument probability. Rank lower bound10 is not sufficiency of a10D realization, particle count, spacetime or3+2 derivation. No separate n=0 feedthrough, time-dependent maps or nonlinear models in excluded class; no wholesale transfer to other source histories.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:specified-original-pair-ordered-response-composition"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b7df72f2cb190d27e448abc2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-conformal-primary-multiplicity-source-factorization",
      "titleEN": "Common conformal primary/multiplicity structure of native core",
      "statementEN": "Original J-positive mode1 polynomials are all Virasoro primary because u_a.u_b=0: L0=d,Lm>0=0. Actual4/5/20 carriers thus have(c,h,r)=(8,1,4),(8,4,5),(8,3,20). For all Virasoro descendant words Gram=G_(8,h)(lambda,mu)delta_ij. Generated source cycles factor as common unitary highest-weight representation modulo common nulls tensor actual multiplicity; native G31 acts on second factor. No R_neut branch, individual root or family omission is needed.",
      "scopeEN": "Given canonical E8_1 stress field and original neutral Cartan-Fock embedding. Conformal weights are not particle counts or physical time; no new irreducibility/gauge-group premise. Analytic all-word theorem; finite Fock checks only accompany it.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:canonical-source-stress-all-mode-history"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6760293e4e2648cfbdbbf348"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:canonical-conformal-erasure-forces-primary-twenty-carry",
      "titleEN": "Canonical conformal erasure Ward action forces primary twenty carry",
      "statementEN": "From [L_m,a_a]=-bar u_a(m+1), a_a L_-2 f_i=L_-2g_ia+t_ia with t_ia=bar u_a(-1)f_i. Original h3,c8 level2 Gram[[16,18],[18,84]] and overlap(1,0) uniquely give r_ia=t_ia-(7/85)L_-2g_ia+(3/170)L_-1²g_ia. These20 neutral weight5 primary states have Gram(78/85)I20 and exact original rho5 tensor bar rho4 action. Three existing native reflection lifts give60 literal intertwining checks. Full first Ward output Gram is19I20; code partial return is76I5 or312/85 I5 for primary remainder. No coupling or fitted field identification is chosen.",
      "scopeEN": "Unique orthogonal primary remainder relative to specified original erasure descendant block, not classification of all weight5 primaries. Mathematical decomposition, not executed projection. Neutral native twenty, not charged E8 F20 block or physical fermion/Higgs identification. First full/primary return Gram selects no3+2 mark.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:canonical-source-stress-all-mode-history"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6c1362f9745eb221108d2a5d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:all-canonical-stress-histories-scalar-on-native-code",
      "titleEN": "All pure canonical stress histories stay scalar on native code",
      "statementEN": "All modes/words of given canonical T_E8 act in generated code cycle as common Virasoro representation tensor I5. Every code compression is scalar, including excursions to higher grades and return; code-preserving unitary endpoint is a common phase only. No such pure stress history implements given nonscalar R5 or selects P2. U_conf=exp(i pi L0/2) agrees with native J on4/5/20 seed carriers, but acts as+i on newly forced weight5 twenty whereas native J there remains-i. Common Casimir phase does not repair this relative discrepancy.",
      "scopeEN": "Pure original canonical stress histories in given source frame only; not all geometry/metric variations, affine KZ histories with other field insertions, noncanonical/nonstress fields or general P1 processes. No physical time identification or union with prior separate zero-mode exclusions.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:canonical-source-stress-all-mode-history",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:16c6d4e371357ef886a66ec0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-local-current-ope-forces-erasure-and-carry",
      "titleEN": "Full local current product connects native erasure and carry",
      "statementEN": "Actual current product obeys j_ubar_a(z)F_i(0)=G_ia(0)/z²+sum_k>=0 z^k/k! :partial^k j_ubar_a F_i:(0), without simple pole. Double pole is original erasure twenty; regular t_ia=ubar_a(-1)f_i contains exactly prior h5 primary r=t−7/85L_-2g+3/170L_-1²g, Gram78/85I20 and rho5 tensor conjugate4 action. [ubar_a(1),j_u_b(w)]=delta_ab also shows pure erasure is global Fourier mode, not an operator localized in a proper interval of given current net. OriginalP1 defines locality by support and A/A*-invariant restriction, not global compression.",
      "scopeEN": "Existing E8_1 Cartan-Fock source and literal native embedding; no P1 pullback, code=H_adm identification or physical field assignment. No general ban on global P1 operations. New bridge connects previously checked carry to actual local OPE; prior checks are correlated groundwork.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-cartan-current-local-smearing-and-weyl-class",
        "premise:canonical-source-stress-all-mode-history"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c2536b3e06839cda2ea661dd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:all-real-local-cartan-profiles-erasure-third-bound",
      "titleEN": "Full local current response and sharp erasure one-third bound",
      "statementEN": "For every smooth real8-vector profile with Vhat1=p.u+q.ubar, actual five-code obeys P J(V)²P=(3||q||²+||p||²+Tail)I5, Tail=sum_m>=2 m||Vhat_m||². Grade3 erasure squared norm is ||q||². Its fraction is at most1/3, strictly smaller for nonzero properly local profile with q!=0. Equality requires global rotating first harmonic; fixed real polarization has tighter1/4 bound. No profile produces only erasure output. Full first positive response Gram is scalar and selects no3+2 mark.",
      "scopeEN": "All smooth Hermitian Cartan-current smearings in original neutral Fock module. Norm fractions are not measurement probabilities. Grade decomposition/code projectors are analysis only, no executed projection. No claim all higher field correlations are scalar or all other source fields excluded.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-cartan-current-local-smearing-and-weyl-class"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6ab3d3b32725836057f5c515"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:closed-cartan-weyl-histories-only-logical-phase",
      "titleEN": "Closed Cartan-Weyl histories have only scalar logical action",
      "statementEN": "Actual CCR fixes [J(V),J(W)]=i sigma I and exp(iJ(V))exp(iJ(W))=exp(−i sigma/2)exp(iJ(V+W)). Every finite ordered Cartan-Weyl history is phase times total displacement. Every nonzero total displacement turns any nonzero finite Fock polynomial into exponential nonpolynomial in Bargmann realization. Exactly code-preserving endpoint forces zero total displacement; neutral zero modes are trivial and only common phase remains. Entire stated class provides neither marked R5 nor3+2 selection. Nonzero individual profiles may cancel in total.",
      "scopeEN": "Analytic theorem for finite unitary Cartan-Weyl-only histories and original neutral code-Fock embedding. Not general nonunitary field products, root currents, interleaved stress/current histories, open processes with memory or all E8/P1 operations. No original P1 time law or new code-preservation axiom. Do not unite separate exclusions.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-cartan-current-local-smearing-and-weyl-class",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8d91ccc9ea2dbd35b0235453"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-existing-local-e8-hull-of-native-code",
      "titleEN": "Minimal full local source hull is E8 vacuum space",
      "statementEN": "Four original Cartan annihilators take nonzero quartic to vacuum; all original root currents generate all E8 lattice charges, negative Cartan modes all oscillators. Algebraic mode hull ofC5 is exactlyV_E8; closed local smear hull isH_E8. Both twenties are included. Full character prod_m(1−q^m)^−8 sum_lambda q^(lambda²/2)e^lambda determines all horizontal grade decompositions; grades0..6 dimensions1,248,4124,34752,213126,1057504,4530744. Grade2=1+248+3875 checked by complete Freudenthal recurrence. Controlled grading preserves finite mode word above maximal intermediate weight; smooth local profiles retain controlled infinite Fourier tails.",
      "scopeEN": "Existing level1 lattice/current realization, not rawP1 or physicalH_adm. Distinguish mode hull and Hilbert closure of smooth local fields. No exact10D/45D model or particle count; irreducible affine module differs from finite horizontal E8 decomposition.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f32b1211c9b3102b9b142a92"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-local-quartic-wick-ladder-and-unprojected-native-actions",
      "titleEN": "Full local quartic Wick ladder gives code/erasure action",
      "statementEN": "Actual local F_i(z)F_j#(w) has exactly five Wick contraction classesr0..4 with all Taylor terms. Leading weight8/6/4/2/0 Grams areI25,4I25,(18^1,8^9,0^15),4|I><I|,|I><I|. r1=sum_a g_ia conjugate(g_ja) contains actual erasure20; isolated3creation/3annihilation mode component actsEij tensorI4 on that grade3 carrier.4/4 componentsEij=P_i(u_-1)conjugate(P_j)(ubar_1)/sqrt(NiNj) on ENTIRE weight4 are exactly|f_i><f_j| plus0 on rest, without intermediate projection. Full local products permit nonscalar logical action and entireM5; old pureCartan-Weyl exclusions are not all-field exclusions.",
      "scopeEN": "Mode components are not entire local zero modes or selected physical instruments. Matrixunit law only weight4, not all grades. Leadingr2 is not whole fourth-pole coefficient; retainr3 Taylor term. Wick contraction is field algebra, not executed measurement. ChosenM5 coefficients available, not physically selected. Endpoint map A→PAP is not multiplicative for full field algebra; M5 is realized by stated code-preserving weight4 family, not a representation of all source operations onC5.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9b095120bb8ac5952325b53a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:unmarked-native-w6-simplex-from-full-quartic-ope",
      "titleEN": "Original unmarked W6 simplex from full local quartic OPE",
      "statementEN": "Actual2+2 flatteningsH_i of normalized original quartics give ten intrinsic logical rank1 raysv_t in localr2 product, sumP_t=2I5, Tr(P_tP_s)=1/9. Configuration fixes projective real structure through antiunitary fixing all rays unique up to common phase. On intrinsic real projective locus, sum_t(v_t.w)^4>=2/5 has exactly12 oriented equality points, hence six axes with regular simplex Gram6/5I6−1/5J6. All1024 sign cases exhausted. OriginalN introduced ONLY AFTERWARDS matches literally w_jw_j^T=(6/5)N_pi(j)N_pi(j)^T without fitrotation. Previously separately used UNMARKED W6 simplex thus gains concrete common local field-operator origin.",
      "scopeEN": "Geometric data reconstruction in given source, no physical minimization/real-state rule. Full complex state space has additional continuous minimacosθw1+i sinθw2; explicitly checked, never discarded. Overallantipode/permutation remain. No positivepolar transport or physical3+2 mark. Quartic code remains input; no new independent empirical confirmation or priority claim.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0831c109151fc28714388244"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-e8-current-products-fix-stress-and-exterior-ward-cancellation",
      "titleEN": "Full current products fix stress and exterior Ward cancellation",
      "statementEN": "With actual cocycle dual sign full240-root OPE gives sum_alpha alpha tensoralpha=60I8 and h_dual30. Thus T_Sug=(1/62)sum248:J^AJ_A:=(1/2)sum8:h²:=T_E8,c8. Same stress follows within same source fromr3 quartic Wick ladder. ForT_n=sum248J^A_-nJ_A_n full endpoint factors onC5 atn0..3=(134,103/2,5,1/2), exterior-defect Grams=(100,225/4,9,1/4)I5. FULL source vectors obey(T0/2+T1+T2+T3)f_i=124f_i: exterior pieces cancel exactly, not just compressions. No root/family branch or fitted rate.",
      "scopeEN": "Canonical stress now follows from given normalized full current OPE rather than independent stress premise. Level1/E8 realization remains input. Invariant source operator identity, not physical selected intervention/time law, particle clock or3+2. Correlated source constructions are not independent experiments.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:dafd3cfb82296f64f2a2bdf3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-source-simplex-does-not-select-original-polar-mark",
      "titleEN": "Full source simplex structure does not select original polar mark",
      "statementEN": "Six OPE-reconstructed axes give15 equivalent rank2 pair planes. None equals actual originalP2; minimum squaredHS distance is(21−6sqrt6)/25>0. Full logical field-mode imageM5 is irreducible with centerC, no distinguished3+2 superselection. With all exterior data invariant, fully contracted LINEAR code return/memory kernels stay scalarI5 by native irreducibility even with every exterior path. Nontrivial uncontracted OPE tensors remain and are not excluded.",
      "scopeEN": "No all-E8/P1 no-go or exclusion of covariant density channels, open outcomes, noninvariant preparation or spontaneous branches. No identification of real reconstruction functional with physical potential. Existing polar-fibre/clock theorem remains comparison; new source gives unmarked geometry, not physical selection.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:native-g31-concrete-event-representation",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1f8a98e4ce61403d7573429d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-full-field-event-gram-reconstructs-relative-polar-mark",
      "titleEN": "Original full event fields reconstruct relative polar tensor",
      "statementEN": "Actual native reflections at givenq produce five local quartic difference fieldsDelta_j=F_nj−F_nq; full vacuumGramG=I+J, arbitrary common smooth local smearc_fG. All Wick classes/Taylor terms retained. Original three/two clockorbits give response tensorsKC=DQC D*,KW=DQW D* andR=KC+KW. Without insertingP2/targetangle, mathematical positive RELATIVE tensorR^−1/2 KW R^−1/2=UQW U* is exactly existing originalP2, U=D(I+J)^−1/2. Polar prescription thus has concrete common field/event-response interpretation as relatively normalized quantity.",
      "scopeEN": "Given native E8 realization, clock and marked input, not physical selection of them. Positive normalization computable and unique WITHIN positive normalization class, not P1-derived execution/readout or3+2 matter. Three/two are originalsigma orbit sizes, not independent particle count. Injective r0 field-tensor map is not matrix-product homomorphism.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark",
        "premise:original-native-event-difference-fields-and-state-controls"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:603de2f564f7542ddff393e0",
        "source:8ecb2b89f237d24bd80e7101"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:raw-event-state-positivity-does-not-execute-polar-normalization",
      "titleEN": "Raw event response and state positivity do not execute polar prescription",
      "statementEN": "Actual raw orbit kernels have spectraKC=(4,1,1,0,0),KW=(3,1,0,0,0), coefficient-matrix commutatorHS²72 and do not preserve originalP2. GNS supplies metricG; originalslotcutQW is notG-selfadjoint ([G,QW]HS²12). Oblique transport has antihermiticitydefect²2, rawWeakSupport distance²(28−8sqrt6)/25 fromP2. Full weight8 regular quartic insertion on given marked source state hasGq=(43/5)I+(73/5)J; same vacuum-normalized fields retain eigenvalues68/5,43/5^4 instead ofI. NativeJ fixes quartics. Positive source metric alone therefore does not select physical positive normalization/readout law.",
      "scopeEN": "No all-E8/P1 no-go or claim physical instruments need orthogonal outcome states. Weight8 control disproves corresponding full formal normalization identity, not replacement of all local profiles. Given instrument or other originally grounded nonvacuum history not excluded. Full source,both20s,exterior/memory paths retained.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark",
        "premise:original-native-event-difference-fields-and-state-controls"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:68717556516bcdf3e306b416",
        "source:748b7940e88d21a0f908d8c7",
        "source:a9e0479abeec3c6a6739d295"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:determinant-cover-not-literal-full-cartan-lattice-event",
      "titleEN": "Determinant cover is not same complete Cartan-lattice event",
      "statementEN": "Existing coupled determinant lifth=e^−iπ/4 r acts onquartics as−rho5(r). Coherent incidentresponses−nj−nq haveGramI+J/3 rather thanI+J; positivepolarmark distance²48/25 fromoriginalP2. Unchanged linearCartan actionofh also fails actualE8 charge-lattice preservation:45degree rotation sendsrawroot(2,0,...,0) to(√2,−√2,0,...), outside lattice. All60native r preserve all240roots; all60phase-shifted lifts failsame root test. Hence noVOA-automorphism with EXACTLYthis Cartandictionary.",
      "scopeEN": "Literal Cartan/lattice automorphism dictionary, not allE8operations,moduleintertwiners orphysicalsources. Prior innerE8lift on DIFFERENT chargedC4/F20currentblocks and finite representation comparison remain valid, not identicalCartanregistermap. Do not treat coherent relativephase as irrelevant rayphase.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark",
        "premise:original-native-event-difference-fields-and-state-controls"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ad286d55a50f3556d037c97b",
        "source:b135691a786978adb92f73d8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:clock-free-quartic-product-spectral-sectors-and-native-five",
      "titleEN": "Clock-free quartic product links spectral sectors and actual five",
      "statementEN": "Actual local holomorphic multiplicationM:Sym²C5→fullsourceweight8 hasGram28^1,10^5,18^9. Canonicalprojectorsgive1+5+9; literalH_holo=10I15+(S2* S2)|Sym² with existingconjugatedoublecontractionOPE. Five-sector hasexplicitisometricintertwiner withsameactualnativerho5,notonlydimension5; all15quotientevents checked. Common smoothlocalvacuum smearing ofprimarycomposites preservesGram up toc_f. CentralidentityOPE coefficients aredataofsame*-fieldalgebra,notchosenGNSresponses.",
      "scopeEN": "Acceptedquartic/E8/adjointvacuumnormalization remainpremises.1+5+9 arecomposition/representationsectors,notspacetimedimensions orparticles. Gramcomparison doesnotidentifydifferent sourceweights. No new3+2/physicalselection.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5cc03cabfee782eb7fbb9bdf",
        "source:54e65adc1545fc3acfbf425a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:six-complex-native-simplex-rays-from-holomorphic-product-quadrics",
      "titleEN": "Six complex native simplex rays from original product quadrics",
      "statementEN": "Withoutclock,q,polartarget,realformchoice orNinput, originalproductGram determinesrank9spectralprojectorPi9. ActualsourcerelationPi9(v⊗v)=0 givesninequadrics andexactlysixCOMPLEX projectiverays. Completeelementarycaseproof andGroebneraffinecharts includingallinfinitycharts excludefurthercomplexsolutions. OriginalN introducedonlyafterwards matchesall6raysliterallyasprojectors,withoutfitrotation. Reconstructionstrengthensearlierreallocusminimumsimplex andlinksgeometry toactualproduct/eventfive.",
      "scopeEN": "Algebraicconfiguration,notphysicalpreferencefornullcomponents/states. EarliercomplexminimaofDIFFERENTfourthmomentfunction remainphysicallyunexcluded. OriginofacceptedquarticfromrawP1 separate. Covariantunderbasis/metrictransport,notuniversalreference/preparationindependenceoffullresponses.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bafc56e4329fa815500cc0aa"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:intrinsic-relative-response-covariance-and-state-boundary",
      "titleEN": "Relative response is metric covariant; complete state response remains dependent",
      "statementEN": "Field/labelbasis changes musttransportmetric/adjoint. R=T L^-1 T*,K=T Q L^-1 T* invariantunderT→TA,L→A*LA,Q→A^-1QA;sourcecongruence givesunitarilyequivalentHermitianrelativetensors. InjectiveT givesE(Q)=WQW* inheritingrank/spectrumofsuppliedQ ratherthanselecting3+2. Canonicalstate-relativeformH0^-1/2H_omegaH0^-1/2 dependsonstatepair: completeoriginalf0/f4controlsspectra(19,8³,5),(5,9³,16),markedq gives1+4. Changingresponses leavescentralOP E tensors ofsamealgebraunchanged.",
      "scopeEN": "No unprovedGNSHilbertspaceidentification. FormalcentralOPEidentity isnotuniformUVlimittheoremforall singularstates. Controlsneedfinitecommonmoments,notautomaticallyadmissibleP1seeds;RP,clustering,relativeaction,time/collar mustadditionallyfit.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3560eef2dc447625deed64d5",
        "source:a9e0479abeec3c6a6739d295"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:intrinsic-event-composition-retains-shared-source-and-correlation-data",
      "titleEN": "Event composition needs shared source and correlations",
      "statementEN": "Independenttensor sources/productstate factorizeGram/polartransportexactly. Insameoriginalfieldnet fullcommonprofileholomorphiceventproducts killantisymmetriclabels: orderedmultiplicationC5⊗C5→H8 hasrank15,kernelwedge²C5 dimension10,whileMonSym²isinjective. OriginalDelta0 firstnorm²2,fullleadingpairnorm²64 ratherthan4independentcopies;100actualerasureLeibnizactionsretainallgrade7outputs. Twosourcestateswithsamemarginalsbutclassicalcorrelation give differentjointGrams with exactterm(Bq−I)⊗(Bq−I)/4. Fullfieldassociativityretained;reducedsingle responsesalonearenotgeneralcompositionlaw.",
      "scopeEN": "10Dkernelisrelationspace,notnew10Dsourcesystem. Commutativityargumentforthisholomorphicfieldclass/commonprofiles,notallE8/conjugate/noncommutingfields. Correlationcontrolnotselectedphysicalpreparation. Universalraumlinkisnecessaryretentionofproduct/correlationinformation,notexistenceproof.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:858030ec4c11f15cfd2c8a30"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:clock-free-event-geometry-fixes-clock-class-and-mark-orbit-not-member",
      "titleEN": "Clock-free event geometry fixes clock class and marking orbit, not one member",
      "statementEN": "All15differenceedgesofsixderivedraysgiveA5tightframe,Gram6^5,0^10,cyclerelations;relativeeffectsE=P_root/3sumtoIonresponsesupport,notprojectors. Givenqstargives5ONprojectors,noselectedrank2cut. All6markers/2subsets giveexactly60distinctpolarmarks. Withoutoldclock,225logicaltranspositionpairs give15identities,90doubletranspositions,120noncommutingproductsin40threecycles. Their120orientedfixedpointflagsgiveEXACTsame60polarmarkorbit. Uniqueintrinsiccovariantmarkcanonly haverank0/5underS6,or0/1/4/5underqstabilizerS5. OriginalP2needsadditionalq+unorderedtwosubset;oldclockprovidessuchdata,butisnotderiveduniqueelement.",
      "scopeEN": "ClockclassinactualfiveS6quotient,notautomaticallysamefour/20/fullfieldclockliftorphysicaltime. Symmetryobstructionforexactunmarkedsymmetricinput,alsononlinearuniqueselectors,notallP1sourceswithadditionalanisotropies,states,spontaneousbranches. Noprefernoncommutationruleimposed. Earlier15matchingP2exclusionsconcernadifferentprojectorfamily.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c004475952311327cd8937a7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-charged-seam-character-recovers-global-native-event-pair",
      "titleEN": "Original charged seam character reconstructs global native event pair",
      "statementEN": "Full internalE8Z4character(rootphasecounts52,60,64,64)hasactualG31stabilizer64/logicalimage16;decksquare3072/image48. Bothsplitthesixliteralquarticraysinto{0,1}|{2,3,4,5};exactly{0,1}amongall15globalpairsetsisinvariant. Originalglobaleventpairthereforefoundwithoutoldthreeclock/P2/coupling. Withqoutsidethispairremainfourflags(2,S),(3,S),(4,S),(5,S). LiteralexistingOframe,nofit.",
      "scopeEN": "GiveninternalcharacterandoriginalJ-equivariantE8embeddingremainpremises;notrawP1originofcharacter. Pairiseventlabels,notphysicalrank2/fermions. ActualchargedquarterfoldisDIFFERENTcharacter;noidentification.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:450aa03c97b13407219fc224"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:internal-seam-vacuum-and-original-neutral-tensor-do-not-select-flag-root",
      "titleEN": "Internal seam,vacuum and original neutral tensor do not select flag root",
      "statementEN": "Fullinternalcharacter+E8vacuumhasnofixedq/flag;oldcomparisonflag(5,{0,1})isin4orbit. OriginalR_neut/retained48givesstabilizer16/logical8=C2³,q-pairs01|23|45,allsame4familyomissions. ExplicitfullE8isometryG=(x3,x4,x1,x2,x5,x6,x7,x8)preservesJ,v,Rfield,48span,vacuum,OPEandactsasquartic(45). Itswapsflags(4,01),(5,01)withactualpolarHS²distance(816−176sqrt6)/625>0. Nouniquecovariantselectorfromthesetesteddatapossible. Supplyingonlyq5stillleavesinvariantpairs01and23.",
      "scopeEN": "OnlyspecifiedinternalE8vacuum/character/Robject. R/48includesgivenfamilyomission;preserving48spanisnotpreservingnewcoherentsourcecoefficients. NOexclusionfororiginalfulltwistedCARcovariance,additionalphysicalTheta,allP1sources. Individuallatticeliftsuffice,noglobalsplitsectionassumed.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8250d5d3ac09056f811847e8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-quarter-fold-shift-removes-native-symmetry-obstruction-without-flag-selector",
      "titleEN": "Actualquarterfoldshiftremovessymmetryobstructionwithoutflagselector",
      "statementEN": "UnchangedoriginalMforalpha1/4,3/4givesd=(-1/2,0,alpha/4,-1/2,0,(alpha−1)/4,-1/4,-1/4),norm²85/128. Actualchargedg²order8,28fixedroots,NOTinternalZ4character. Stabilizernative4/logical2fixes4q/16flags,notuniqueone. Fulldhasnativestabilizer1,alsojointwithinternalcharacter;ALL60flagsfixed. Oldsymmetryobstructionthereforegoneford. ThischecksCartanshiftorK=L0+d.h0,notfullC_foldcovariance. OrdinaryE8h0Ω=0,not〈h0〉=d;Kstillscalar4onneutralcode. FixedVirasoroweight85/256twistedfoldstateisnotuntwistedE8vacuumundersamestressintertwiner;twisted/defect/referencetransportopen.",
      "scopeEN": "NodidentificationwithchargedE8Fockvector/fullCARstate,noremovalofchargedholonomy. Nofittedphysicalclock/coupling. Trivialstabilizermeansallcandidatespassthatsymmetrynecessarytest,not60physicalP1theoriesorimpossibilityofsource-selector.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c089ca726a744bf5220299e6",
        "source:81c69732e4c43d34dd491bc1",
        "source:edf8b3ebd03805049e070290"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fold-shift-equivariance-needs-actual-source-response-map-not-another-symmetry-no-go",
      "titleEN": "Foldshiftneedsactualsourceresponsemapratherthananothersymmetryno-go",
      "statementEN": "OnactualfreenativeorbitG.d,everyoneof60seedflagshaswell-definedcovariantextensionS(gd)=gS(d)becausestabilizertrivial. Covariancealonedoesnotselectone. Mathematicalnonuniquenessofcriterion,not60physicalmodels. Missingmapisnowfulloriginalfield/state/normalorderingtransportfromF C_alpha F*withtwistedseam/adjoint/timeintonativequarticeventsandchargedintermediates. InternalresidualswapMUSTNOTextendtoas-yet-unmappedactualstate; furtherneutralvacuummomentsareblindbyexisting scopedallwordtheorem.",
      "scopeEN": "Precisedictionary/selectiongap,nogeneralabstractresetorno-goforactualstate-dependentfieldresponses. No max-overlap,minimization,newmeasurement/clock/couplingrule. Fullphysical3+2originopen.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:dcbb4a596b2e3601599753af",
        "source:097e1f9453172bdddc48c882"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-fold-covariance-current-counterterm-and-quartic-twisted-transport",
      "titleEN": "Original fold covariance yields current counterterm and quartic transport",
      "statementEN": "ExacteigenchanneldecompositionofF f_(8l+k,α)withUα,rk=e^(2πi(k+α)r/8)/sqrt8diagonalizesSAMEF Cα F*,no8sourcecopies;arccorrelationsretained. NegativeDsea l≤−1,originalpositiveα1−a,j≥1sea l≥0. FiniteNSpointsplitcountertermis±(μ−1/2),currentorderingtransported. FixedconformalcurrentreferencegivesactualF_i^d=:f_i(h_++b/z):,b=U_+^T O^T Mδ,nocouplingfit. Sourcetime8[N+p²/2+δ.p]andgroundsubtractionretained. GivenE8extensionhasLi gorder16,g²8;shiftonce. Explicitconditionalneutralfield/statebridge,notphysicalreference/P1selection.",
      "scopeEN": "Fixedconformalcurrentdictionaryisapremise;M/Orootmatchalonedoesnotselectit. NorawP1/fulloddCAR-E8extensionornewvacuumselection;E8p0andadditionaldegeneraterootprimaryseparate. OppositeshiftsignleaveshomogeneousquarticGramsunchanged.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1a8c7c3f539e779301a7377d",
        "source:d5555d06d1c9debd3230c12c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fold-state-full-quartic-kernel-and-erasure-protected-low-order-response",
      "titleEN": "Full quartic state kernel and erasure-protected low-order response",
      "statementEN": "SameoriginalpolynomialsgiveENTIREtwisted2pointkernelΣD_r/[(z−w)^(2r)z^(4−r)w^(4−r)],D_r,ij=Σconj∂νfi(b)∂νfj(b)/ν!. D0conj(m)m^Tretained. AllpositiveBk=Σbinom(k+r−1,2r−1)D_r;first4recoverD1..4bydet1triangularmatrix. Actual20erasurederivativeorthonormalityforcesD3=||b||²I=85/256I,D4I. Codeprotectsdirectioninformationatquadraticstateorder;anisotropystartsorder4despitetrivialshiftstabilizer. B4=(383/128)I+10D2+4D1literallymatchesindependentfullsparseFockcalculation,allpartitions4,31,22,211,1111retained.",
      "scopeEN": "Analyticallposition/allmodetwopointkernelinstatedreference,notuniversalcontactterm/UVlimit/chosenphysicalsmear/instrument. Heisenberg/quarticderivationnotphysicalmatterdictionary.NoclaimedC5closure.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4a2dd2b1b4432415ec2c4185"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-fold-quartic-mean-and-spectral-responses-do-not-match-sixty-flags",
      "titleEN": "Originalquarticmeansandspectralresponsesmatchnoneof60flags",
      "statementEN": "Bothoriginalquartercases:onepointRieszraymatchesnoneof6native rays;D1rank4hasuniquekernelalsononeof6. NONEof60P(q,S)commuteswithD1orcompleteB4;thereforenoneisaspectralprojectorofthesematricesandnocommonreducingpolarflagforfull2pointfamily. Exactsymbolic,nothreshold/fit. FullfixedoriginalinputmodeexternaloscillatortermsretainedinB4.",
      "scopeEN": "ONLYstateddirectmean/kernel/spectralidentificationsinfixedreference. Physicalprojectorneednotcommutewitheverysourceresponse;NOsuchnewaxiom. NoallP1/state/3+2no-go,norejectionofotheroriginalobservables/chargedhistories/specifiedprofiles. Noeigenvalue/overlap/profilefit.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:760f3dccdc538a55f8078a63"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-winding-full-state-response-removes-vacuum-rank-two-shortcut",
      "titleEN": "Originalwindingfullstateresponseremovesvacuumranktwoshortcut",
      "statementEN": "ActualpreviouslyderivedglobalchiralW4:p→Pp+a,a1^40^4,Pk↔k+4. LiteralexistingG=O^TMPM^TOgivesu0→iubar0,u1→−u1,u2→u2,u3→−iubar3,notunchangednativeU4clock. Homogeneousquarticframeoverlapdiag(1/2,0,0,1/2,0)rank2. FULLoriginalR_bwithinputcharge0underW4isΓG R_bonoutgoingMa;literaloutgoingfieldshaveb_out=U_+^TO^T(d+Ma). Crossmatrixrank5BOTHquarters,fullW4outputGram=inputGram. Sourceincrements7/9(fold7/8,9/8)matchoriginalWard,chargecarryandallpolarizations/modesretained. Apparent2+3vacuumchartdeficiencyisnotactualstateresponse3+2.",
      "scopeEN": "OriginalW4isglobalCARimplementerofgivensource/evenD8E8extension,notP1localinstrument. Oppositepolarizationnotcreation/annihilationmixing. CrossGramfullmatrixelementswithoutgoingcharge,noperformedprojection/required5closure. Noallwinding/historyno-goorphysical3+2selection.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:abb4fd492e0f00cc6b30f73c",
        "source:fabe84fd503520f0b51727b0",
        "source:1a8db88614570db5aa2d1c62"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-source-global-time-winding-history-factorization",
      "titleEN": "All original global time-winding histories reduced exactly",
      "statementEN": "Given Ward increments are c_n(q)=Falpha(q+n)-Falpha(q), Falpha(q)=q(q-1)/16+alpha q/8. Thus K-Falpha(Q) is winding invariant and alpha independent. Actual CAR space factors via W_n as ell2(Z) tensor H_Q0, not an assumed rotor. Every finite ordered time/winding word has the stated exact normal form; all n=8z+r checked symbolically. On a fixed neutral R_b,k field mode the input multiplicity is unchanged. Charge-return acts scalarly in actual B_k metric, retaining all intermediate charges/modes. W1 lies in original odd vector sector; W2 is smallest even winding and ends at an actual E8 root.",
      "scopeEN": "Only given global free source time/W_n/Q phases, not all local fields. No closed-C5 axiom or performed projection. Total time acts on grade superpositions. E8 half-sector needs its lift; global W2 is not local root vertex.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:charged-car-negative-sea-source",
        "premise:fixed-scalar-quarter-hardy-source"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5c9992f6b6699b2675439471"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-local-density-folds-to-correlated-root-current-and-erasure-response",
      "titleEN": "Original local density reaches quartic and actual erasure",
      "statementEN": "Original scalar phase folds in fixed Fourier dictionary to Vphi,kl=sum_r phi((x+2pi r)/8)exp(2pi i(l-k)r/8)/8; frequency m couples k-l=m mod8. J-1 is exactly seven adjacent CAR zero modes plus wrap mode-1, no fitted root weights/Klein phases. Complete R_b,4 field response is independently reconstructed in original CAR; Gram exactly matches prior sparse Fock Gram. Both quarters: J+-1 takes source energy32 to31/33, retains all16 signed cyclic root charges and full vector CCR. Both Grams rank5; lowering response nonscalar relative B4. Actual erasure a_a R_b,4 f_i=R_b,3 partial_a f_i and all20 nonzero Ward outputs [a_a,J-1]=sum_r(barV_(r+1,a)-barV_(r,a))a*_(r-7)a_r exact without free coefficients.",
      "scopeEN": "Given negative-D CAR and conditional field reference. No physical P1 profile/coupling/detector selection or matter/Higgs assignment. J+-1 are global Fourier controls of existing local density. Correlated offdiagonal fold class differs from earlier independent diagonal Cartan-Weyl exclusion. All external modes/charges retained.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:454c9c15591c77a2d77d8ac1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-current-all-mode-energy-and-geometric-stress-bridge",
      "titleEN": "Original current modes, energy and twisted geometry connected",
      "statementEN": "Original c1 Sugawara identity 8K=Q(Q-1)/2+alpha Q+sum_m>0 J-m Jm is checked on full R_b,4 inputs as all32 response Grams summing to32B4; higher lowering modes vanish by positive source energy, not chosen truncation. Original Lcal_m^alpha has fixed r+m/2+alpha coefficients and ground weight(alpha-1/2)^2/2. Full vector Wards [Lcal1,J-1]=Q+alpha-1/2 and [Lcal1,Lcal-1]=2Lcal0 hold. Folded c8 geometry is twisted Yd(T), Lhat_n=Lcal_8n/8+21/64delta. Original Lcal+-1 changes fold energy by1/8 with cyclic root charge outputs, outside prior unshifted c8 stress/primary-vacuum theorem.",
      "scopeEN": "Twisted and unshifted stress/input pairs must not be identified. Prior scoped exclusions retained. Exact CAR window follows maximum source energy33; no physical time calibration or external coupling.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ff3dfc51c9c3e9279c4736d4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-current-geometric-response-pair-has-no-common-polar-sector",
      "titleEN": "Density and geometric responses have no common 3+2 spectral sector",
      "statementEN": "Both quarters: B4^-1G_J and B4^-1G_L are B4 selfadjoint with common commutant dimension1 overQ(i), hence generated complex response *-algebra M5 on input labels. No common reducing rank2/3 decomposition of these actual response forms. Density response has five distinct generalized eigenvalues. In COMPLETE mode family J30 response rank2, but rank3 kernel matches none of60 original polar flags; Adjacent rank3 J29 response is not ORTHOGONALLY complementary in B4 metric, but joint rank5 gives an oblique algebraic direct sum. Positive relative normalization for this supplied mode pair remains possible; neither its original selection nor a literal normalized polar comparison is claimed. Mode30 lowers source energy by30, not a derived unitary Coxeter30 action.",
      "scopeEN": "ONLY common spectral-sector identification for these forms and literal mode30 polar shortcut. Not a physically executable compressed M5 algebra, no axiom requiring physical marks commute with every response. No exclusion of nonlinear intrinsic event relations/other full field histories/all P1/3+2. Mode30 not adopted as selected intervention.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:44efd0b9e63961a63c5b69a7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-current-ordered-hall-kernel-and-actual-folded-field-products",
      "titleEN": "Complete ordered original-current response and actual folded-field products",
      "statementEN": "Actual five neutral sourceE32 states map exactly by original Maya occupations to Schur states. All32 lowering-current VECTORS independently match Young ribbons, stress1/2 matches fixed Sugawara and full CCR, both quarters. All state coefficients saved. Kij(u,v)=<Pi,exp(sum um pm)Pj(pm+mvm)>Hall gives all mixed current correlations; Weyl response additionally retains Gaussian sum over ALL profile modes, not only1..32. Every finite smooth density/source-time history follows with original BCH phase. Actual folded quartic fields remain on eight original preimages: A_a=Ualpha diag(Vka)Ualpha*, scalar source operation gives Gphi(x+)dagger A_a Gphi(x-). Entire existing point splitting/reference subtraction conjugated, no second b shift. Separated Heisenberg field products follow from finite Wick Pfaffians using same ordered Calpha/1-Calpha.",
      "scopeEN": "Given c1 CAR source and explicitly conditional NS/native dictionary, not all E8/P1. Hall is a STATE/current intertwiner, NOT a point-local cover identification with weight32 field. Finite stress-mode words yes; arbitrary exponentiated geometry or new unsmeared coincidences require analytic control. Mixed amplitudes retaining implementer are not bare vacuum Pfaffians. No physical profile/reference/readout selection.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d66d84767ab74dd6dead437e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-seam-grades-full-density-geometric-products-and-energy-response",
      "titleEN": "Original seam grades full density/geometric products",
      "statementEN": "Existing full internal seam character v=(0^5,1/2^3) gives original CAR phases[-1,i,1,-i]^2 via same M. Exactly tv Jm tv^-1=i^mJm and likewise original Lcal_m^alpha; full products carry total Fourier grading including central OPE terms. Known global tv=exp(-4pi iK)exp(i pi(1+alpha/2)Q)=(-1)^Q Walpha^-1 reused on all charges, not claimed new. Entire32-mode energy response splits without profile fitting into four original character classes Grho summing to32B4, both quarters.",
      "scopeEN": "Internal order4 character remains distinct from actual quarter holonomy. Retain odd CAR parity; no physical holonomy compensation or clock selection. Energy response forms are not an executed measurement or entire local E8 algebra.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9c3e343fa357d190546e1ea5"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-seam-complete-density-grading-not-sharp-32-input-sectors",
      "titleEN": "Complete original seam response does not yield sharp3+2 input sectors",
      "statementEN": "All four complete Grho are EXACTLY positive definite rank5 in BOTH quarters, sum32B4. Hence Erho=(32B4)^-1/2 Grho(32B4)^-1/2 lies strictly between0 andI, as does every proper nonempty coarsening. Deck-even/odd responses both rank5. Exact common commutant of(32B4)^-1Grho has dimension1 overQ(i). No sharp deterministic character/deck classification of five input directions or common reducing3+2 spectrum of these forms.",
      "scopeEN": "ONLY sharp input-sector/common-spectrum identification excluded. No axiom that physical mark must commute with every response; no exclusion of all nonlinear event relations, histories, output rules or P1. Existing intrinsic six rays/60flags and global seam pair retained. Mathematical response effects are not postulated/performed POVM.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:00201148084da040553b008c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-density-all-profile-mean-work-scalar-on-native-packet",
      "titleEN": "Original mean density work is scalar on entire event packet",
      "statementEN": "Original CCR/time give exactly Wphi* K Wphi=K+i[K,Jphi]+sum_m>0 m²|phim|²/8. Since all five actual inputs haveQ0,K4 and linear term shifts nonzero energy, full matrix <Pi,Wphi* K Wphi Pj>=(4+sum m²|phim|²/8)B4ij for EVERY smooth real original profile. Mean work does not distinguish these input directions, although their full coherent response is directional.",
      "scopeEN": "Exact matrix elements, no performed projection, energy-minimization rule or no-go for full work statistics. Primitive action and P1-INSERTION-TANGENT reread at original: physical source family/reflection/domain/eta not supplied by this work identity; no blanket relative-action isospectrality for arbitrary phase.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f067afc6d09113ee38f416dc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-p1-gap-normalized-action-covector-and-scalar-holonomy-class",
      "titleEN": "Original P1 differential with actual gap dependence",
      "statementEN": "chi=1/lambda forces delta(D/chi)=lambda deltaD+deltaLambda D. For isolated simple signed gap branch deltaLambda=sgn(E0)<u0,deltaB u0>; entire corresponding term in relative action differential derived without commutativity. Clusters, constant nullity, moving R/domain/reference/eta correctly scoped. In actual scalar quarter circle, EVERY smooth real v gives Balpha+v unitarily equivalent to Balpha+mean(v). On fixed holonomy branch mean(v)=0, gap/chi unchanged exactly while Pgap moves. This supplies a source covector, not a selected physical source variation/event functional; scalar gauge orbit is not inequivalent-minimal-P1 model theorem.",
      "scopeEN": "Regulated trace or controlled trace-class source curve with legitimate domains. Circle lemma does not imply entire relative-action isospectrality with fixedR; same phi symbol is no physical insertion dictionary. Given scalarCAR/reference conditional relative toP1. Earlier P1-INSERTION-TANGENT/master/minimality boundaries reused. Physical deltaD/deltaB/embedding/event relation remains open.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress",
        "premise:declared-p1-p2",
        "premise:typed-source-structures",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:charged-car-negative-sea-source",
        "premise:original-gap-normalized-primitive-relative-action"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:73d0a24ec0525512e02c49a0",
        "source:bf3bcaffac300236017a96f6",
        "source:00ef724485f28224dfc3bca0",
        "source:748b7940e88d21a0f908d8c7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-p1-gap-car-component-not-native-sharp-32-event",
      "titleEN": "Source-fixed gap occupation is not a sharp native3+2 mark",
      "statementEN": "Actual original gap definition selects mode0 foralpha1/4 and mode-1 foralpha3/4, gap1/4 each. Within same stipulated CAR, Qgap=sgn(E0):a_r*a_r: is full particle/hole projector without rank fitting. On complete actual R_b4 inputs, B=I*I,H=I*QgapI obey EXACTLY H>0 and B-H>0, both rank5. Correct metric response strictly between0 andI, nonscalar/nonidempotent; exterior H-HB^-1H strictly positive rank5, bothquarters. This direct spectral bridge from original scale function is not a sharp3+2 input mark. Qgap is global spectral mode, not insertion localized in proper interval.",
      "scopeEN": "ONLY literal identification of this canonical gap-CAR component with sharp native3+2 mark excluded. Qgap itself NOT claimed P1-selected physical event; no measurement, executed projection, closedC5 requirement, no exclusion of all unsharp/nonlinear events or allP1. Boundary eigenmode/internal direction/physical species distinct; original sixrays/60flags/globalpair/E8 retained.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress",
        "premise:declared-p1-p2",
        "premise:typed-source-structures",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:charged-car-negative-sea-source",
        "premise:original-gap-normalized-primitive-relative-action"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5d82a44c6fc947bc1883a1d1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:complete-positive-scalar-first-order-circle-source-normal-form",
      "titleEN": "Complete positive scalar first-order source fiber classified",
      "statementEN": "Every operator in declared class has B=-i(a d+a_prime/2)+c,a>0,c real. T=integral1/a,omega=2pi/T,beta=integral c/a/(2pi),x_prime=omega/a,eta_prime=(omega beta-c)/a yield unitaryUf=sqrt(omega/a)exp(ieta)f(x),BU=Uomega(-i dx+beta) on fullH1 domains. Whole spectrum omega(Z+beta), no mode cutoff. SameB determines unique-up-to-phase uniform wind1 representative u_B=exp(ix),[B,u_B]=omega u_B andQ_B=exp(iTB/4),Q_B^4=exp(2pi i beta)I: spacing,proper-timecoordinate/chargedquarterreturn fromoneoperator,not newclock/interventionselection. Original fixedquarter holonomy andgap1/4 giveomega1; unmarked one-particle source sameBalpha up to coordinate/phase transport. Four fixed marks require all arc travel times/possible endpoint phases, not dimension/species identification.",
      "scopeEN": "Only smooth scalar positive elliptic local differential class on given source. Not all minimalP1 fiber or matrix/defect/nonlocal/E8 classification. One-particle unitarity permits no reset of CAR reference sea,normal order,Schwarz/central term,J or relative action. Retain native sixrays/60flags/globalpair/full field response.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures",
        "premise:positive-scalar-first-order-source-comparison-class"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b587f0919f97419214d0132d",
        "source:69c14eb7dd7840670dfed8e3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-source-time-seam-ward-rigidifies-scalar-principal-symbol-with-carry",
      "titleEN": "Fixed original time-seam Ward fixes scalar principal symbol",
      "statementEN": "Whole class satisfies[B,Z]=aZ. Retaining same original constantWard[B,Z]=Z forcesa1 without metric minimization. Given wind1symbolu=exp(iphi) requiresa phi_prime=kappa,henceomegakappa. Additional fixed quarter rotation makesc quarterperiodic; continuous originalbranch mean c=alpha leaves quarterperiodic gauge transport fixingZ/all4marks. Globally retainmean c=alpha+N: actualQalpha=exp(i pi alpha/2)Q4,Qalpha^4=exp(2pi i alpha)I,joint invariant exp(i pi B/2)Qalpha*=i^N. Literalclock/endpointframes retainNmod4, exactoriginaltimequarter equality forcesN0mod4;4Zlargegauge/sea carry not deleted. Reference sea fixes originalN0branch.",
      "scopeEN": "Ward retained as already given-source object, NOT derived fromP1 spectral flow. Separate continuous marked gauge fiber and globalinteger branches. No autonomous clock/new species/unchangedFockstate/physical intervention inferred. No3+2 derivation or closedC5 requirement.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures",
        "premise:positive-scalar-first-order-source-comparison-class",
        "premise:given-original-fixed-one-particle-time-winding-ward"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:19cbd8763cf10007a1ad5113",
        "source:b288393e012288e30f485532"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:unit-spectral-flow-gap-and-four-marks-do-not-imply-fixed-source-ward",
      "titleEN": "Unit flow, gap and four marks do not force original Ward",
      "statementEN": "For arbitrarya>0,Z*BZ=B+a,pathB_s=B+s a has eigenvaluesomega(n+beta+s):0<beta<1 gives exactlyone upwardcrossing independentofa. UnitSF is not constantunitWard. Exact controls a=(1+epsilon cos(ktheta))^-1,c=alpha,abs(epsilon)<1,k1/4 have samegap1/4,holonomy,SF1;k4 additionally preservesall4marks,equalarctimes/geometricquartercovariance. Yet[B,Z]=aZ differsfromZ forepsilon!=0. Controls not claimed completeP1models; under fullcovariantdatatransport they represent sameunmarkedsource.",
      "scopeEN": "ONLY implication from named weakercircleconditions to fixedoperatorWard excluded; premise list deliberately does NOT include fixedWard. No completeP1/E8countermodel or physical3+2/eventno-go. Do not identify rawP1 seamindex symbol with givensourcecircle without actuallocalization/operator dictionary.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures",
        "premise:positive-scalar-first-order-source-comparison-class"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:19cbd8763cf10007a1ad5113"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:four-native-starts-have-distinct-original-fold-state-correlations",
      "titleEN": "Four native starts have distinct correlations in same fold state",
      "statementEN": "Actual unitquarticrayswq=sqrt(6/5)nq,q2..5,S01 in same originalFCαF* fixedconformalNS/M/Odictionary give phase-invariant connectedc1=wq*D1wq. Common denominator1006632960,numeratorsα1/4=(1200580,1300621,982285,1446340),α3/4=(1308100,1521805,1089805,1338820);all6pairs distinct perquarter. c2=4335/131072,c3=85/256,c4=1 equal; firstdifference alongtheserays sixthorderinb. Alsotr(P(q,01)D1) givesfour pairwisedistinctQ(sqrt6)values perquarter. Therefore noall-response-preserving fixed-state*-equivalence transporting actualquarticspace andtheseplanes; universalOPE-I metric forcesunitarity. Obstruction doesNOTrelyonlyontrivialG31stabilizer andplane-onlytestneedsnoextra distinguished-raypreservation.",
      "scopeEN": "Only markedobservables in statedexistingfield-state/coordinate/adjoint/reference dictionary. Notfourunmarkedtheories orphysicallyadmissibleP1preparations. Larger maps abandoningactualquarticspace/sourcecoordinates/referenceobject notclassified. Nomaximum/minimum/overlap/measurementselector or3+2derivation. Sourcecontainsallfourfields simultaneously; distinguishabilitydoesnotselect.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:four-starts-fixed-state-versus-whole-datum-comparison"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3a46ba5c4f3e9376094c3f18"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:four-starts-full-joint-kernel-and-charged-covariant-transport",
      "titleEN": "Complete joint four-start response and charged covariant transport",
      "statementEN": "Forall4q/bothquarters complete separated25-fieldkernels ofquartic5,actualerasure20/allcrossblocks computed,five25x25Wickcoefficientspercase/allmodesdetermined. ALL-WORDlattice-Wickgenerator withorderedcocycle,d/z,chargedintermediate/endvector specified; originalh5carry retainedthroughwholeconstructor/Deltatransport. ActualG31lifts from46080rootactionsconnectq5toq2/3/4withinternalseam; d->Gd/full-datumtransport givesUGYd(a)UG*=Y_Gd(UGa),H_exc=8(L0+d.h0)/sigma_d transported. All240unwrappedroot-time/twistpairings/all5quarticWicktensors exactlycovariant. AtFIXEDd chargedresponsesdiffer; datumtransportisnotfixedsource-statesymmetry.",
      "scopeEN": "25fields notcompleteE8basis;wholealgebraspecifiedbygenerator.PassiveLqframesnotactiveerasureoperations;activefullbar4actionretained. Individual latticeliftswithcocyclecochain,notglobalG31splitsection;notautomaticoddCAR/P1automorphism. Smoothinfinitehistoriesneedpreviousdomain/tailcontrol. ConjugatingALLdata includingreference/originalwinding isrepresentationcovariance,notphysicalgaugeredundancyproof.NoclosedC5/executedprojection,newcoupling/physicalsource.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:four-starts-fixed-state-versus-whole-datum-comparison"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:309fb4a3ccbe359a28d58a45",
        "source:20e65a506e2060b766c641e3",
        "source:b89a87b341ed721ed3ea54be"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:four-native-polar-marks-not-fixed-source-state-gauge-equivalent",
      "titleEN": "Four polar planes are not a fixed-state equivalence of the quartic space",
      "statementEN": "Excluded is identifying the four marks as all-response-preserving symmetries of the FIXED original fold state within the specified actual quartic space. Universal central OPE metric forces such action unitary and preservation of tr(Pq D1), whose four exact values are pairwise distinct per quarter. Not a universal classification of physical P1 gauge equivalences or exclusion of passive whole-presentation transports.",
      "scopeEN": "Only markedobservables in statedexistingfield-state/coordinate/adjoint/reference dictionary. Notfourunmarkedtheories orphysicallyadmissibleP1preparations. Larger maps abandoningactualquarticspace/sourcecoordinates/referenceobject notclassified. Nomaximum/minimum/overlap/measurementselector or3+2derivation. Sourcecontainsallfourfields simultaneously; distinguishabilitydoesnotselect.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:four-starts-fixed-state-versus-whole-datum-comparison"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3a46ba5c4f3e9376094c3f18"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-pointer-template-requires-source-context-identification",
      "titleEN": "Original measurement template exists; its source context requires identification",
      "statementEN": "The original text explicitly provides a Lueders record instrument for an assumed complete orthogonal pointer family. Optional Q supplies preparation rho0 and readout. The source problem is identifying this instrument in the same physical source algebra, not inventing a new Born rule. The passage identifies no pointer with P(q,01).",
      "scopeEN": "Source audit of these original passages only; no global P1 underdetermination, new probability axiom or executable native pointer. Existing operational seed equivalences are not preparation definitions.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-stable-pointer-instrument-and-given-context"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:53b6d87d18e29b7777d4a65b",
        "source:c8ef963f5038c33640fe1ce3",
        "source:d09bebd241166ec59c03b808"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:four-polar-context-algebra-and-source-crosscoupling",
      "titleEN": "Four polar contexts give C+M4; original correlation couples to full M5",
      "statementEN": "All four actual Pq at fixed S01 satisfy Pq=Z+|vq><vq| with common rank-one Z and overlap (11+4sqrt6)/25. A spectral polynomial of sum Pq constructs Z; products generate full M4 on Z-perp, hence mark algebra C+M4 and commutant C². All six pairs are noncommuting and admit no common sharp pointer refinement. Original D1 couples Z to its complement with squared crossnorms7882461/4398046511104 and3201175/13194139533312, giving full response algebra M5 and scalar commutant.",
      "scopeEN": "Complete exact classification only of this four-mark menu plus original D1 on native quartic observation space. D1 is a correlation coefficient, not an executable intervention. 1+4 is not full-source superselection; no axiom requiring physical pointers to commute with every response. Contextual/sequential/unsharp instruments remain possible. Ray overlap-1/5 uses native coefficient metric, not physical R_b4 preparation Gram. No q/3+2/P1 selection.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:four-starts-fixed-state-versus-whole-datum-comparison",
        "premise:original-stable-pointer-instrument-and-given-context"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:35e5f29e7b993fed5e840e5f",
        "source:8c4a6d5c4e0fda83298311c0",
        "source:4c11dff3f32958352d671648",
        "source:8c375ecf1628bac0064dc8e2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:every-native-quartic-has-all-eight-original-car-supports",
      "titleEN": "Every nonzero native quartic has all eight original CAR supports",
      "statementEN": "In unchanged M/O/NS dictionary the highest eight-fermion CAR coefficient map of all five original quartics has exact rank5:70x5 map, raw Gram determinant495/8, normalized165/131072. For EVERY original preimage and both quarters its degree7 CAR commutator has Gram G/2 and rank5. No nonzero quartic ray or polar-plane field cancels its contribution at any of the eight source locations. Both b shifts and lower-CAR-degree normal-order/derivative terms cannot remove this witness.",
      "scopeEN": "Field support in the given conditional eightfold dictionary, not a dimension identification or a point-local Hall weight32 replacement. Quotient locality pulls back to eight preimage arcs. Other composites, state-matrix-element cancellations and physical P1 localization are not classified; no q selection or general locality prohibition.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ad3bca563e6c50294157de6c",
        "source:eecc661416a6346889457a77",
        "source:c1f122c2dcc4ef8c6a31f21c",
        "source:28efd8fc9f729c363fbd0266",
        "source:4d453fbed1be6e93e8fc28c8",
        "source:cb77c5277bbc071fef6c65ff",
        "source:0802a899af816cd836c30849",
        "source:1363e3cb16a51acd0216a866",
        "source:7d74f6bdb1b978286f32e13f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:bounded-proper-local-source-operation-cannot-exactly-prepare-positive-eigenpacket",
      "titleEN": "Bounded proper-local operation cannot exactly prepare positive eigenpacket from same sea",
      "statementEN": "In the given full positive CAR vacuum net, local separation of Omega and A Omega=psi,Hpsi=Epsi,E>0 for bounded proper-local A imply alpha_t(A)=exp(itE)A. Then A*Omega would have energy-E; positivity and separation force A0. Actual original constructor confirms both quarters: five full source states neutral in every residue, only H_alpha32, Gram rank5, supports694/710/711/713/688. Thus the lemma covers all nonzero actual R_b4 target directions without a closed-code assumption. Positivity extends the exclusion to pure or mixed exact E32 outputs of normal instruments with finite/countable bounded Kraus operators in the same proper interval algebra: every Kraus vector would lie in that positive eigenspace and vanishes.",
      "scopeEN": "Conditional on the same full CAR source, support-preserving source time and local vacuum separation, not merely finite compression4I. Exact preparation from same sea by ONE bounded proper-local operator, including products fitting in a larger proper interval. No approximation/probability/cost bound, no ban on unbounded field insertions, other initial states, global protocols or all P1 physics. NS/quarter reference transport explicit; physical P1 net identification remains open. No classification of abstract AQFT-local CP maps without such local Kraus implementers.",
      "status": "conditional",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress",
        "premise:same-full-positive-energy-separating-local-car-source"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c189c4cc12f68f892cc1dc8f",
        "source:eaf337b88e7664a64a70ba90",
        "source:1363e3cb16a51acd0216a866",
        "source:7d74f6bdb1b978286f32e13f",
        "source:2cf32f6456e67051d6c9cdc8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-original-erasure20-and-joint25-have-all-eight-source-supports",
      "titleEN": "Full original erasure20 and joint25 retain all eight source arcs",
      "statementEN": "The actual20 fields g_(i,a)=partial_a P_i/sqrt(N_i) have original Fock GramI20. Their highest six-fermion CAR map is56x20,rank20,nullity0,raw Gram determinant1032386052096,normalized194481/1099511627776. Every original-sheet commutator has Gram3/8G andrank20 in both quarters; original b shifts retain the principal term. Quartic5 and erasure20 cannot cancel their distinct highest CAR degrees8/6 and commutator degrees7/5. Every nonzero combination of the complete existing joint25 field space therefore has detectable support on ALL8 preimage arcs.",
      "scopeEN": "Exactly the original neutral erasure20, original norms and given M/O/NS eightfold dictionary; not a charged E8 twenty or physical particle identification. Completeness only within the existing linear25-field space, not allE8 fields/nonlinear products/admissibleP1 operations. No separate E24/joint25 preparation theorem or physicalP1/q/3+2 selection; earlier preparation-lemma hypotheses remain separate.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "attemptIds": [
        "contract:joint-native-algebra-selection-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:11f660e4757ed598338ce090",
        "source:5e00c3454e0a31e551fc1dab",
        "source:e96ec8bb71fd31c2fa031c8e",
        "source:bd90560cd77fc46b62991b44",
        "source:0479aaf48d8cf6679fd0b729",
        "source:2ffab260aa55f6cf581409fe",
        "source:57e2ac7147dc587a75bbc6ea",
        "source:52fea530de6bf6eeb87dd9ab"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:two-face-collar-fixes-face-current-phase-and-distinguishes-relative-endpoint-lift",
      "titleEN": "The same two-face collar fixes the current phase while common and relative boundary transports remain distinct",
      "statementEN": "UR.COLLAR.FACE_CURRENT.01: In the existing scalar quarter circle, the original G_ell Cauchy graph under the explicit charged-CAR/quasifree premise gives exactly the original level1 current cocycle on its second face, its negative on the first, and zero for the common lift. This holds for all smooth real profiles by sum_r(n_r-n_(r+k))=k, not a mode truncation. The same n gives beta=2ell, full thermal current response, the charge-retaining Hall/winding partition and a controlled limit to the original negative sea. Common g-direct_sum-g transport and I-direct_sum-g have the same second-face covariance but distinct full G and coherent phases. Even four-mark-fixed quarter-periodic sin4theta,1-cos4theta give exp(2ist) on one face versus1 jointly. A concrete geometric repair g_chi=exp(i chi(r)phi(theta)) gives L_phi=g_chi Lg_chi*=partial_r+B_alpha-i chi_prime phi-chi phi_prime and T_phi=g_phi T in the actual scalar transport block; its boundary graph is independent of the interior frame interpolation. This does not select physical execution.",
      "scopeEN": "Given scalar quarter circle and full product collar with actual charged CAR quantization; no P1-derived statistics or physical source selection. No novelty is claimed for general current algebra. Infinite analytic formulas plus exact finite controls, not finite CCR representations. Relative endpoint transport is an explicit frame/operator family, not a proven original boundary intervention with fixed reference/domain/Padm. Phase distinction needs full source access or coherent control; one-face conjugation channels can agree if the opposite face never recouples. Normal distance is not physical time; original time, zero mode and absolute reference remain separately retained. No native3+2 selector, pointer/record law,4D determinant-line theorem or T1-T8 closure. Existing4/5/20/carry/E8/eight-preimage structure remains.",
      "status": "conditional",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:charged-car-pure-two-face-cauchy-graph-state",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:charged-car-negative-sea-source",
        "premise:original-single-circle-local-density-and-geometric-stress",
        "premise:typed-source-structures"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:46b86d7dc07d591bc7fdcd20",
        "source:209a12d2ff10b0240383e799",
        "source:f59d608b6369a82e3b80f25e",
        "source:29354f2e8470dbbad010cb34",
        "source:d66d84767ab74dd6dead437e",
        "source:5c9992f6b6699b2675439471",
        "source:8654660dd2532a6fd5cfa43a",
        "source:bbe7a2bb6abcf0f1edd55351"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-dirac-cauchy-vector-cocycle-cancels-and-endpoint-domain-distinction",
      "titleEN": "Automatic full Dirac identification of the chiral current phase fails",
      "statementEN": "Excluded is the automatic identification of the complete normal-commuting Dirac-CAR vector current with the original nonzero chiral current phase, only under the stated premises. UR.COLLAR.FACE_CURRENT.01, DIRAC-LIFT continuation: For a complete Lagrangian Dirac Cauchy projection C with N C N*=1-C, c_(1-C)=-c_C. For implementable X,Y commuting with N, unitary covariance also gives c_(1-C)=c_C, hence c_C=0. In the existing product collar B=diag(A,-A), occupations n(A) and1-n(A) on ONE boundary face give -2i,+2i and total0 for the original four-mark-fixed profiles. This differs from the earlier two-face cancellation of one scalar block. Fixed Clifford symbols force g I2 on this two-component module; diag(g,I) changes the normal/tangential symbol. The complete lift D_phi=D-i chi_prime phi Jn-chi phi_prime Jn Gamma is a bounded Hermitian perturbation. Transported domain/reference/Padm give frame covariance; a fixed original selfadjoint domain remains analytically valid but specifies a relative boundary attachment not physically selected here. Explicit extra Dref/Drel commutator terms are retained at fixed geometric R; fixing R alone does not break covariance when U commutes with R. Nonconstant four-mark-fixed profiles do not preserve the old APS sign subspace, which is not a selfadjointness no-go. Original Gamma already identifies D_plus, but not its physical measure/line connection. The prior scalar result remains conditionally valid.",
      "scopeEN": "Original complete two-component Dirac collar and explicit CAR/Lagrangian/implementability class; no novelty claimed for standard current/Dirac theory. No exclusion of all P1 sources or chiral-measure/inflow realizations. Cauchy projection, APS sign subspace and OS Padm stay distinct. No computed fixed-domain spectral response, physical event execution or 4D no-go. Higher-dimensional trace formulas need separate control. All original native4/5/20/carry/E8/eight-preimage structure retained; no new finite-code closure requirement. Prior measure/log-profile boundary and open chiral/determinant-line contracts reused, not closed.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:charged-car-pure-two-face-cauchy-graph-state",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures",
        "premise:complete-lagrangian-dirac-cauchy-car-quantization"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3085dc15b0f4ce661023e40c",
        "source:fe7081bdbdacccc20d8d89bc",
        "source:82c18921eb56ec7a4eb344f8",
        "source:ce1306c78c5a375e7f2de960",
        "source:bbe7a2bb6abcf0f1edd55351",
        "source:7af7894ef3e81fd54f22b386",
        "source:a81c4e5c9d5aca545235ab66",
        "source:748b7940e88d21a0f908d8c7",
        "source:428bf398a2eb0e44a7cc2b7f",
        "source:741f0cb7ef057806b4f08a4d",
        "source:6e712a71a2fb68462ed31a33",
        "source:18f41a2a3ea361e49328f939",
        "source:8654660dd2532a6fd5cfa43a",
        "source:615b42f3cb2f1a62a54bf4ff",
        "source:41131a5d79fd2724483e0e21"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:unchanged-qwz-full-finite-energy-spectral-exhaustion",
      "titleEN": "Full finite-energy carrier of unchanged QWZ source exhausted",
      "statementEN": "22Oct: Three rho ranges in h²=sin²p I+(H0+rho Z)² show at most two eigenvalues per momentum have magnitude<1/2; all others cost>=N/(4pi). Fixed energy E enforces finite,N-independent |j-alpha|<=pi E/2. Both small branches give |j-alpha| with opposite edge orientations. For E outside the limit spectrum the ENTIRE Fock spectral rank stabilizes,not merely fixed words. Tr exp(-beta H_N) converges for every beta>0 to product_j(1+exp(-beta|j-alpha|))²; bounded mean energy gives subsequential compactness.10 exact source identities,2 direct full-builder and12 spectral controls passed; all-N reasoning independently reviewed.",
      "scopeEN": "Same full free cylinder,sea,time,energy scaling. No extra independent finite-energy multiplicity; NOT a complete classification of local scaling nets. Eightfold folding with another coordinate/locality/stress dictionary remains possible. Other defect sectors,vacuum subtractions,sources or interactions need a new map. No P1/E8/T1-T8 closure.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:unchanged-quarter-qwz-full-excitation-source",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0032533122964010595ba225",
        "source:145d80a175fc976e65a5434d",
        "source:7e7ce950dcb6a08725766da5",
        "source:24824c7109cbe7fd4585f56e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:uniform-z4-d8-locality-and-both-spinor-chirality-time-census",
      "titleEN": "Scalar Z4 menu: only half twist D8-local; spinor chiralities separated",
      "statementEN": "q=(r/4)^8+m gives q.(e1+e2)=r/2+integer: only r0,2 relatively local to ALL original D8 currents. The64 weight1 quarter dressings are relatively odd but fail stronger full monodromy-1; parity projection/cocycle signs alone cannot repair this. Half twist has two128 chiralities. At unchanged delta full half-integral cosets have unique minima K0 even andK1/32 odd in BOTH quarters; leaving the +/-1/2 cube costs>=17/32. Prior extra-zero-state objection applies only to even extension. Unchanged integer Cartan generators still exclude every nonzero half-charged operator satisfying actual integrated covariance. Original W4 contains permutation and integer carry,not pure spinor translation.",
      "scopeEN": "Only four uniform scalar twist classes in GIVEN D8 target with fixed time/charge dictionary. Integer periodicity/W4 distinction reuse original findings. Monodromy establishes neither new local fields,chirality/gauging selection nor exclusion of all P1 defects. New sector representation with shifted target Cartan spectrum leaves unchanged-carrier premise; its origin remains open.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-d8-uniform-z4-twist-and-fixed-fold-time",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a98ada144c7ab42d495bb073",
        "source:145d80a175fc976e65a5434d",
        "source:7e7ce950dcb6a08725766da5",
        "source:24824c7109cbe7fd4585f56e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:odd-spinor-global-refielding-and-unit-source-winding",
      "titleEN": "Odd-spinor re-fielding preserves H/Q/vacuum but fails original local inclusion",
      "statementEN": "22Oct joint The reviewed audit: Phi=I on even D8,rho=Pp+r on odd v with oscillator permutation is an exact global unitary Z8->D8+c preserving full H,Q,vacuum. [Pr=-r,Pdelta=delta+r,r²/2+delta.r=0] proves all energies; theta Q/parity controls throughE32 agree in bothquarters. SOURCE winding1 transports to q->R^5q+lambda,lambda=(1/2)^5(-1/2)^3,charge1,K-increment(Q+alpha)/8,eight-step carry(1)^8. But a local target Cartan Weyl unitary becomes Pi_even W+Pi_odd W*,whose commutator with remote odd CAR-B equals parity B(W-W*)!=0. No unchanged proper-local CAR inclusion. Separately,v774 anchor bit fails uniform Spin10-invariant NS/R-label identification since rank[C,E45]=4.",
      "scopeEN": "Global comparison at same source energy/charge,with changed odd D8 action. No local spinor/FE-GEN/ALG-EXH/P1-core-circle theorem. Other gauged observable nets and outer DHR extensions not excluded. SOURCE W1 remains global with inherited cocycle phases; both edges retained. Symbol-only Pfaffian/J-grading proposals rejected by type checks.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-eightfold-source-odd-refielding-dictionary",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:580a1d0a402fe8b1b494ffd7",
        "source:04a11f0880f29b5df2157461",
        "source:039515d08dcfe3995ea18b99"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:sharp-half-flux-register-quotient-and-local-normality-exclusion",
      "titleEN": "Direct sharp half flux fails register/quotient locality and local normality",
      "statementEN": "22Oct pasted half-flux report independently checked: F_A Z F_A*=-Z while registerZ stays even; finite matterAdP_A inner despite transport/fusion/exchange relations; v746 pair-currentK_j even,clock-invariant and half-flux-flipped in each base window. Direct sharp chiral sign change has non-HS covariance difference near jump with log((eps+delta)^2/(4epsdelta)) divergence; Araki root-HS necessity and even crossed-product extension exclude local normality also on standard even free net. Current v1033 builder Nx8Ny8 confirmsR(d,k)=(2,1),NS(0,0); uniform fixed-filled R has<nLnR>0 versus quasifree1/4,purity1/2. Common flux changes both edges. F_A does not identify complete prescribed NS/R state responses.",
      "scopeEN": "Only unchanged sharp actions under their separate actual contracts. Smooth punctured-circle sectors may be locally normal and globally inequivalent and remain open; full-CAR implementability does not imply trivial even sectors. Phi/Sigma witnesses not identified without a map. RightHom(s tensor beta,beta) absorber distinguished from charged field. No all-P1 assertion or microscopic E8 closure. Unavailable user18+38 package not claimed replayed; own original controls and analytic proofs separated.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:sharp-half-flux-original-net-state-contracts",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:df2a5401306661b3e68da4d6",
        "source:e7d4f4f5c19989e834d72ae6",
        "source:6e76c0d2734378cbcb546dff"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:all-word-register-charged-local-field-limit-obstruction",
      "titleEN": "Register charge obstructs renormalized local half-flux fields under full word contract",
      "statementEN": "Any arbitrarily long/smeared/renormalized original grade2 sequence obeys exact omega(T*Z*T Z)=-omega(T*T); a bosonic field local away from retained even local Z gives +omega(T*T). Positive nonzero field norm and full joint words exclude locality even without bounded/unitary limit. Shared ZL=ZR excludes faithful left-only flux flip under same full label contract. An old A/A*-projector retaining full even matter and actual QWZ time is register-diagonal; retaining F/D ties r,r+2 or all r. It does not remove register obstruction.",
      "scopeEN": "Only specified grade2/register/word/projection contracts. Changed physical nets, globally supported register Wilson loop, other originally derived sector actions and edge absorbers not excluded. No all-P1 no-go and no assertion that every spinor has this register grade.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-register-retained-in-joint-charged-word-limit",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5e0bfe8df070870d74184d55",
        "source:0a88d06f3f5f7ff6bd5fec85",
        "source:59b8e222ba90e5b16d524e13",
        "source:bf388a41fad7eea97a09280a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:exact-parity-gauss-locality-completion-of-register-source",
      "titleEN": "Exact conditional parity-Gauss representation localizes half flux without new physical dimension",
      "statementEN": "Explicit gauge-orbit isometry E is onto full Gauss space for all sizes, E*E=1,GxE=E,HnewE=EHold,WE=EZ,tau_a^x E=E F_[0,a]. Full even register-matter dimension, all transported state words, positivity, adjunction and common original time preserved; old local register Z becomes GLOBAL Wilson loop. Exact whole128dim control and48 actual width8 one-body gauge cases check signs; all-size theorem rests on orbit proof. Mere word-preserving gauge representation cannot give complete Dirac vector-current response a new central phase.",
      "scopeEN": "Redundant kinematic generators and local Gauss/observable rule are ADDED premise, not P1-derived. No new physical dimension relative to EVEN original carrier, but different local net. No QWZ/Dirac-source identification, spinor-field limit, FE-GEN/ALG-EXH/E8, chiral measure selection or mirror absorption. f(Z) references can become nonlocal.",
      "status": "conditional",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:conditional-local-parity-gauss-completion-with-common-H",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0bbdaa9c57c61e2955a69da0",
        "source:d2dc058b5833c352f31393ee",
        "source:fed5fe27aaa30ea059550c82"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:cover-half-flux-not-fixed-charge-eightfold-spinor-twist",
      "titleEN": "Cover half flux is not uniform eightfold spinor twist in fixed charge dictionary",
      "statementEN": "Original one-copy eightfold: C(-h)^8=-hI, while desired uniform spinor twist (-C(h))^8=hI. No complex charge-preserving intertwiner of given holonomies. Both-quarter h=±i countercontrol: real SO16 O=realify(diag((-1)^j))K DOES conjugate holonomies but reverses Jcomplex and original U1 charge. Uniform BASE Z2 spin lift is invisible to cover holonomy at even degree; global parity×deck relabel still creates no localized charged intertwiner.",
      "scopeEN": "Exclusion only for fixed charge/connection dictionary. No blanket SO16 or spinor-sector no-go. Eight independent copies, physically derived charge conjugation or changed field/domain connections separate. Source/P1-circle, base-deck/clock, chiral fermionic measure and local field products still require derivation; no new internal Z8^f/Arf branch. Neutral-pair refinement: eight-preimage parity pairs T_E with canceled register and unchangedh are NOT excluded by this single-sector comparison.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-one-copy-eightfold-connection-charge-dictionary",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6fc2989e27f03b60e7dcab48",
        "source:59b8e222ba90e5b16d524e13",
        "source:bf388a41fad7eea97a09280a",
        "source:313c1e348521a83ec6854722"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-neutral-eightpreimage-parity-pair-has-uniform-cut-action",
      "titleEN": "Original neutral eight-preimage pair gives uniform16component cut action",
      "statementEN": "T_E=product(F_B F_A*)=I4 tensor(-1)^N_E is an actual original register-grade0 operation. Periodic sigma(theta+2pi/8)=sigma(theta) acts on all8complex/16real folded fields as(-1)^1_I and retains r,h. SINGLE cover-half-flux argument C(-h)^8!=(-C(h))^8 does not apply to this NEUTRAL PAIR. Full original QWZ Nx32Ny8 mass1 control retains all256occupied modes perquarter; both edges changed, old seam phase retained. Finite-band comparison factorizes exactlyD_l(I)^8; odd-l half-circle blocks vanish, artificial second Fermi edge explicitly retained.",
      "scopeEN": "Constructed neutral pair and finite field action, NOT a new single spinor sector or analytic OPE-monodromy theorem. Eight-preimage support remains multilocal on source. No FE-GEN/ALG-EXH,128,P1-source/time/measure derivation. The reviewedRound5 pair misidentification retracted inRound6 after explicit counterexample; no uncritical review adoption.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-neutral-eightpreimage-parity-pair",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:464594647b8384cdb8e871cc",
        "source:365702fd5602ce55d7719123",
        "source:ef40c09054447febd7cd65ba",
        "source:f645673042284a489bfc48d0",
        "source:6d457b142e96cea3d8e1c602"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:complete-dirac-vector-phase-pair-has-zero-spinor-Ward-charge",
      "titleEN": "Complete Dirac vector phase pairs have no half Cartan Ward charges",
      "statementEN": "Implementable commuting vector phases obey[J_i,vec(h),V_vec(f)]=0 because opposite grading cocycles cancel and noncentral term vanishes. At pi interval profile separate chiral components have opposite half endpoint residues; full vector sum0. Thus not a spinor pair withlambda_i=±1/2 under SAME8vector Cartan currents,including scalar renormalization and mixed-word limits. Finite exact control for any Hermitian C andunitaryg: chi_(1-C)(g)=detg conjchi_C(g),normal-order-corrected complete amplitude|chi_C|².",
      "scopeEN": "Only smooth vector-phase class and unchanged mixed Ward action in stated complete Dirac contract. No all-spinor/P1 no-go,arbitrary global-loop-holonomy theorem or infinite determinant theorem. C/1-C are grading components on one face. Chiral source, changed current representation and other original operations outside scope.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:complete-vector-phase-word-Ward-comparison",
        "premise:complete-lagrangian-dirac-cauchy-car-quantization",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f6c0e5e9ebb6337826fb8874",
        "source:ef40c09054447febd7cd65ba",
        "source:f645673042284a489bfc48d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:smooth-unitary-endpoint-removal-diverges-at-fixed-source-time",
      "titleEN": "Smooth unitary endpoint removal diverges at fixed compact source time",
      "statementEN": "Original Weyl/CCR time formula andphi(theta)=f(8theta) give exactDeltaK=8sum_n>0 n²|f_n|²=(2/pi)int|f'|². Any pi->0 return squeezed intoeps costsDeltaK>=2pi/eps. Normalized W(phi)Omega states therefore have no bounded-energy separation limit under same global K reference; scalar normalization leaves Rayleigh quotient unchanged. Class lower bound,not profile scan. Known conditional K_lambda=K_0+lambda.p+lambda²/2+delta.lambda retained; its positive charged sectors are NOT excluded.",
      "scopeEN": "Only normalized smooth UNITARY vector-state sequence on fixed compact source circle. Nonunitary sums/field intertwiners,microscopically derived charged covariance cocycles and decompactified time outside scope. Local normality away from removed point is not finite global original energy. Individuallambda_i±1/2 distinct from totalQ=sumlambda_i; two-point exponent/energy alone no128/FE-GEN/ALG-EXH proof.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:smooth-unitary-pair-return-fixed-compact-source-time",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7566f68b820415fbb5ed7162",
        "source:f1007794ff1be3b54ce13326",
        "source:ef40c09054447febd7cd65ba",
        "source:f645673042284a489bfc48d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:continuous-original-time-nonunitary-limits-stay-in-old-source-folium",
      "titleEN": "Nonunitary limits with continuous original time stay in old source folium",
      "statementEN": "Arbitrary v_N=T_N Omega_N in fixed full strip obey tail_E<=[||v_N||²-<v_N,e^(-tH_N)v_N>]/[1-e^(-tE)]. Finite nonzero norm and limiting-kernel continuity at0 imply energy tightness. Entire finite spectral windows yield norm-subsequence compactness; fixed low-window operator matrix elements transfer all retained bounded-observable states into old global folium. Real original time also suffices: tail_E<=2[n_N-a^-1 int_0^a ReG_N(t)dt] forE>=2/a. No bounded mean energy,||T_N|| or word degree needed. Under fixed D8/even-CAR dictionary no additional s/c spinors; right edge only adds multiplicity.",
      "scopeEN": "Only unchanged full compact source/sea/time/observable comparison and full norm/time kernels. B is an operator property independent of v_N: disjoint-state limits do not automatically violate B; with fixedA,B,C they must failD. Divergent mean alone is not escape. No classification of all local scaling nets/P1 realizations or derivation of8copies. Originally derived changed net/Gauss/operator/time comparison outside scope; elementary spectral compactness,not a claimed new abstract theorem.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:unchanged-full-source-observable-map-and-continuous-time-insertion-limit",
        "premise:unchanged-quarter-qwz-full-excitation-source",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3fb8a599d631bdf830ad65a6",
        "source:3b863788d1d51c2e83bfc1bc",
        "source:8ef03fbc6ad7f4afa2db28b1",
        "source:fd1e0d846cf3f2cf8921ba3d",
        "source:3d7d87574a95fddc26d3cfcb",
        "source:3f7dc4f54ac4d9adf5c943f1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:common-register-vacuum-reference-uniform-and-local-grade-reduction",
      "titleEN": "Uniform common register reference and local mixed-grade reduction",
      "statementEN": "Remote locality to original evenZ gives exact||(Z-i^r)v_N||²=sum_q|i^(r+q)-i^r|²||v_qN||²,allnonzero-grade weights>=2; arbitrary register-changing vacuum components vanish in norm. Actual Bloch ground functione=-Tr|h|/2 has only cusp-|p| at0 and e'' of finite total variationV. Fourier bound|e_m|<=V/(2pi m²) and exact sampling give allN/all4flux |N(E0_alpha-E0_beta)/(2pi)|<=V/6. With ONE initial vacuum reference H_full>=-V/6,so off-grade components also vanish in full fixed-time kernel. No independently chosen flux energies.",
      "scopeEN": "Retained localZ,full joint words and actual mass1width8Bloch matrix. Register-neutrality alone identifies no spinor; totalgrade and halfCartans distinct. New Gauss rule with globalWilsonZ changes premise and remains underived. AllN bound analytic,not extrapolated from finite energy/cusp controls; Ramond zero-mode mixture not replaced by Wick.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:retained-local-register-with-one-common-original-vacuum-reference",
        "premise:unchanged-quarter-qwz-full-excitation-source",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e9718f276569e0db18a8eec6",
        "source:8ef03fbc6ad7f4afa2db28b1",
        "source:f2c230c3ea8d4fafaf32baa5",
        "source:3d7d87574a95fddc26d3cfcb",
        "source:3f7dc4f54ac4d9adf5c943f1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-heat-filtered-neutral-pair-full-state-time-and-separate-chiral-limit",
      "titleEN": "Actual pair heat filter with complete state and separate chiral sharp limit",
      "statementEN": "Actual e^(-sH_N)P_E Omega_N is pureSlater: Zp=B A^-1,Zp_s=e^(-s eps+)Zp e^(-s eps-),C_s=V_s(I+Zp_s*Zp_s)^-1V_s*. All finiteCAR words follow; exact normalized time kernel det(I+Zp_(s+t/2)*Zp_(s+t/2))/det(I+Zp_s*Zp_s). Nx32Ny8/bothquarters/all512modes checked independently by direct Slater/QR;8JOINT residues retained,both edge responses nonzero. SEPARATE given chiral Weyl comparison atd=pi has exact F_s(t)=[(1+r e^-t)(1-r)/((1-r e^-t)(1+r))]^4,r=e^-2s. s->0 gives norm1at0,kernel0fort>0; onlythis comparison limit explicitly violatesD.",
      "scopeEN": "Finite actual full-state/time control and analytic SEPARATE chosen-chiral comparison. No unproved transfer of Weyl sharp kernel to lattice parity continuum; actual filter not proved normal or spinorial asN->infinity. JOINT Bloch occupations not automatically separate chiralD8Cartans,no universal spinor-invisibility claim. Fixeds regularizes given chiral pair but removes neitherendpoint. NoP1 preparation selector,128/OPE/FE-GEN/ALG-EXH. Actual full-stripfilter usesH_N,thegivenchiralcomparisonK=H_cover/8; fixedpositive timeconversion preservescontinuity/compactness anddoesnotdivideprimitive spectralflow.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-neutral-pair-heat-filter-and-separate-chiral-Weyl-comparison",
        "premise:original-neutral-eightpreimage-parity-pair",
        "premise:unchanged-quarter-qwz-full-excitation-source",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9e484dc3636ef19c82b260ff",
        "source:ff426f7576e028837af3ab72",
        "source:3d7d87574a95fddc26d3cfcb",
        "source:3f7dc4f54ac4d9adf5c943f1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:holomorphic-kms-extension-assumes-charged-net-and-not-microscopic-generator",
      "titleEN": "Holomorphic KMS theorem assumes charged net and supplies no microscopic generator",
      "statementEN": "Originalarticle§1/§4 assumesB,mu_B1,c8,index4A=B^Z4 anddefinesomega_beta=Phi_beta^B|A. KMSextension existence is therebygiven; groupaverageE/invariantstateuniqueness applyonexistingB. Eprojectsneutralgrades,doesnotgeneratechargedlocalfields. Originalconclusion explicitlyretainsmicroscopicnonbilinear/lineidentificationgap. RotationalKMSclassification usesL0,notuncheckedH_source=8(L0+delta.p).",
      "scopeEN": "Source-reviewedconditionaluniqueness reused,notrefutationofabstractmaintheoremorgeneralKMSreconstructionno-go. ThistheoremalonedoesnotcloseFE-GEN/ALG-EXH/P1. MCPnavigationlimits separatelydocumented: exactclaimnot_compiled despiteknownproblemreviewedfindings;450kpacketexceeds60kAPI. Completecanonicalprogram.jsonrecordchecked; noserverfixorfullMCPpacketdeliveryclaimed.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-holomorphic-kms-inclusion-and-local-global-modular-domains",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:92a785187fd48304811b13e6",
        "source:6f0ef64f047c61a68ddacaee",
        "source:119da8298cca0baf8ce9ea12",
        "source:30d9db2da466f25271ab90c7",
        "source:002b1c2b9d0b82e840b1e9c6",
        "source:e4f36f144a0face88971d870"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-interval-rotation-modular-chain-fails-local-state-takesaki-repairs",
      "titleEN": "Fixed-interval rotation/modular chain fails; local-state Takesaki repairs it",
      "statementEN": "OriginalKMSarticle§4lines181–211,(4.6)/(4.7),incorrectlyinferssigma_global(A(I))=A(I)fromsubnetrotationcovariance. GlobalKMSmodulargroup=tau_-beta_smovesI. AnalyticevenCAR exteriorcommutator[n_f(t),a*(f_t)a(h)+a*(h)a(f_t)]=a*(f_t)a(h)-a*(h)a(f_t)!=0 refutesfixedI. Correct:E_(R_tI)tau_t=tau_tE_I; OR localphi_I=Phi|B(I),omega_I=phi_I|A(I) giveTakesakiE_Isigma_phiI=sigma_omegaI E_Iandlocalrestriction. Thislocalflowisnotglobalrotation.",
      "scopeEN": "OnlyprintedfixedI modular/rotationidentificationexcluded;independentgroupaverage/expectation/KMSuniquenessretained. NotrefutationofcontinuumHSMI/BWresultsorP1. ActualfullQWZNx8Ny8controls/bothquartersconfirmtimetransport,noauxiliarynetintroducedasP1. Originalpaperunchanged,scopederratuminAtlas; The reviewedRound12independentlycheckedliteralwording.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-holomorphic-kms-inclusion-and-local-global-modular-domains",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:9825461170fd1b3c355015d4",
        "source:d0b830318255c6bd1db118f6",
        "source:2810a99cd90e2d7f0a0ea6cc",
        "source:e8e98cc9bb19c37e56c494e5",
        "source:44674ed3f672d41299666494",
        "source:a5cde3695d717539f1e48089",
        "source:e4f36f144a0face88971d870"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-winding-cartan-four-word-and-two-edge-kms-gso-discriminator",
      "titleEN": "Source winding/Cartan four-word and two-edge KMS/GSO distinguish global spinor refielding",
      "statementEN": "KnownPhi preservesH,Q,vacuumvector/allunflavouredpartitions,bute^2pi_iNkold=IandPhi*e^2pi_iNktargetPhi=P=(-1)^Q. GivenunitarySOURCE W1withPW1=-W1P givesfullfourwordW1*U_kW1U_k* exactly+Iold/-Itarget,alreadyvacuumexpectation+1/-1;fixednormalorderingphasescancel. Thermal targetresponseS/Z<1forallbeta>0. TOTAL-evenbothedgesretainsodd/odd,targetresponse(ZLeZRe-ZLoZRo)/(sum)=2r/(1+r²)<1forequalspectra,r=S/Z. LEFT-evenwoulderasewitnessbutPi_eW1Pi_e=0.",
      "scopeEN": "KnownCartanperiodicityobstructionappliedtoconcreteKMS/GSO/windingtest,notclaimednewabstractsectortheorem. Retainnamedoperators/fullwordsincludingchargedintermediatestates. Notmerelyvacuumvector/spectralcomparison;noGibbsstatephysicallyselectedfromP1. SOURCEcirclenotidentifiedwithprimitiveP1core,nospectralflowdivision. Totalparitymayretainpairedleft/rightpump;noindependentmicroscopicedgepumpasserted. OriginallyderiveddifferentphysicalCartan/net/Gaussdictionarynotexcluded.",
      "status": "excluded_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:canonical-source-gibbs-and-parity-probe-with-retained-winding",
        "premise:given-eightfold-source-odd-refielding-dictionary",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bbdb384d0f8e387c7a62e4e3",
        "source:d30493478ff5a2d727f2c8ff",
        "source:832deb2e8febdccf35d7f1b4",
        "source:a5cde3695d717539f1e48089",
        "source:e4f36f144a0face88971d870"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:p1-parity-gauss-net-selection-undecidable-without-original-localization-map",
      "titleEN": "P1 parity-Gauss net selection undecidable without original insertion/localization identification",
      "statementEN": "Literal scalar P1 names seam, reflection positivity, unit winding and c3; stronger boundary data supply A_+, and the operational seed explicitly takes A_loc as input. Admissible local net restricts supplied local insertions. These definitions do not identify primitive physical space and local algebras with the existing Gx=1 gauge net. Overall verdict: UNDECIDABLE DUE TO SPECIFIED DEFINITION GAP. With old local Z fixed, existing gauge isometry is not support-preserving because FZ=-ZF; the neutral pair has restricted compatibility by telescoped Gauss laws. Global Phi retains its old locality failure and cannot be composed with E without a domain/net identification.",
      "scopeEN": "Original definition/source comparison, not logical independence or two complete alternative P1 models. Neither universal nonderivability nor incompatibility with every P1 seed proved. A specified full seed already includes its net as input. No new construction or numerical suite and no physical premise removed.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:conditional-local-parity-gauss-completion-with-common-H",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:mixed-current-origin-20261014"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:18b2ebeb40b126e4015340c6",
        "source:708a2f923b0f4362b6ce639f",
        "source:5eb2ddf4e2af86e59da5d0cf",
        "source:748b7940e88d21a0f908d8c7",
        "source:fbb9116de80cad8c5c228e87",
        "source:c8c515b9e4b5884e2a8b915e",
        "source:3c14d86e7cd75e05530d89f2",
        "source:13568e45061254a84400a940",
        "source:8b905689699d46cf8ce7de26",
        "source:30521c2c3b194b93710c7b5c",
        "source:ec822b41143b3a7213e3b815"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-minimality-does-not-reconstruct-operational-source",
      "titleEN": "Boundary minimality proves neither seed inverse nor unique source",
      "statementEN": "From d_seed=d o C_seed one obtains minimization only over im(C_seed). The original proof supplies neither attainment of the global minimum in that image nor classification of the equal-minimum fibre; well-foundedness alone gives no object uniqueness or unit spectral flow. Under explicit scale-covariant reference, action and cutoff conditions, B_lambda with lambda D and lambda B retain defects but have different spectra for a compact self-adjoint realization. This rescaling theorem remains conditional. An honest OS inverse needs complete supported Schwinger data with OS II assumptions, or a full Euclidean net/action, regular RP state and time-zero condition; arbitrary positive-time insertions do not automatically act on the OS quotient.",
      "scopeEN": "Precise proof/definition audit of the cited arguments. No independence theorem, two complete P1 models or unconditional rescaling of undefined finite-block/action classes. No new physical model; historical problem status is preserved.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:literal-boundary-minimality-and-first-order-domain-statements",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:779362541d06ffd1f3ff62ef",
        "source:34834afdab4fe034886709c2",
        "source:e817426e320054f489a52981",
        "source:9ac6500624fcafbca0d85dc2",
        "source:9bdf5655093c70332c8d7d57"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:generic-first-order-relative-bound-zero-counterexample-and-correct-domain-repair",
      "titleEN": "Explicit counterexample to the generic relative-bound0 assertion",
      "statementEN": "A=-i d/dx on the interval with periodic H1 domain is a self-adjoint elliptic modified APS realization: tangential operator0 and periodic trace diagonal a kernel Lagrangian. B=-A is symmetric first order with bounded coefficients but has exact A relative bound1; |n|<=a|n|+b forces a>=1. A+B=0 on Dom(A) is not self-adjoint. This disproves the original generic assertion. The valid replacement requires symmetry on Dom(A) and actual relative bound a<1. A sufficient reflection condition is a specified domain-preserving bundle lift with identical principal symbols, making D_rel bounded order0; reflection oddness alone does not lower order.",
      "scopeEN": "Counterexample to the generic mathematical perturbation theorem within its stated boundary-condition type. The intended special TFPT perturbation is neither excluded nor constructed; its principal symbol, domain and actual anchor require verification. No ledger or paper promotion.",
      "status": "established_scoped",
      "problemId": "problem:common-source-state-event-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:literal-boundary-minimality-and-first-order-domain-statements"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d5aabfc244ca5d1f44ba9f0f",
        "source:666f49c8dea3f8819e27c103",
        "source:3c0ae86fab5e4ee416985f68",
        "source:e993abf4a3f9753255772a5c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-discrete-data-vs-connection",
      "titleEN": "Discrete classes are not a selected common connection",
      "statementEN": "The theorem lists [nabla_F*] and Chern classes in its singleton. The audited lift formula constructs the carrier action only once A_E is supplied; the original connection on the common carrier and Phi therefore remain to be specified as a source step.",
      "scopeEN": "Applies to connecting discrete/topological classes to a concretely acting common carrier; it does not claim that the holonomy class asserted by the original theorem is undefined.",
      "status": "conditional",
      "problemId": "problem:seam-family-connection-compatibility",
      "topicIds": [
        "topic:origin",
        "topic:flavor",
        "topic:e8"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:source-boundary-lift-selection-20260922",
        "contract:source-joint-spin-family-lift-20260922"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:82ece7f2b46a77680766390b",
        "source:6a305348323aa6fc36099df1",
        "source:1cd9b5eb7d414ba9fd8ae9d8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:parallelity-excludes-2plus2-only-conditionally",
      "titleEN": "2+2 excludes 3+1 only under common parallelity",
      "statementEN": "Under the explicitly additional premise that beta preserves the fixed marked irreducible SU(3) family connection, its commutant is scalar and beta must have the 3+1 form diag(b,b,b,-3b). Thus a beta packet with eigenvalue multiplicities 2+2 is excluded under that premise only; no original parallelity rule follows.",
      "scopeEN": "Only if the same marked family connection is irreducible and beta preserves it in parallel; without this added premise the 2+2 packet is not excluded. A noncommuting common source-derived connection remains open.",
      "status": "excluded_scoped",
      "problemId": "problem:seam-family-connection-compatibility",
      "topicIds": [
        "topic:origin",
        "topic:flavor",
        "topic:e8"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "premiseIds": [
        "premise:parallel-irreducible-family-connection"
      ],
      "attemptIds": [
        "contract:source-boundary-lift-selection-20260922",
        "contract:source-joint-spin-family-lift-20260922"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bca909d92ac2c26d0cee8213",
        "source:a91b0de030fb5de78bbadf6a",
        "source:1cd9b5eb7d414ba9fd8ae9d8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:sign-projector-does-not-determine-time-magnitude",
      "titleEN": "Sign projector does not determine energy magnitudes",
      "statementEN": "For C=(I+sgn H)/2, H_a=diag(1,a,-1,-a), a>0, gives the same fixed projector C and rho_0 but different positive energies. Thus [rho,C]=0⇒[rho,H]=0 is false without an extra premise. The counterexample concerns only inference from state/sign covariance to complete dynamics.",
      "scopeEN": "Exact finite-dimensional counterexample for zero-temperature sign projection; refutes neither modular uniqueness for a fixed standard pair nor a complete TFPT source derivation.",
      "status": "excluded_scoped",
      "problemId": "problem:physical-time-projector-transfer",
      "topicIds": [
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:sign-covariance-only"
      ],
      "attemptIds": [
        "contract:seam-state-dynamics-injectivity-20260918"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:70def93c1e8a3f30f5e3e1bc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-faithful-kms-or-transfer-recovers-magnitudes",
      "titleEN": "Full faithful KMS covariance or transfer reconstructs magnitudes",
      "statementEN": "For known nonzero beta and faithful finite KMS covariance 0<C_beta<I, H=beta^-1 log((I-C_beta)C_beta^-1) is injectively determined. Alternatively, a full operator T=exp(-tau |H|), known tau, and [T,sgn H]=0 reconstruct the gapped H=sgn(H)(-log T)/tau. A population or eigenvalue list is insufficient; physical identification of TFPT transfer with this T must be shown separately.",
      "scopeEN": "Applies on a faithful finite KMS sector or the same gapped transfer sector; physical TFPT transfer remains unidentified.",
      "status": "conditional",
      "problemId": "problem:physical-time-projector-transfer",
      "topicIds": [
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:known-faithful-kms-or-full-transfer"
      ],
      "attemptIds": [
        "contract:seam-state-dynamics-injectivity-20260918"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6d33fef06ce547b9aac2c084",
        "source:d429ae993d8b660151f5a311",
        "source:972eb1bcd65714d88c3d6372"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-two-face-collar-recovers-signed-operator",
      "titleEN": "Complete collar graph reconstructs the signed operator",
      "statementEN": "The actual product equation gives T=exp(−ell B) and G=[[A,C],[C,1−A]], A=(1+exp(−2ell B))⁻¹. B=log(A/(1−A))/(2ell) reconstructs signs, magnitudes and operator frame. For unbounded T, T is the closure of C A⁻¹; the raw composition is defined only on D(T²). The executable reader needs no supplied B and rejects sign-only projections.",
      "scopeEN": "Exact spectral calculus for a supplied full product collar and known normal length. Without ell only ell B; no independent derivation of the original P1 kernel.",
      "status": "established_scoped",
      "problemId": "problem:physical-time-projector-transfer",
      "topicIds": [
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-product-collar-two-face-data"
      ],
      "attemptIds": [
        "contract:seam-full-collar-reconstruction-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7d058823f6da37baadfb3b2f",
        "source:72b0f747bc0d26d22a63a12e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:two-face-graph-state-time-same-datum",
      "titleEN": "The same collar graph connects restricted state and time",
      "statementEN": "The second face of the supplied pure quasifree graph state has n=1−A=(1+exp(2ell B))⁻¹. Thus log((1−n)n⁻¹)=2ell B, without separately inserted occupations or a second time generator. This realizes the already known faithful KMS inverse through the full collar boundary relation.",
      "scopeEN": "Conditional on charged CAR/Wick identification and the same graph covariance. No P1/P2 selection of physical statistics, normal length, marking or events. Existing quarter holonomy is retained; Clifford quarter-turn algebra is not a holonomy derivation.",
      "status": "established_scoped",
      "problemId": "problem:physical-time-projector-transfer",
      "topicIds": [
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:charged-car-two-face-graph-state"
      ],
      "attemptIds": [
        "contract:seam-full-collar-reconstruction-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:29354f2e8470dbbad010cb34"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:shared-register-gkls-embedding-exact-q-interval",
      "titleEN": "Shared register hierarchy is homogeneously embeddable exactly for 2/9<=q<=1/4",
      "statementEN": "For the specified family Psi_N,q=sum_g w_g(q) Ad(u_g tensor N), 0<=q<=1/3, a consistent time-homogeneous GKLS continuation on the same registers exists iff 2/9<=q<=1/4. Necessity already follows on two registers using fixed sector projections, simple block spectra and conditional Choi positivity of the symmetric part of every possible generator; intermediate S3 covariance is not assumed. Explicit nonnegative rates construct the continuation for every N. q=0 is noninvertible; q=1/3 has a Choi-rank jump from five to six.",
      "scopeEN": "The entire specified finite shared-event family on the same registers; time-homogeneous GKLS generator in dimensionless step units. Source proof reviewed, without independent external peer review or fresh proof execution. Single-register continuation, enlarged environments, time-dependent dynamics and conformal/modular source time remain separate; no proof of fundamental discrete time or physical q selection.",
      "status": "established_scoped",
      "problemId": "problem:physical-time-projector-transfer",
      "topicIds": [
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:specified-shared-s3-register-channel-family"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e3978c46487a84aba5231d0b",
        "source:360814d967e036ed3e3246b4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:marked-m4-channel-all-powers-homogeneous-gksl-excluded",
      "titleEN": "The fixed marked M4 channel has no homogeneous GKSL logarithm for any positive integer power",
      "statementEN": "For Phi(X)=7X/12+sum_{j=1}^5 Gamma_j X Gamma_j/12 on M4 with the specified Clifford matrices and 1+5+10 spectral blocks, no Phi^n for positive integer n is the exponential of a time-homogeneous GKSL generator on the same M4. The proof covers all logarithm branches using block traces and Clifford twirling; the forced canonical coefficient beta=n log(3/4)/16 is negative. This is a different channel from the shared S3 register hierarchy.",
      "scopeEN": "Only the specified M4 endpoint channel, positive integer powers, same system and homogeneous GKSL time. Intermediate covariance is not assumed. Positive GNS Hilbert transfer and classical B recovery semigroup remain valid; larger systems and time-dependent dynamics are not excluded. Contract remains PARTIAL and physical source derivation open; source review is not a fresh kernel/numerical run.",
      "status": "excluded_scoped",
      "problemId": "problem:physical-time-projector-transfer",
      "topicIds": [
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:specified-marked-m4-clifford-channel"
      ],
      "attemptIds": [
        "contract:source-continuous-marked-time-search-20260922"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e73bb08212750b6ea7931901",
        "source:910b3aa85ba3b7b1aa82f897",
        "source:5da03c9bc80987d3faaef62d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:flavor-ratio-closed-absolute-anchor-open",
      "titleEN": "The 55/117 ratio is closed; absolute scale remains a separate anchor",
      "statementEN": "The active TFPT text states that Q geometry, det R=8, and rigidity of c_u/c_d=55/117 are established on the derived stratum; the continuous wall point U_f* is needed only for absolute amplitude normalization. The ratio is not an open monodromy/amplitude calculation.",
      "scopeEN": "Applies to the documented derived discrete stratum and c_u/c_d; it does not determine U_f* or absolute amplitudes.",
      "status": "established_scoped",
      "problemId": "problem:flavor-ratio-amplitude-readout",
      "topicIds": [
        "topic:flavor",
        "topic:e8",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "premiseIds": [
        "premise:declared-p1-p2"
      ],
      "attemptIds": [
        "contract:source-flavor-origin-20260920"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e78c5db089a075b210d1564c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:alpha-equation-is-fixed-input-closure",
      "titleEN": "Minimal EM transfer is exact in its stated response contract",
      "statementEN": "For the defined rank-one projector U_Sigma^min and stated parameters, T_Sigma=(1-delta_top exp(-2 alpha))^(-5/4) and the displayed scalar closure equation follow algebraically. This calculation does not independently prove physical selection of that projector, parameter set, or transfer to the Thomson readout.",
      "scopeEN": "Historical minimal-transfer definition with fixed readout; the single line has since been canonically reconstructed on the old circle. Neither this reconstruction nor independently proved root uniqueness is retracted. Original physical P1/EM mapping and renormalized Thomson observable remain separate.",
      "status": "conditional",
      "problemId": "problem:alpha-fixed-input-root",
      "topicIds": [
        "topic:alpha",
        "topic:origin",
        "topic:e8"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:fixed-input-models-scoped"
      ],
      "attemptIds": [
        "contract:source-flavor-origin-20260920"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2d1bbebd47ea974d18a07759",
        "source:b016474460b2741b2d4ef790"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:alpha-global-positive-root-unique",
      "titleEN": "Existence and uniqueness of the positive root are proved",
      "statementEN": "Log-convexity of the stated seam response and the sign before x=2c³ prove exactly one positive simple root globally. For M=41 its reciprocal is approximately 137.0359992168407. The analytic proof is distinct from the 10 rerun symbolic/interval checks. It holds for every M>0 and therefore does not select M=41.",
      "scopeEN": "Mathematical theorem for the fixed function; not a cubic polynomial because the seam response depends on x. No parameter or physical Thomson-transfer derivation; ledger Numerical unchanged.",
      "status": "established_scoped",
      "problemId": "problem:alpha-fixed-input-root",
      "topicIds": [
        "topic:alpha",
        "topic:origin",
        "topic:e8"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "premiseIds": [
        "premise:fixed-em-seam-function"
      ],
      "attemptIds": [
        "contract:em-positive-root-convexity-20261013"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3ccf6cd6ceaf16ffb0706cad"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:marked-e8-sector-grade-response-realizes-five-quarters",
      "titleEN": "The marked D5 grade response derives exponent5/4 from the same E8 source",
      "statementEN": "Exactly G_u(q5,q3)=[(1-u)/(1-uq5)]^(5/4)[(1-u)/(1-uq3)]^(3/4). Hence G_u(q,1)/G_u(0,1)=(1-uq)^(-5/4); the common-time diagonal G_u(q,q) instead has exponent2. Powers follow from actual charge norms and the convergent oscillator series. Normalized local T5 insertion has Ward coefficient5/8. Fixed C/J do not generally preserve P5 but jointly transport charge and marking covariantly.",
      "scopeEN": "Exact response in the specified existing source, not a new field or fitted exponent. Does not derive physical preparation, u=48c3^4, q=exp(-2alpha), outer uq, baseline1/(6pi), or original EM instrument. Common time is not sector-resolved D5 readout. Replay26October2026:21/21; finite coefficient checks through degree12 do not replace the general series proof.",
      "status": "established_scoped",
      "problemId": "problem:alpha-fixed-input-root",
      "topicIds": [
        "topic:alpha",
        "topic:origin",
        "topic:e8"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "premiseIds": [
        "premise:marked-e8-regularized-charged-grade-response",
        "premise:fixed-input-models-scoped"
      ],
      "attemptIds": [
        "contract:charged-sector-readout-clock-20261013"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a60e8c86577a5d18e0f6da64",
        "source:f6faa71f114cfc07b3701f0d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:alpha-exact-coefficients-and-root-retain-specific-physical-ward-obligation",
      "titleEN": "Exact alpha output and coefficients retain a specific Ward-origin obligation",
      "statementEN": "The active original explicitly treats the three-term decomposition and coefficient identities as exact, retaining the unique alpha root. The same section retains EM.WARD.01/ALPHA.QUILLEN.EXACT.01 as the existing origin obligation for the actual AQFT/zeta determinant functional. Separately the old circle canonically gives Pi and det_F(1-qPi)=1-q. Its actual local EM response, relative Quillen norm and susceptibility exponent5/4 still require identification. This does not retract compiler identities or root uniqueness.",
      "scopeEN": "Source-reviewed status/type correction, not a new general nonderivability theorem or gate. P1/P2 remain accepted starting principles; being axioms is not an objection. The line is derived on the old circle, not an arbitrary vector to select again. v382 replay26October:6/6; literalTrue status checks do not prove open functional origin. Ledger Numerical and full physical status remain unchanged.",
      "status": "established_scoped",
      "problemId": "problem:alpha-fixed-input-root",
      "topicIds": [
        "topic:alpha",
        "topic:origin",
        "topic:e8"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "premiseIds": [
        "premise:fixed-em-seam-function",
        "premise:fixed-input-models-scoped",
        "premise:declared-p1-p2"
      ],
      "attemptIds": [
        "contract:em-positive-root-convexity-20261013"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f1e49977bd7a7304bf82bc2c",
        "source:b016474460b2741b2d4ef790",
        "source:0a7513fbdfbf46c4cb1db1bc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:alpha-archive-term-provenance-and-master-functional-scope",
      "titleEN": "Historical alpha factors and definition steps reconstructed from original sources",
      "statementEN": "The reviewed older originals provide concrete provenance contracts: V1.06 uses g=n/(8pi²), n=1 and g=8c3²; v2.7 couples the defect through J=d SF=2; v4.2 gives gamma=5/6, tr(S+)Y²=10/3, b1=41/10 and B gamma=5/4. The minimal rank one transfer yields exactly (1-q)^(-5/4). These numbers must not be dismissed collectively as unexplained fitting factors. The same originals state a narrower complete identification: v2.7 calls the CFE coefficient motivation heuristic, while v4.2 supplies P_loc'(alpha)=alpha³-2c3³alpha² as a condition and defines Gamma by integrating the desired response. The master proof factorizes blocks and then identifies the U(1) block with the already defined EM action; this passage does not evaluate an original coupled Dirac determinant to obtain that particular F. It therefore does not additionally close the existing physical Ward origin obligation.",
      "scopeEN": "Source provenance and exact algebra under each stated normalization, carrier, primitive sector and defect response contract. No general nonderivability theorem, no retraction of the canonical circle defect line, marked D5 response or positive root uniqueness. No new physical selector or ledger promotion. Historical linear, exponential, quadratic and resummed openings are different calculation contracts; similar coefficients do not prove identical physical actions.",
      "status": "established_scoped",
      "problemId": "problem:alpha-fixed-input-root",
      "topicIds": [
        "topic:alpha",
        "topic:origin",
        "topic:e8"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:fixed-input-models-scoped"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:379ac089d4a6f7b42c9c3507",
        "source:b2fd6645a9ae63a7e0e8223f",
        "source:3d71560751889525f0373327",
        "source:bccd1d35797f4d0dc5470ebb",
        "source:0af7337bb0e4dcce412f637d",
        "source:d0d2d4b97ab82dd0478a1b11",
        "source:26871fe86226852f0ca71ed1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:matter-observations-do-not-fix-geometric-response",
      "titleEN": "Matter readouts do not fix geometric response; original functional remains fixed",
      "statementEN": "In the matter-only observation-class audit, geometric replica responses remain indistinguishable; the scope correction explicitly states that W→W+lambda Q[g] is therefore not automatically an admissible change to the original profile-free Gamma_grav. The original functional is fixed once the full operator, reference, domain, and continuation are fixed; its common off-shell geometric family and normalization must be derived from the source.",
      "scopeEN": "Applies as an identifiability limit for matter-only observations and an open bridge to the fixed original functional; it is not an alternative TFPT source or universal gravity no-go.",
      "status": "conditional",
      "problemId": "problem:gravity-flow-normalization",
      "topicIds": [
        "topic:gravity",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures",
        "premise:fixed-input-models-scoped"
      ],
      "attemptIds": [
        "contract:source-observation-identifiability-20261013",
        "contract:seam-gravity-source-bridge-20261013"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e5b52e9192676bba8f47c41d",
        "source:d3f0dad65d270331bedd539d",
        "source:38e9a3afb73e6c91d67556f8",
        "source:43cf0944fa4e07dd8e13ef01"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:four-clock-fields-complete-quadratic-response",
      "titleEN": "Four clock fields generate complete quadratic responses",
      "statementEN": "P5, CPCᵀ, JPJᵀ and C²P(C²)ᵀ generate all36 real-symmetric8x8 matrices through Jordan words up to degree4. The double-pole OPE realizes these products. An explicit rational inverse reconstructs A from36 mixed responses Tr(BℓA)/2; prescribed trace leaves35 directions.",
      "scopeEN": "Complete matrix reconstruction in the specified neutral quadratic vacuum sector; neither four measurements nor all charged, state or multitime responses of a physical source.",
      "status": "established_scoped",
      "problemId": "problem:clock-linked-neutral-response-reconstruction",
      "topicIds": [
        "topic:clocks",
        "topic:quantum",
        "topic:alpha"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T6"
      ],
      "premiseIds": [
        "premise:native-current-clock-ope-access"
      ],
      "attemptIds": [
        "contract:clock-jordan-response-reconstruction-20261015",
        "contract:neutral-response-tomography-20261013",
        "contract:native-mark-memory-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b2ae113e9519e618def79b2a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-j-covariant-source-transport",
      "titleEN": "J transports the whole source tuple",
      "statementEN": "The original cocycle admits a unitary lift UJ with UJ⁴=I. It intertwines Kδ,Qq and the full quarter transition with KJδ,QJq,tJτ on the entire stipulated Fock space. The four frames are a covariant family; q must be transported.",
      "scopeEN": "Given E8 completion; no physical sectors, switching rates or local instruments selected from P1/P2. As a torus operator τ is identifiable only modulo the dual lattice.",
      "status": "established_scoped",
      "problemId": "problem:clock-source-covariant-transport",
      "topicIds": [
        "topic:clocks",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:stipulated-e8-clock-tuple"
      ],
      "attemptIds": [
        "contract:clock-source-twist-transport-20261015",
        "contract:seam-joint-ward-state-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:709ff65f9a84b7a578422fea"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-source-affine-j-obstruction",
      "titleEN": "The same fixed time operator disallows this affine J lift",
      "statementEN": "An isometric affine lattice lift Ap+r with A²=−I and unchanged oscillator level would require r=Aδ−δ and hence −2δ=(I+A)r in the E8 lattice. Adjacent coordinate differences of2δ are1/4; this fails exactly. Also Jq≠q.",
      "scopeEN": "Exclusion only of the affine lift model at fixed K,Q and oscillator level; covariant tuple transport remains possible.",
      "status": "excluded_scoped",
      "problemId": "problem:clock-source-covariant-transport",
      "topicIds": [
        "topic:clocks",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:stipulated-e8-clock-tuple"
      ],
      "attemptIds": [
        "contract:clock-source-twist-transport-20261015",
        "contract:seam-joint-ward-state-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:08d8715a472c9308b81a7a8c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:neutral-vacuum-allword-twist-blindness",
      "titleEN": "All neutral vacuum words remain twist-blind",
      "statementEN": "Each admissible intermediate insertion stays in M(1)⊗|0>. There Kδ=N,Qq=0,tτ=I. All ordered vacuum multitime and Gram responses in this class are therefore identical at arbitrary word length, even with complete36-dimensional quadratic tomography.",
      "scopeEN": "Individually all-Cartan-neutral insertions and fixed vacuum; not charged intermediate fields, charged Gibbs traces or δ-dependent probe operators.",
      "status": "established_scoped",
      "problemId": "problem:charged-twist-response-identifiability",
      "topicIds": [
        "topic:quantum",
        "topic:clocks",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:neutral-current-vacuum-insertions"
      ],
      "attemptIds": [
        "contract:clock-source-twist-transport-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c6f96f98c291af5b08553a75"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:eight-charged-responses-reconstruct-twist",
      "titleEN": "Eight independent charged response directions reconstruct δ",
      "statementEN": "Cδ(p,t)=exp[−t(|p|²/2+δ·p)]. With yi=−log[Cδ(bi,t)/Cδ(−bi,t)]/(2t), y=Bᵀδ and δ=(Bᵀ)⁻¹y. Eight independent directions suffice and are necessary for unrestricted δ in this linear data class.",
      "scopeEN": "Known preparation/time normalization in the given E8 Fock space; identifies δ, not q,τ, physical instruments or P1/P2 source selection. Eight directions require their respective ± responses.",
      "status": "established_scoped",
      "problemId": "problem:charged-twist-response-identifiability",
      "topicIds": [
        "topic:quantum",
        "topic:clocks",
        "topic:origin"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:normalized-charged-primary-time-access"
      ],
      "attemptIds": [
        "contract:clock-source-twist-transport-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:30a933b0dd1d84c5f36f676e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-invariant-response-not-fixed-chiral-twist",
      "titleEN": "Unchanged native source is not the fixed chiral response",
      "statementEN": "The native ratio is one; the fixed quarter twist gives exp(−2tδ·Bp), which differs from one on at least one original basis direction.",
      "scopeEN": "Only the fixed marked response identification at these starts and the same time.",
      "status": "excluded_scoped",
      "problemId": "problem:native-charged-seam-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-full-charge-field-source",
        "premise:native-c-invariant-start",
        "premise:fixed-nonzero-quarter-twist-comparison"
      ],
      "attemptIds": [
        "contract:native-charged-conjugation-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:954f7513e48c73700eed506e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-opposite-charge-response-symmetry",
      "titleEN": "Native fields exist; opposite-charge responses agree",
      "statementEN": "Original C T_p C=T_−p, T_p*=(-1)^e(p)T_−p and C H C=H. At an invariant start all C-conjugate bounded words agree.",
      "scopeEN": "Unchanged finite source and specified invariant start; different states or operator dictionaries are not excluded.",
      "status": "established_scoped",
      "problemId": "problem:native-charged-seam-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-full-charge-field-source",
        "premise:native-c-invariant-start"
      ],
      "attemptIds": [
        "contract:native-charged-conjugation-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:954f7513e48c73700eed506e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-chemical-mark-visible-in-charged-corners",
      "titleEN": "C0 does not hide charged intermediate sectors",
      "statementEN": "η·Qtot is zero on C0. T_p enters Cp; full propagation yields ratio exp(−2tη·p). For v=Bp, conditionally η=Bᵀδ. Only the odd factor is matched.",
      "scopeEN": "Balanced W remain within the sector; T insertion/removal responses require Cp. No derived physical measuring instrument.",
      "status": "established_scoped",
      "problemId": "problem:native-charged-seam-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-full-charge-field-source",
        "premise:native-zero-sector-chemical-comparison"
      ],
      "attemptIds": [
        "contract:native-charged-conjugation-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:954f7513e48c73700eed506e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-hopping-quarter-phases-retain-antiunitary-discriminator",
      "titleEN": "Fixed hopping phases do not produce the required asymmetry",
      "statementEN": "C and K may separately break; A=CK preserves H for all fixed link phases and T_p→T_−p. Invariant starts retain equal Euclidean opposite-charge returns, including quarter phases/flux.",
      "scopeEN": "Fixed phases and corresponding invariant starts; real time retains conjugation/time reversal. No assertion about all P1/P2 sources.",
      "status": "excluded_scoped",
      "problemId": "problem:native-charged-seam-selection",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-full-charge-field-source",
        "premise:native-fixed-link-phase-a-invariance",
        "premise:fixed-nonzero-quarter-twist-comparison"
      ],
      "attemptIds": [
        "contract:native-charged-conjugation-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:687fa3c1dde1b23080b9786f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:constructive-phase-class-and-full-winding",
      "titleEN": "Finite search closed, actual winding and parity equivalence",
      "statementEN": "262144 candidates on two H200: four universally Lean-checked presentations. X_plus=Pi X_minus preserves source,Q,K,quarter marker and canonical state; two marked P classes remain. Full T1 and Ward are checked. Graded C lifts realize both P signs; scalar X covariance does not follow from the integer endpoint.",
      "scopeEN": "Global crossed operators; no local field equivalence or physical selection.",
      "status": "established_scoped",
      "problemId": "problem:constructive-seam-lift-state",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-car-crossed-half-charge-search"
      ],
      "attemptIds": [
        "contract:seam-constructive-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3210cc2a0ae23b6cce71b031"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:constructive-positive-state-extension",
      "titleEN": "Positive finite-word state extension",
      "statementEN": "E0(y*y)=a0*a0+phi^-1(a1*a1) proves positivity of omega0 o E0. General algebra/star/positivity and dual uniqueness theorems are Lean-checked; concrete finite-lattice transfer is analytically proved.",
      "scopeEN": "No complete concrete Finsupp kernel instantiation, physical state selection or automatic K-invariance of the bare shift algebra.",
      "status": "established_scoped",
      "problemId": "problem:constructive-seam-lift-state",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-car-crossed-half-charge-search",
        "premise:fixed-positive-crossed-state"
      ],
      "attemptIds": [
        "contract:seam-constructive-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:65689976fca07a79209f5a48"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:constructive-current-group-selects-positive-p-lift",
      "titleEN": "E8 current group conditionally determines the P sign",
      "statementEN": "In the supplied positive E8 module X=E_s commutes with SU8 root currents because alpha.s=Q(alpha)=0; oscillators are fixed. C=Z_e0 R gives CXC^-1=±iX and P sign+1. This is a direct global operator bridge, not X=Y(s).",
      "scopeEN": "Only the stipulated even E8 lift; full odd-Z8 sectors remain additional. No transfer of the different (9,1) source. The ±i path orientation is not selected.",
      "status": "established_scoped",
      "problemId": "problem:constructive-seam-lift-state",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:stipulated-even-e8-seam-lift",
        "premise:fixed-car-crossed-half-charge-search"
      ],
      "attemptIds": [
        "contract:seam-constructive-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:39d3078f6c1650fbaaff599b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:constructive-state-algebra-resolution-and-source-test",
      "titleEN": "The same shift functional hides distinct ground states",
      "statementEN": "All dual-invariant ground mixtures diag(a,1-a) on {0,r0} give the same shift functional. Original Cartan vacuum values select |0><0|; additional Rc invariance requires I2/2. These two conditions conflict.",
      "scopeEN": "Normal ground densities in the supplied K space; no state selection from P1/P2. The ground space was already known.",
      "status": "established_scoped",
      "problemId": "problem:constructive-seam-lift-state",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-car-crossed-half-charge-search",
        "premise:fixed-positive-crossed-state"
      ],
      "attemptIds": [
        "contract:seam-constructive-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:77e85380be2d50b5c2261fb6",
        "source:3d55efcd0ce6b349d1a63043"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:constructive-all-phases-fail-unchanged-source",
      "titleEN": "No phase hit realizes the unchanged source",
      "statementEN": "All four hits add the same half-integer Cartan sectors and second K-zero vector. The already known integer-Cartan/ground-space obstruction therefore excludes equivalence to the unchanged source; positive algebraic extension remains possible.",
      "scopeEN": "Only the named unchanged CAR/QWZ representation with the same time. No TFPT no-go; choosing a state removes no added zero vector.",
      "status": "excluded_scoped",
      "problemId": "problem:constructive-seam-lift-state",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-car-crossed-half-charge-search",
        "premise:unchanged-quarter-car-qwz-source-comparison"
      ],
      "attemptIds": [
        "contract:seam-constructive-search-20261015",
        "contract:quotient-locality-e8-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e82749a82ff17ca9c5c87435",
        "source:b26f361e5f9452cb414771d1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:partner-carrier-charges-and-state-types",
      "titleEN": "Concrete pair operator; source neutrality is not hypercharge neutrality",
      "statementEN": "epsilon1 epsilon4 produces u1∧u4 in the carrier: Y=1/6 and source charge change0. Root operator, spinor carrier vector and affine root-current state have different types. The exterior unit is the internal nu^c label, not the affine vacuum.",
      "scopeEN": "Original carrier plus supplied E8 charge dictionary; no physical field identification.",
      "status": "established_scoped",
      "problemId": "problem:seam-partner-charge-state-time",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:oriented-p2-exterior-carrier",
        "premise:fixed-e8-fold-quarter-dictionary"
      ],
      "attemptIds": [
        "contract:seam-partner-original-action-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:96a7f7e834d6b08af22ce600"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:partner-fixed-quarter-time-splits-sm-multiplet",
      "titleEN": "Fixed quarter time splits the color/weak multiplet",
      "statementEN": "Mdelta=(-1/2,0,alpha/4,-1/2,0,(alpha-1)/4,-1/4,-1/4). The six (3,2) root energies are (0,1/2,1/2,1,1/2+alpha/4,1+alpha/4). K therefore does not commute with the fixed full SM action. The quarter phase is retained.",
      "scopeEN": "Only the supplied affine dictionary. Backgrounds or time-dependent covariant symmetries have different premises; no general gauge-physics no-go.",
      "status": "established_scoped",
      "problemId": "problem:seam-partner-charge-state-time",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:oriented-p2-exterior-carrier",
        "premise:fixed-e8-fold-quarter-dictionary"
      ],
      "attemptIds": [
        "contract:seam-partner-original-action-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:02b662eabf932257ad20f26f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:partner-original-carrier-cross-sheet-conjugation",
      "titleEN": "Explicit conjugation for the existing sheet pairing",
      "statementEN": "J_C=∏(epsilon_i+iota_i)K is antiunitary, exchanges S± and reverses Y. Exactly Lambda0 and Lambda5 have Y=0. J_C dGamma(h) J_C^-1=tr(h)I−dGamma(h). It is fully Spin(10)-equivariant. Reuse CAR.PAIR.01's bilinear pairing; CAR.PAIR.02's Hermitian selection inference has been corrected and is not evidence.",
      "scopeEN": "Representation with metric/orientation; J_C is not yet the actual boundary/OS conjugation. Two carrier labels are not two vacua.",
      "status": "established_scoped",
      "problemId": "problem:seam-partner-charge-state-time",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:oriented-p2-exterior-carrier"
      ],
      "attemptIds": [
        "contract:seam-partner-original-action-20261015",
        "contract:seam-joint-conjugation-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c8740952e71547e23d446acf",
        "source:48db3028a5eb826da0bb985b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:partner-chiral-quarter-conjugation-state-time",
      "titleEN": "Actual partner map between quarter domains",
      "statementEN": "n→−n−1, alpha→1−alpha gives C D_alpha C^-1=−D_(1−alpha). Particles become holes and conversely; normal charge reverses and positive excitation energy is preserved. The unique sea state maps to the other sea state without adding a zero vector within one domain.",
      "scopeEN": "Given chiral source. No selection from P1/P2, no equal responses within one fixed twist, and no identification with affine r0.",
      "status": "established_scoped",
      "problemId": "problem:seam-partner-charge-state-time",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-chiral-opposite-quarter-domains"
      ],
      "attemptIds": [
        "contract:seam-partner-original-action-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:04ae73dea3e04eaa4ed71fd0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-bilinear-hermitian-correction",
      "titleEN": "Bilinear sheet pairing is not Hermitian kernel selection",
      "statementEN": "CAR.PAIR.01 counts complex-bilinear singlets. The Hermitian scalar <f,g> already exists on S+; CAR.PAIR.02's 'scalar iff sheet-odd' inference is false in this reading. The previous J_C includes reversion signs and is fully Spin(10)-equivariant.",
      "scopeEN": "Correction of the finite selection inference; no identification of I with the actual Calderon operator and no P1 countermodel.",
      "status": "established_scoped",
      "problemId": "problem:seam-partner-charge-state-time",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:oriented-p2-exterior-carrier"
      ],
      "attemptIds": [
        "contract:seam-joint-conjugation-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:48db3028a5eb826da0bb985b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-quarter-transports-marking",
      "titleEN": "Actual quarter conjugation transports the supplied marking",
      "statementEN": "n→−n−1 forces j→7−j and O=−MRM^T with O(x)=(x4,−x5,−x6,x1,−x2,−x3,x8,x7). O d_alpha=d_(1−alpha); P5_beta=O P5_alpha O^-1 and k_beta=k_alpha∘O^-1 need no new marking choice. Sea state and positive time are transported; the E8 current lift assumes the existing extension.",
      "scopeEN": "Exact map of the supplied source and conditional E8 lift; first marking, source realization and physical event law are not derived from P1/P2. Both quarter domains remain explicit; no switch to another branch to solve a fixed-sector question.",
      "status": "established_scoped",
      "problemId": "problem:seam-partner-charge-state-time",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-chiral-opposite-quarter-domains",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:given-first-marked-quarter-character"
      ],
      "attemptIds": [
        "contract:seam-joint-conjugation-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1e85b4e0a16e59c397c00f0b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-fixed-time-marking-repair-excluded",
      "titleEN": "No time-stabilizing orthogonal repair of the fixed marking",
      "statementEN": "After actual quarter conjugation the D5 projections of the time axis have distinct squared norms 129/256 and 137/256. Hence no orthogonal T satisfies T d_beta=d_beta and T O(P5)T^-1=P5. This excludes every Weyl correction in this fixed comparison.",
      "scopeEN": "Only fixed fold time and fixed 5+3 marking. Covariant marking transport is positively constructed; other sources or dynamical dictionaries are not excluded.",
      "status": "excluded_scoped",
      "problemId": "problem:seam-partner-charge-state-time",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-chiral-opposite-quarter-domains",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:given-first-marked-quarter-character"
      ],
      "attemptIds": [
        "contract:seam-joint-conjugation-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:49403a86fdc26c526449d2cd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-spinor-not-source-coefficient",
      "titleEN": "Spinor16 is a state sector, not a 16-real one-particle field",
      "statementEN": "D5_1 has ten real vector fermions; S± each contain 16 complex Ramond/spin-field states. Using S+ as an ordinary CAR coefficient would give c=16 and Spin(10) level 4. The documented c=8 connection uses 10+6 real fermions and mixed spin fields of weight 5/8+3/8=1.",
      "scopeEN": "Representation types of the supplied free realization; no selection from P1/P2 and no new spinor-CAR replacement.",
      "status": "established_scoped",
      "problemId": "problem:seam-partner-charge-state-time",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:oriented-p2-exterior-carrier",
        "premise:given-d5-a3-free-fermion-realization"
      ],
      "attemptIds": [
        "contract:seam-joint-conjugation-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:55e1a01319dc1feaa105883e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:typed-operator-search-calibrated",
      "titleEN": "Operator synthesis implemented and calibrated on known cases",
      "statementEN": "A CEGIS word search generates 2048 Majorana word/linearity classes and recovers the known five-mode particle-hole map. An automatically found imaginary mixing component eliminates the linear candidate. A second solver constructs simultaneous linear/antilinear intertwiners from exact operator pairs; evaluation identities include constraints, code and search configuration. These are software and recovery results, not new source selection.",
      "scopeEN": "Supplied finite representations. Clifford monomial grammar and generic equal matrix dimensions up to16; not a complete operator-program, kernel or continuum search. Twelve generic Lean transport lemmas; concrete matrices checked separately and exactly.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-finite-operator-synthesis-inputs"
      ],
      "attemptIds": [
        "contract:seam-operator-synthesis-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:aa1aaec9a745ed8fef0ad24b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:positive-kernel-construction-with-exact-discriminator",
      "titleEN": "Unknown kernels constructed, exactly completed and discriminated",
      "statementEN": "The new moment search takes no supplied H, rho or target K. A one-mode result has an exact flat GNS certificate. Two additional minimal five-mode completions replay all 2245 moments through degree4. Checking the original source requirements adds finite clustering: a previous result with 27 stationary directions fails; two replacements each have exactly one stationary direction. Both yield finite unitary field time from the same T and first differ at degree5 by 1/4 versus 3/4. An independent offline verifier confirms full kernels and separation.",
      "scopeEN": "Declared finite CAR/transfer class. Five-mode completion additionally assumes a minimal irreducible realization with inferred pure occupation state; no uniqueness inferred from truncated ranks. Floor and cluster gap 1/4 are search bounds, not quarter holonomy or physical scale. Finite clustering is not a local OS net. No original selection of marking, statistics or events. Historical extremal calibration; since2026-10-16 implementation defaults to feasibility with explicit transfer classes.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:finite-positive-kernel-search-class"
      ],
      "attemptIds": [
        "contract:seam-positive-kernel-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3734b8aaac09ec694bb7b3a4",
        "source:59a0025e96161e52261effe3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-typed-kernel-search-controls",
      "titleEN": "Search conditions corrected; duplicated control separated from the actual charged source pair",
      "statementEN": "The default is feasibility without optimizing state or response. The explicitly duplicated lowest-mode calibration gives1/16; the actual lowest quarter-source particle/hole pair gives1/256. A global floor1/4 is an artificial restriction. Thermal GNS transfer with spectrum1,1,1/4,4 passes at bound4; bound1 is a class mismatch. An unsupported pure Fock completion remains inconclusive.",
      "scopeEN": "Executable finite software and source controls; no physical source selection. Historical min/max results are calibration endpoints, not preferred solutions. The actual charged-pair SCS status is optimal_inaccurate; the exact matrix construction independently proves feasibility, not clean numerical optimality.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:98908893829c9b25307ca6b3",
        "source:35c4cbe57698a68a495db270"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:collar-car-projection-multifield-ray",
      "titleEN": "Complete CAR boundary projection determines the multi-field operator ray",
      "statementEN": "If the full two-face graph G is the actual CAR covariance, positivity and CAR force its state ray without a separate Wick assumption. The specified oriented input/output pairing reconstructs Q proportional to the direct sum of Lambda^n R; multi-field amplitudes are minors and Q(R2R1)=Q(R2)Q(R1). Complex frame changes and noncommuting composition are checked. Vacuum and one-particle responses alone are insufficient.",
      "scopeEN": "Canonical fermionic quantization of supplied full boundary data. A geometric Cauchy projector is not automatically a physical CAR covariance; boundary pairing is also a premise. The absolute scalar, partition determinant and phase are not recovered from normalized G. Original action permits higher interaction vertices; general OS sewing from complete Schwinger functions remains separate.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:actual-car-graph-and-oriented-boundary-pairing"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:936bbaa228bdfb76d90d3069",
        "source:e5406c6947f6213b777a58dd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:known-quarter-source-full-multifield-control",
      "titleEN": "Known quarter source fully controlled with state and operator tail bounds",
      "statementEN": "In the supplied sea-relative chiral CAR model the same particle-hole map produces charge N_+-N_-, positive energy and W=exp(2pi iH)=i^(N_+-N_-). The original signed two-mode amplitude diag(1,1/4,64,16) becomes diag(1,1/4,1/64,1/256) through that map and the separate sea factor64. The infinite weighted l2 domain, geometric trace tails and explicit operator-norm/Choi-HS bounds control state and time beyond finite windows.",
      "scopeEN": "Complete construction within the already supplied free source. No P1/P2 selection or infinite particle-hole unitary in empty Fock space. Convergence is in a common HS/Choi space, not of raw filled Slater vectors in empty Fock space. Relative partition sums do not recover the divergent absolute sea scalar. A single chiral D_alpha branch; the entire doubled graded collar is not identified with the same time/loop generator.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-chiral-opposite-quarter-domains",
        "premise:charged-car-negative-sea-source"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7407cf7f677ae10e6ee1afd1",
        "source:c96010a6c43cc845d4f81335"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-reference-amplitude-retained",
      "titleEN": "Reference amplitude retained as search input; direct false certification closed",
      "statementEN": "Search and both entry paths retain T Omega=lambda Omega with explicit positive lambda, matching bounds and cache identity. A rational scaled control kernel passes at lambda=1/16 and contradicts the same moments at lambda=1. Pure Fock completion accepts only vacuum_effect, lambda=1 and ceiling1; other classes remain inconclusive. omega(1)=1 normalizes only the conditional state and does not reconstruct Z[0]. In the actual original OS call, unital translation fixes [1] and its matrix element is time independent. This does not identify it with the nonstationary old cap vector as proposed by The reviewed. Retain the original reflected insertion caller omega_rel(Theta F tau_t G); a cap insertion must identify the actual old sea vector. The reference cancels from Zrel[J]/Zrel[0], not from geometric variation of logZrel[0].",
      "scopeEN": "Software correction with supplied lambda; no original absolute amplitude selection. The scaled control matrix is not a new physical quarter source. The added unit test concerns one fixed OS system; unnormalized unit norms may vary across changing geometries/sources. No independently proved pointwise scalar identity or general origin route is excluded. Distinguish source derivatives from geometric derivatives and reuse the existing coupled-reference result.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:1e05458c8429100dc9fa72c3",
        "source:e1a6c5a201a7ac85333fd4b0",
        "source:7741540ac9c9596256db151e",
        "source:b863e920383f1bf4f9fe9f09",
        "source:e85978cda3b6a23613bbbd81",
        "source:ce9c60dab12bf2e414a8ac29"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-fermionic-source-schur-functional",
      "titleEN": "Field response and unnormalized factor from the same free integral",
      "statementEN": "Direct Grassmann integration gives det K exp(bareta K^(-1) eta). Schur reduction jointly retains det K_ii and the inverse effective boundary/mode matrix. Two collars of the actual lowest quarter particle/hole pair under the supplied fermionic trace give det K=69649/65536 and occupations1/17,1/4097. Direct identification of the primitive spectral action with integrated complex fermions requires x f'(x)+1=0, hence a logarithmic profile; arbitrary f is insufficient.",
      "scopeEN": "Exact for supplied free K, measure and source coupling. The example integrates a hole mode, not a geometric collar interior. Coherent source contraction K^-1 is not normal-ordered occupation. No general no-go for a separate bosonic spectral action plus fermion determinant and no original P1/P2 quantization.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-complex-fermion-source-quantization"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6e712a71a2fb68462ed31a33"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:quarter-circle-absolute-zeta-green-eta",
      "titleEN": "Quarter circle: absolute determinant1-i and joint Green/eta response",
      "statementEN": "For supplied D_alpha, zeta quantization gives det D_alpha=1-exp(2pi i alpha), exactly1-i at alpha1/4 with eta(0)=1/2. The same operator gives G_-=i/(h-1), G_+=ih/(h-1), jumpi and retained holonomyh=i. The joint source derivative contains partial_alpha log det=pi cot(pi alpha)+i pi; the extra i pi is the eta contact term. The general determinant formula also retains zeta(K²;0).",
      "scopeEN": "Supplied zero-mode-free angular circle operator with fixed spectral cut. Not the full physical TFPT source operator, not thermal occupation, and no identification of the diagnostic reference branch with D_ref. Transport periodic operator and source frames together when varying alpha.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-angular-quarter-zeta-cut"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f5621a3895c2d1617ccf299f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:quarter-sea-absolute-thermal-central-phase",
      "titleEN": "Absolute thermal sea regularization retains central phase",
      "statementEN": "The declared Abel/zeta subtraction gives E_sea=-1/96. At beta=2ell=8log4, q_beta=1/65536 and Z_beta[0]=exp(-beta E_sea) times the complete particle/hole product. Its two-mode factor is2^(1/6)69649/65536. Adjoint field action stays i/-i; the absolute time-loop operator additionally carries exp(-i pi/48). Existing tail bounds apply at the same beta. Under the same Hurwitz prescription E_sea=eta(0)^2/8-1/24 and d_alpha E_sea=-eta(0)/2. The logarithmic alpha derivative of the unnormalized thermal partition sum agrees with the occupation response including the sea term, checked by an independent Fock trace and explicit derivative tail bound. The resulting actual reference amplitude2^(1/12) passes the existing CLI moment search with206 source moments; the same data with reference amplitude1 are infeasible. This is a numerical software control under the same supplied regularization.",
      "scopeEN": "Conditional absolute extension of the supplied single chiral source. Regularization is input; neither subtraction nor bulk/eta cancellation of the central phase is proved from P1/P2. Angular determinant and thermal partition sum are different functionals. The finite excitation-product control already retains the full regularized sea term. The response is twist-conjugate spectral charge, not a new physical event law.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-chiral-opposite-quarter-domains",
        "premise:charged-car-negative-sea-source",
        "premise:given-thermal-sea-abel-subtraction",
        "premise:given-angular-quarter-zeta-cut"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2997b27dc68242a95af418be",
        "source:772a3a6580a01c439035ef5f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-operational-seed-and-given-green-pairing",
      "titleEN": "Original reconstruction uses the stronger operational seed",
      "statementEN": "P1/P2 does not fully specify the primitive kernel's field arguments. The archived reconstruction starts with algebra, time flow, state and collar operator; CAR and anticommuting sources are later premises. For a supplied product Dirac operator, the classical Green boundary form follows from normal symbol and boundary metric. Identification with the quantum field amplitude does not follow.",
      "scopeEN": "Source audit and reuse of the known geometric Green identity. No derivation of fermionic statistics or physical operator from P1/P2. the reviewed source checked against current Ludewig/Roos primary text1909.04212v4: algebraic twist also needs closed harmonic determinant factor; published2020 coherence proof correction is in v4. This is no new original source derivation or established error in direct TFPT collar proofs.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:731f8635e9a50cd4bccc72b6",
        "source:2878f4a3eb2d7c2fff4fc830"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:order-one-infinitesimal-bound-inference-fails",
      "titleEN": "Bounded coefficients do not imply infinitesimal relative bound",
      "statementEN": "The inference in original source01:397-405 is invalid: P=aA has relative bound |a|. The independent quarter/reflection control A=sigma_x p_theta+sigma_y p_r, P=a I p_r retains the quarter domain; at a=1, A+P on H1 is not closed. Repair: an actual relative bound<1, bounded symmetric perturbation, or a separate theorem for the total elliptic operator and boundary domain.",
      "scopeEN": "Only the general proof step is excluded. The a=1 control is not an admissible elliptic Dirac operator or a P1/P2 countermodel.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:first-order-perturbation-graph-estimate"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f5940a5e0bdab92a4edecfb3",
        "source:6ebfcec3dce985bf660507cf"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-ward-two-field-data-miss-fixed-four-field-response",
      "titleEN": "Joint Ward and two-field data do not select the multifield response",
      "statementEN": "For all alpha,beta, H and UHU* retain the full thermal partition, charge, quarter phase, sea energy and joint eta/sea/Ward identity. U fixes vacuum and one-particle sector and hence all vacuum two-field time responses. Yet the fixed neutral pair response at t=log2 is 1/2 versus13/50 after removing the same common sea factor.",
      "scopeEN": "Exact independently checked inverse-data control. Equivalent when all fields are conjugated together; locality of U is unproved. Not a physical alternative candidate or full P1/P2 countermodel.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-field-four-mode-inverse-data-control"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:25fbfbdcb2bf913f05c1a2f8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:complete-car-kernel-fixes-nongaussian-link-functional",
      "titleEN": "Complete CAR kernel also determines the interacting link action",
      "statementEN": "The full coherent CAR kernel is invertible and sews exactly. Its4^n duality values determine finite gluing; T00·exp(-S_nil) reconstructs all link vertices. Existing five-mode certificates give actions through degree10. The charged interacting control retains actual quarter time and absolute sea factors.",
      "scopeEN": "Standard coherent reconstruction, implemented and applied exactly here;1–5 modes. No P1/P2-selected field dictionary, geometric locality or original Φ-dependence. The minimum's term is an objective artifact. T00, reference eigenvalue, matrix logarithm and Grassmann logarithm remain distinct.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:complete-labeled-even-car-kernel"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e670d07f141adeb24d19c501"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-covariance-jet-and-mixed-face-interface",
      "titleEN": "Exact field variation of the existing covariance reconstruction and its boundary faces",
      "statementEN": "The Frechet derivative of the actual v258 reader multiplies each matrix element in an eigenframe by the strictly negative divided difference of h. For fixed sector projectors commuting with the background covariance, each sector block vanishes iff its covariance-variation block vanishes. A moving carrier embedding has additional derivative terms. The Calderon projection is not already a faithful mixed occupation: restriction to its own range gives I. The existing two-face construction correctly gives n=1-A and h(n)=2ell B, thus recovering the variation already present in B without selecting it.",
      "scopeEN": "Analytic finite/regulated derivative result plus exact reuse of the given positive particle/hole collar. No general non-Gaussian state reconstruction, Phi provenance, statement for noncommuting sector projectors or unchecked unbounded limits.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:faithful-differentiable-covariance-chart",
        "premise:actual-product-collar-two-face-data",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6d0c479df52320b2894a2fab",
        "source:ba95a95c05bce132e9f526b6",
        "source:900b4050f5a1bf51fd3f7b04"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e8-grade-two-explicit-spinor-current-action",
      "titleEN": "Actual action of the60 grade2 currents between the64-dimensional current sectors",
      "statementEN": "In the existing E8 dictionary J_r,0 acts on a grade1 root-current state as epsilon(r,p)|r+p> exactly when r.p=-1. The existing separated-point reader confirms960 nonzero actions among3840 pairs,15 per input and rank16 per root action. Twelve ordered distinct A3-family channels carry80 actions each;1024 same-family pairs of grade1 currents cannot be neutralized by any grade2 root. This is the actual internal (10,6) current action, not a selection of a Phi coefficient function.",
      "scopeEN": "Stipulated positive E8_1 representation and its internal quarter grading. Bosonic current states are not physical fermions; same family denotes the four given A3 weights, not already three physical families. No exclusion of all composite/dressed fields or later basis changes.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5a7a14ecc4366719e7aa6cc2",
        "source:5b7555a41d7d16e6f982b12c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:intrinsic-source-jet-removes-pure-field-frame-motion",
      "titleEN": "Intrinsic source variation separates frame rotation from genuine source/embedding change",
      "statementEN": "For C_F=Q*C_Sigma Q, with a=Q*partial Q and N=(I-QQ*)partial Q, exactly nabla C_F=partial C_F+[a,C_F]=Q*(partial C_Sigma)Q+N*C_Sigma Q+Q*C_Sigma N. The existing faithful modular reader obeys nabla h(C_F)=Dh(C_F)[nabla C_F]. Pure frame motion can generate ordinary nonzero off-diagonal entries while both covariant variations vanish exactly. Genuine normal embedding motion remains; the identity does not select Q, Phi or their original provenance.",
      "scopeEN": "Supplied finite/regulated charts; the state interpretation of h requires the quasi-free premise. No new physical gauge connection, Phi coupling or global anomaly/determinant-line triviality. Compression is not interchanged with functional calculus.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:differentiable-isometric-source-frame",
        "premise:faithful-differentiable-covariance-chart",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:741f0cb7ef057806b4f08a4d",
        "source:dc84d41cae9789f103a3c591"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:unchanged-ns-vector-generators-cannot-create-d5-spinor-fields",
      "titleEN": "Known NS vector fermionization cannot supply the missing Spin10 spinor through local products",
      "statementEN": "The existing fermionization route supplies (10,1)+(1,6), as established previously. The central kernel element of Spin10->SO10 acts trivially on each local generator but as minus1 on the required internal half-spinor. Products, derivatives, OPE coefficients and algebraic/norm/weak closures in the same NS representation therefore remain centrally trivial. Choosing V_a coefficients or searching further local composites in this unchanged algebra cannot repair the matter identification.",
      "scopeEN": "Reused representation result with analytic extension to the unchanged NS generator algebra, not new fermionization. No exclusion of Ramond/twisted states, charged sector intertwiners, dressed fields with additional source, other extensions or a universal TFPT model.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fermionized-ns-vector-algebra-fixed-d5",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016",
        "contract:source-z8-parity-descent-20260921",
        "contract:source-sector-reconstruction-20260920"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c49c4688e62f68b881befb92",
        "source:8f56a372e400abaf67a0bec5",
        "source:c3e4ca1a10fd981d4018c09e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:two-face-noncommuting-geometric-response-calculus",
      "titleEN": "Noncommuting two-face response with product and coherent kernel",
      "statementEN": "The full given graph yields L_f=A^1/2 M_f A^1/2, L_fL_g=A^1/2 M_f A M_g A^1/2 and positive Gram kernel <L_f x,L_g y>. The scalar quarter source yields a bilateral weighted shift with [L*,L]e_n=a_n(a_(n+1)-a_(n-1))e_n nonzero for all n. No internal algebra or coupling is inserted. This nonlocal geometric compression is not a unital multiplicative representation of scalar insertions; physical chronological execution does not follow.",
      "scopeEN": "Given full geometric collar with conditional quarter-source control. No original physical intervention, preparation or Born derivation; no internal carrier algebra or3+2 selection.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:geometric-two-face-response-and-kernel-quotient",
        "premise:typed-source-structures",
        "premise:quarter-circle-coordinate-local-algebra"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:cf1956e1880c77301ab425df",
        "source:39c4bd48295a8835244d6810"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:raw-face-mask-fails-source-kernel-null-descent",
      "titleEN": "Raw face insertion fails null stability; graph symmetries classified",
      "statementEN": "For K_G=<x,Gy>, P0 sends the null vector (-t,1)/sqrt(1+t²) to squared norm t²/(1+t²)²>0. The raw mask is not a quotient operation; W*W=G and OW=WP0 are also impossible. Compression repairs only mathematical descent. Separately, block unitaries diag(U0,U1) preserve the full graph iff U0=U1 spectrally commutes with B. Degeneracies may retain nonabelian commutants; interventions need not be symmetries.",
      "scopeEN": "Excludes only the raw mask action on this exact K_G and exact ancillary intertwiner repair. Does not exclude other history kernels, altered sources or physical interventions.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:geometric-two-face-response-and-kernel-quotient",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:df1dfb05512163de580304ab",
        "source:7ec4c91a99b298d39468318d",
        "source:39c4bd48295a8835244d6810"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:action-response-sewing-does-not-select-lf-intervention",
      "titleEN": "Action variation and boundary sewing do not select L_f as a physical intervention",
      "statementEN": "The primitive action derivative needs supplied D_rel/ref[j], domain, chi and eta families; logZ derivatives additionally retain measure/domain variation and a second contact term. The given collar yields T_ell=e^-ellB with geometric sewing, not A_ell: A0=I/2 and (log a_ell(lambda))''|0=-lambda² exclude a common scalar semigroup normalization on the quarter spectrum. Under the separate boundary-kernel reading K_f=F M_f F with identity kernel A, inverse-Gram sewing uniquely yields K_f#K_g=F M_fg F, commutative for scalar insertions. Ordinary noncommuting L_f operator multiplication remains valid. As f1 geometrically is an actual face mask, this kernel reading is not automatically the physical law.",
      "scopeEN": "Exact conditional normalization/sewing test and original-source comparison. No universal prohibition of compressed instruments, no selected physical sewing or identification of normal distance with physical time. Actual boundary intervention and history kernel remain underived.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:quarter-circle-coordinate-local-algebra",
        "premise:geometric-two-face-response-and-kernel-quotient",
        "premise:boundary-kernel-frame-sewing-interpretation",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ec9289e58a4c1e5dd23272fb",
        "source:66f2b2db52873e7dc2f23461",
        "source:748b7940e88d21a0f908d8c7",
        "source:e5365cc62dd86a7a3650d7ef"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:faithful-gns-completion-closes-automated-source-query-feedback",
      "titleEN": "Mixed-source completion and automatic discriminating query in the existing search path",
      "statementEN": "The normal search entry point now offers optional faithful CAR GNS completion instead of stopping thermal data at an incompatible pure-Fock ansatz. In the old supplied quarter source, two exact candidates replay all51moments through word length4. The search generates the shortest missing joint response of length5 and obtains its value only from the same existing source. All16/16transfer metric entries are then fixed in this representation; an explicit full basis intertwiner verifies the actual source action. The16dimensional two-mode control preserves neutral transfer products.37appropriate new/old regressions pass, with independent source/algebra review accepting the scope. This improves automated source recovery and software validation, not physical original-P1 source selection.",
      "scopeEN": "Additional finite CAR-cyclic representation ansatz, validated on previously given one/two-mode quarter controls. Exactness applies to rational inputs or explicitly rational-recovered numerical moments; no new P1 Wick value, physical time/reflection derivation, larger-dilation/continuum uniqueness, absolute Z scalar or T1-T8 closure. The actual local P1 insertion and joint connected four-field response remain to be derived.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:finite-faithful-car-gns-source-completion"
      ],
      "attemptIds": [
        "contract:seam-positive-kernel-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7c28e8bf9ff5c5840e8af7e9",
        "source:18120fda194dea4796ad2c24",
        "source:8bdfe9e0c9db0b04775dae2b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-quarter-channels-identified-by-exact-internal-kernel",
      "titleEN": "Identify all fixed whole quarter channels by one exact internal kernel",
      "statementEN": "For one p>0 in the already given constant odd Clifford source the occupation defect D_p on F+ is positive and kerD_p=F+ intersect kerPhi. The existing whole field/state/reflection/same-time map makes every resulting constant channel an identification of all scalar future responses. Known Phi needs only its exact kernel, without exponentiation or directional scanning. A direct actual-v252 control finds no such channels in the existing invertible input; rank-defect controls find2/1 positive and1/0 neutral directions. On nu_R^c tensor C3 the kernel is exactly ker[MR;entrywise_barYnu]; a nonreal control rejects replacement by adjoint.",
      "scopeEN": "New automatic use of existing rigidity and whole source map, not a new general GNS/learning algorithm. Same scalar future relative to the declared alphabet; additional P2 insertions must be retained separately. The finite channel decision does not truncate the infinite circle/Fock system. No original P1 source selection; physical interacting successors need not preserve the old free source.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-local-quarter-channel-in-constant-odd-source",
        "premise:actual-full-v252-unimodular-p2-gauge-lift"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:02a45b61c44bd61d15ef2453",
        "source:054e763500be2aab6476a2e4",
        "source:46b298ac7fd2f765602471b6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-joint-insertion-hull-resolves-eight-coefficient-directions",
      "titleEN": "Shared original insertion words reach the whole lepton8",
      "statementEN": "The unchanged exact intertwiner path gives commutant dimension6 for gauge+grading on the actual reducing diagonal lepton8, then1 after adding the actual quarter generator h=gamma/4−i gamma Phi alone. Four original Higgs images remain jointly compatible. From the neutral test input individual fixed h+h_q reach4 directions; common words in the separate original h/Higgs images instead give1→4→7→8→8, closing at depth3. A gauge/grading-compatible nu_R^c phase flip fails h already at entry(1,5) with2i. Root independently decoded the stored rational matrices and exactly recomputed these values.",
      "scopeEN": "Actual finite coefficient contract and minimal coupled identification, not a physical state functional or P1 origin. Input values are controls, not derived masses. Common-phase freedom applies to the given linear tuple; physical antiunitary J/R types are not excluded by the formal same-label antilinear branch. An independently original second operator image is still needed; W Phi W* manufactured from the desired dictionary would be circular.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-diagonal-lepton8-common-insertion-contract"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d60e9887ee5e2b0c02a22cca",
        "source:f205867e0fd7108d23d84e5d",
        "source:ea58b5f9dcee104fcea42ce0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e8-bare-trilinear-and-single-anchor-weyl-class-insufficient",
      "titleEN": "Bosonic E8 trilinear and single-anchor Weyl class do not supply the claimed mass bridge",
      "statementEN": "The antisymmetric E8 current coefficient B_h vanishes if literally used in the same left-Weyl quadratic, since B_h tensor Lorentz epsilon is symmetric. For any skew4x4 family form omega and arbitrary polynomials F,G of the same X=diag(3,-1,-1,-1), X²=2X+3I and Sym(F omega G)=(ad−bc)(omega X−X omega)/2. Every such symmetrized family block is a star matrix with zero triplet block, rank at most2 and complex singular values||v||,||v||,0,0. Exact24-basis checks and independent analytic review close the whole stated polynomial class. The reviewed therefore had no justification for comparing singular values of the unsymmetrized current coefficient directly with physical lepton masses.",
      "scopeEN": "Excludes only the stated one-bracket/one-anchor/same-Weyl identification. Rank2 per4x4 family channel, not the full64 operator. Fixed-omega image at most1D; dimension3 only over all omega. Other original family-distinguishing operations, independent Dirac variables, higher insertions and physical field maps remain open. This is not an E8/Yukawa/TFPT no-go and does not refute independently asserted mass relations.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:one-e8-bracket-weyl-pairing-with-single-anchor-dressing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:c368cad97b5c1958f1b24980",
        "source:fd835bc47bb22f203c8a1b9e",
        "source:0581819ce19c26f3c949d912"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:complete-family-four-cycle-class-separates-native-clock-from-sm-preservation",
      "titleEN": "Complete family-four-cycle lift class separates native clock and fixed SM preservation",
      "statementEN": "The whole exact E8 quarter-lift family[g5,eta C4] is covered by1024 Spin10 torus representatives modulo4D5. Exactly320 have actual native weight-one character(60,64,60,64) and belong to the native inner field class by the already proved complete E8 torus classification. They have3 odd vector planes and even residues0,2; their Spin10 centralizer isA2+u1³ and cannot contain an additional commuting weakSU2 beside colorSU3. The whole original-SM-commuting subclass has16 representatives with only(64,64,56,64) or(70,56,66,56),hence no nativeJhat match. Independent analytic review reproduces all characters and the full histogram. Already Tr248g=Tr45g5−1=2(d²+k−3) decides the load-bearing distinction.",
      "scopeEN": "New complete application to a precisely declared lift class, not1024 new physical sources. A family four-cycle is not a general substitute for native clock. Existing positive C kappa C^-1=Jhat and whole C12 conjugacy remain solved;kappa is not such a family four-cycle. A jointly transported SM embedding in full E8 remains allowed. No new P1 source, physical field statistics or Yukawa selection is proved. The separate odd Cartan-rank gate excludes only fixed real root charts and is not extended to all inner field conjugations.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:spin10-su4-family-four-cycle-quarter-lift-class",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:893de844a62902e7ffbcf8a1",
        "source:37288a423c4f7967c320b778",
        "source:b1c7034d10dfa8476ac047de",
        "source:0b691fea8283ab9f632ed43b",
        "source:9145b12e57c7afb1f88701c6",
        "source:e23fb8064f4d6061d70ed158"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-clock-word-transpose-has-static-rank-four-counterexample",
      "titleEN": "Word transpose is exact but forces neither time ordering nor generic rank two",
      "statementEN": "For K(x,w y),w^t=(-1)^n w_rev with inverted group letters. In the native two-phase lepton class generic h gives [[0,Z],[Z^t,0]],hence(s1,s1,s2,s2). Actual g2 roots e4−e6,e4+e6 with family coefficients eta13=1,eta24=2 give det Sym(eta T)=9/4 and squared singular values3,3,3/4,3/4. Both roots are sigma invariant:[ad_h,Ad_sigma]=0 despite nonzero symmetric pairing. Lack of reversal symmetry therefore proves neither noncommutativity nor physical time ordering. The word is already the actual grade-one affine source correlator <Omega,J^x_1 rho(w)J^y_-1 Omega>.",
      "scopeEN": "Generic whole four-carrier. A narrow Creation30 or single-root contract needs separate checking; marked2+1 three-plane still gives(s,s,0). Arbitrary additional original torus letters lie outside the two-projector alphabet. No physical Yukawa or mass origin. Retain old symmetric source420 and complete normal-clock hierarchy bound.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:native-third-clock-current-word-pairing-class",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029",
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:87aa3e97ecdfefa26a8a2d78",
        "source:df5c6e023d22118a39977dc7",
        "source:84915c30bfd211ca351cc7f6",
        "source:16100a13c722b377e2f157f9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-constant-coupled-source-is-implementable-despite-isolated-insertion-domain",
      "titleEN": "Whole coupled circle source is implementable despite isolated insertion divergence",
      "statementEN": "For actual constant odd V=-i gamma Phi,||[P0(p),V]||HS²=Tr Phi² on every p=n+alpha. The pure insertion group is not implementable in the old sea for all small nonzero parameters. In contrast,||P_-(h)(p)-P0(p)||HS²=(1/2)Tr[I−|p|/sqrt(p²+Phi²)]≤Tr Phi²/(4p²). Thus complete sea Fock representations are equivalent in this1D class and full coupled evolution is implementable. The old sea nevertheless has infinite coupled excitation energy and is outside its energy form domain. The complete two-face G_ell(h) also differs from G_ell(h0) by HS,including crossing blocks.",
      "scopeEN": "All Fourier modes in specified1D circle source,finite K and constant classical odd Phi. No cutoff extrapolation or fitted state. Equivalent representations mean neither identical vacuum nor identical generator domain. Positive P_h sea excitation Hamiltonian is not the thermofield GNS generator of full G_ell state or physical OS time. No higher-dimensional or dynamic bosonic conclusion and no original P1 selection of Phi.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-product-collar-two-face-data"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a00ef03eb014f57051594211",
        "source:273c92a8ea1ba422f3da62f6",
        "source:5be432d5996cfde38eef543d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-quarter-jloc-pfaffian-closure-fails-local-skew-test",
      "titleEN": "Direct Pfaffian closure fails local skew test in fixed scalar quarter chart",
      "statementEN": "Actual old identity gives Jloc Dalpha Jloc^-1=−Dalpha+2alpha S. Thus beta_alpha(x,y)+beta_alpha(y,x)=2alpha<Jhat x,y>. A real compact radial profile in first normal slot with constant circle profile and J_F u=u gives beta_alpha(x,x)=alpha||x||²≠0 at both original quarters. The claimed unchanged beta_Dalpha Pfaffian source is excluded already on the interior smooth core. Old skew theorem at a^J=−a remains valid. Action comparison also requires a log profile with correctly counted full trace; eta alone determines neither magnitude nor source pairing. Later originals allow any declared f but do not thereby select a log profile; existing Frullani bridge explicitly treats scale-measure choice as input.",
      "scopeEN": "Only specified direct Pfaffian candidate at fixed scalar alpha with unchanged operators. No full P1 countermodel or general Pfaffian/TFPT no-go. Preserve given positive whole Clifford source,both faces,products,reflection and circle time. Actual J-odd charge connection or explicitly identified paired sectors are not excluded. Two faces are not automatically two quarter holonomy sectors. New conditional CAR insertion value repeats known target value rather than independently reading original source response.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-scalar-quarter-full-jloc-pfaffian-candidate",
        "premise:typed-source-structures",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029",
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b1180fb2997ae143da994439",
        "source:ed45d8f720520bfbc1c83194",
        "source:6a7cde430df453795a349d3f",
        "source:18d26d01a80ed816c25af880",
        "source:b9d504edd5f7f899d4274859",
        "source:ac74219b3331369a1aff4089",
        "source:7e75a08383696f4aec35bc2d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:same-collar-has-canonical-selfdual-kinetic-pairing-and-charged-determinant",
      "titleEN": "The same collar supplies its canonical selfdual kinetic pairing",
      "statementEN": "The unchanged normal symbol gives new-complex-linear L=−ND=partial_r+B. On the common interior core,C0LC0=−L* and L*L=D². Hence <C0x,Ly>_new is skew,including scalar quarter holonomy. Endpoint defect is exactly [<C0x,y>]_0^ell. In the complete charged chart,L=diag(L+,−bar(L+*)),L+=partial_r+h,and its skew matrix [[0,−L+^t],[L+,0]] has Pf=(−1)^{n(n+1)/2}detL+ on a compatible finite regulator. D and L have the same whole Cauchy graph,transported by T_faces to G(h)⊕(1−barG(h)).",
      "scopeEN": "Exact kinetic dictionary inside the already given geometric Clifford source,with existing smooth normal-independent classical Phi and both total grades. No new source,field copy or J choice. This differs from <Jloc,D>_old;its quarter counterexample remains valid. A closed skew realization requires the actual isotropic boundary domain or C0DomL=DomL*. Cauchy projector is not an inverse Green operator and does not fix the unnormalized determinant scalar. Physical functor use,original reference/phases/profile and OS time still require comparison with the actual original source. A supplied operational Seed requires no additional free state choice.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-product-collar-two-face-data",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:294903a96d4c8ec322f7fb3d",
        "source:4a300d2647442762c1c31458",
        "source:147fc8d41b926a56bdb28e90",
        "source:edda8dad365e90f5ed681b68",
        "source:d524584442118cdae34ed370",
        "source:4aeac9c461cf7d32a75b7b1f",
        "source:e0cc878ce2edc3c03a564c6c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:quarter-cover-pairing-does-not-supply-local-normal-or-select-scale-measure",
      "titleEN": "Quarter pairing supplies neither local normal nor convergence-based scale selection",
      "statementEN": "Existing J'=swap M_exp(−ix)K is a valid tangential antiunitary quarter pairing making C_A selfdual. Its sectors are V=Tpi character spaces of one NS circle. A local old-complex-linear N has sigma1{Bcov,N}=4xiN; anticommutation requires N=0,while actual deck commutes with Bcov. Relative heat trace Delta gives log2 under dt/t and paired Pfaff value log√2. Measure dt/t+c exp(−t)dt also converges,but shifts paired value by c pi sinh(2pi)/[2cosh(2pi)(cosh(2pi)+1)]>0. Relative UV finiteness alone therefore selects no scale measure. Declared annulus values0.701844509492457 and2.62205755429212 were independently confirmed.",
      "scopeEN": "Narrow original-source and candidate comparison. Preserve valid tangential pairing and declared relative log prescription; no new normal-field class,global P1/Moebius exclusion or two complete P1 sources from alternate weights. Convergence cannot replace an additional original dilation rule. Full existing normal Clifford chart and canonical L pairing remain available. A common bosonic-plus-fermionic source need not equate bosonic spectral action with fermion logdet. Origin and reference must be checked at actual joint source call.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-quarter-cover-deck-normal-and-convergence-selection-tests",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029",
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:cca3834e4bf18a987dc2a44c",
        "source:376aed4c81f05e5330d5e032",
        "source:4c2d7a14ffa80ca348ab41d6",
        "source:2940b7c5826854e30f72ec65",
        "source:1f308a0465a4181035a0f4e0",
        "source:7e75a08383696f4aec35bc2d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-aps-source-has-whole-inverse-and-finite-boundary-correction",
      "titleEN": "Whole fixed APS source has exact inverse and finite boundary correction",
      "statementEN": "At each original p,M=P exp(-ell h)P=cosh(ell E)+|p|E^-1sinh(ell E) is invertible and Gfixed(r,s)=1_(r>s)exp(-(r-s)h)-exp(-rh)P M^-1 P exp(-(ell-s)h). Energy identities for L and L* prove ||Gfixed||<=4 over ALL Fourier modes,deltaG=-Gfixed delta h Gfixed,and bound16||delta h||. Moving APS(h) is a different insertion family: at p1/4,m1/3 its kernel violates the old boundary condition with HS²=exp(-5s/6)/5. Same exterior transfer gives fixed/moving cap quotient C_p=(I+|p|E^-1)/2+(I-|p|E^-1)exp(-2ell E)/2. C>=I/2 and0<=I-C_p<=Phi²/(4p²),hence positive nonzero Fredholm determinant on the full circle. Actual96 chart gives Tr(I-C)<=pi²Tr_KPhi²/4. This is the finite boundary correction associated with known HS sea rotation. Original provisional APS choice and Calderon upgrade do not choose a new state for the complete operational Seed,which already contains omega and tau. In the already implemented common sea representation,det_F C is exactly <Omega0,exp(-ell H_exc)Omega0>,with coupled sea energy0 and actual neutral pair gap2E. Normalized midpoint vector exp(-ell H_exc/2)Omega0/sqrt(det_F C) gives the same whole fixed cap state and lies in every finite H_exc power domain for ell>0. Its single odd block has ||[h,Pmid]||HS²=2m²/M² and is nonstationary under coupled source flow at m!=0 and finite ell. For a finite general cap, Zcap=e^(ell Tr(hPh))det_RanP0(P0e^(-ell h)P0). The actual weak addition has {p gamma,tQ gamma}=2ptQ, so the earlier anticommuting C_p reduction does not apply. Retain P0 and signed h in the compression; the cap uses the old boundary vector, not the invariant OS unit vacuum of that same system. Original APSdomprov chooses a given adapted A_partial without identifying it with p gamma_F or Phi0. The whole D_+ Calderon call precedes D_ref/D_rel and survives degeneracy of a later particular split. A fixed domain alone does not identify an original cap preparation. C59's Dgeo=Dref requires previously identified closed total operators and still does not force a moving APS space; bounded zeroth-order perturbations can retain a fixed elliptic domain.",
      "scopeEN": "Analytic closure of constant bounded odd quarter class with fixed original endpoint space; exact minimal control confirms ODE,jump,both boundaries. Not generalized to arbitrary Phi(r,theta). Moving APS kernel and whole Cauchy graph remain valid for their respective boundary contracts. Boundary determinant is relative quotient of same exterior representative; it neither renormalizes logarithmic bulk energy nor determines absolute Zadm,determinant phase,physical time or P1 field source. No second quantization of complete Seed or repeated generic first-order counterexample. Canonically normal-ordered coupled excitation energy is not presented as original absolute bulk energy. Pure midpoint state and thermal face marginal remain distinct given states. The initially finite general cap formula is extended to the whole circle for constantV in actual-weak-cap-converges-on-whole-quarter-circle, retaining that finding's coupled-energy convention. The sigma_z/sigma_x control is general cap algebra, not two full v252 sources with identical original data. Fixed OS time differs from varying the entire collar geometry and its unnormalized unit norm.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-original-aps-quarter-domain-and-constant-odd-insertion",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:af4be0da2c4b52f5684b7582",
        "source:a3bdadfcea9b1004b36c0503",
        "source:722f7991988efbe8f8292148",
        "source:a35130ab46746c0c37571db2",
        "source:dfbfa1c216e71e0ee166a28f",
        "source:666f49c8dea3f8819e27c103",
        "source:0c3af591ac78ed8332145c62",
        "source:38b1537329d8bec338b1b1a2",
        "source:9ce95751dc72a6922f3bd238",
        "source:f6396a970e05d81113556da9",
        "source:8ceffd87669349a91dc63a58",
        "source:b863e920383f1bf4f9fe9f09",
        "source:e85978cda3b6a23613bbbd81",
        "source:ce9c60dab12bf2e414a8ac29",
        "source:eb56309a7bf438a9f0eb1a7c",
        "source:e7c47fc8bdd3d4a176eff69b",
        "source:0bfd452199e2c7e502357b9f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:mass-only-deck-relative-heat-action-fails-free-infinite-trace",
      "titleEN": "Mass-only relative deck operator fails ordinary heat trace",
      "statementEN": "Full tau=S R_r gives exactly Dref=D0+(Z/2)(Phi-Phi_tau),Drel=(Z/2)(Phi+Phi_tau),hence claimed massless reference for even Phi. Fiber S alone instead gives Dref=NZA,Drel=N partial_r+ZPhi. Distinct existing product reflection S gamma_F R_r preserves coupled D and gives Drel0. Under narrow mass-only Drel and ordinary infinite heat trace,already Phi0 fails:f(Drel)=I,so I-exp[-(D0/chi)²] is noncompact. Compact base,gap removal and internal admissibility selection do not remove this UV identity term. Original relative-object table also permits a declared relative pair; this does not replace the explicit even/odd formula without its own source reconciliation.",
      "scopeEN": "Excludes only expressly combined deck identification,heat profile and ordinary infinite trace. No general P1,profile,deck or TFPT exclusion. Actual finite UV domain,other trace or different original relative-pair prescription changes contract and must be explicit. No unique inference of replacement by Tr f(Dfull)-Tr f(Dref),or renormalization condition from chi alone. Preserve valid normal,tangential and product-reflection maps and complete Seed.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:mass-only-full-deck-relative-and-ordinary-heat-trace",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:af4be0da2c4b52f5684b7582",
        "source:9329e2e416e2490900da43e0",
        "source:71d9b0e9792e4c99d88c2544",
        "source:b54c34c09388e6044a7dd009",
        "source:28adffa8f2c767cca19b7efa"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:finite-antiperiodic-scalar-wall-has-no-exact-massless-normal-mode",
      "titleEN": "Finite antiperiodic scalar wall has no exact massless normal mode",
      "statementEN": "In actual claimed finite anti-circle wall class,{S,Q}=0,Q²=-partial_r²+sigma²Phi²+S sigma'Phi,D²=Q²+p². Qpsi0 forces monodromy exp(SPhi∮sigma),positive definite with no eigenvalue−1; odd zero-mean profile gives exactlyI. Thus kerQ0 and each fixed circle has strictly |lambdaD|>=sqrt(p²+mu0²)>|p|. Claimed exact ±p wall modes are excluded; close numerical values give only finite approximations. For zero-mean sigma,full normal inverse is F(r)[1_(r>s)-1/2]F(s)^-1(-N),F(r)=exp(SPhi∫0^r sigma). Given homogeneous anti-Green source correctly reproduces old thermal graph,but local C_faces selects neither global spin clutch nor original Schwinger functional. Infinite single-wall index and existing normal spin-S2-O1 index-one result remain separately valid.",
      "scopeEN": "Complete analytic exclusion only of finite scalar anti-I class with fixed commuting Phi. No uniform positive bound in separation/large-mass limits,no exclusion of noncommuting backgrounds,other clutch or original P1. Infinite isolated wall has index−sigPhi under its asymptotic premises; no general requirement for gamma_F-even P1 mass follows. Finite D_F and geometric D_N are distinct operators. Local reflected signs do not define an original mass wall without actual global trivialization and smooth transport. No physical-origin completion.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:closed-antiperiodic-scalar-wall-with-fixed-hermitian-coefficient",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029",
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e6389b85cf408aeb4a93fcad",
        "source:ffb49b5ccbcbe4ce981c71c9",
        "source:ef0117ac5b3caa584efe473d",
        "source:190b7b20c2dc004b9571a872",
        "source:daa7dca97448f869d36c79fa"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:spectral-heat-covariance-positivity-does-not-imply-time-rp",
      "titleEN": "Spectral heat covariance positivity does not establish time reflection positivity",
      "statementEN": "Original proof calls its Euclidean covariance a positive mixture of reflection-stable heat kernels but defines neither its operator function nor heat-parameter relation to geometric time. For one spectral heat covariance,exactly c_s(2a)c_s(2b)/c_s(a+b)²=exp[-(a-b)²/(2s)]<1. Reflection invariance and positive Laplace weights alone therefore do not imply OS positivity. The entire stated continuous scalar translation-invariant C1 covariance class is settled: ordinary PD and RP force c constant. From c0 c(2t)>=c(t)² and d=1-c/c0 obtain 0<=d(t)<=2^n d(t/2^n)->0. Actual energy-semigroup Gram kernels and suitable positive Stieltjes/resolvent mixtures remain RP; no P1 selection follows.",
      "scopeEN": "If reflection-stable already means OS positivity,the mixture is valid and the property is a hypothesis. If it means only reflection invariance,the general inference fails. No claim about actual unspecified original covariance,no all-P1 countermodel or physical completion. Existing Boltzmann/Schur reweighting counterexample is distinct. Seed RP,whole Clifford RP,valid energy semigroups and free cusp covariances remain intact. No renewed genetic scan in the completely excluded smooth class.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:scalar-spectral-heat-covariance-with-geometric-time-reflection",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:84db513d1e880d5c3b22d1e1",
        "source:8c913963a315a5d8d62b73bc",
        "source:d2816691788c0acb67faaf49",
        "source:8cda86aa53653ad5dde4751f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:quaternionic-sm-mass-winding-is-not-normal-determinant-clutch",
      "titleEN": "Quaternionic SM mass loop is not the normal determinant clutch",
      "statementEN": "Already proved full one-form family gives exactly det M_H=||H||^(2nf)det(YupYdown) per color; three colors exponentiate expression. Every invertible loop has constant phase and winding0. Noncommuting Yukawas do not alter identity. Actual connected SM lift preserves determinant pointwise by matching left/right charge sums. This excludes The reviewed literal identification of this global mass loop with prescribed normal winding-one clutch. General inference neutral=>winding0 is false: neutral A(theta)=exp(i theta) has winding1,and S=[[0,A*],[A,0]] is selfadjoint,odd and S²I. Constant complex Yukawa phase suffices; claimed determinant positivity was too strong.",
      "scopeEN": "New narrow corollary and external candidate correction,reusing old quaternionic classification instead of96-dimensional random search. Singular Yukawas or zeros of H make determinant winding undefined. No claim that all NCG normal indices vanish. Given genuine spin operator on det E2=O(1) keeps indexone; bosonic H0(O1) doublet and conditional product-source transport remain separately valid. Formal connection-plus-potential decomposition supplies neither global Callias Fredholm conditions nor identification with original D_N. No Majorana/PQ selection,original source derivation or physical completion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-global-quaternionic-sm-mass-loop-with-fixed-yukawas",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029",
        "contract:seam-joint-source-origin-audit-20261016",
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:aae6d90f3e1e380aa37dec08",
        "source:e6b2ec8e2768b44a1b9e0294",
        "source:20ba7d005ffba64df6121ea0",
        "source:7fcaffc8aec74e140bcedfb8",
        "source:3d78b16e46af374ab98aea71",
        "source:7ef217dd7e0693e80930b0a9",
        "source:66792dbaa28e80abd9a47492"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:bounded-relative-trace-obstruction-and-whole-genuine-pair-heat-reader",
      "titleEN": "Whole bounded-difference class and finite genuine pair-heat reader",
      "statementEN": "For every bounded selfadjoint V and specified nonzero positive Laplace contract,F(V²)>=F(||V||²)I=cI,c>0. Thus PF(V²)P is noncompact on every infinite-rank retained subspace; no P/V commutation needed. Subtracting trace-class reference does not repair it. This extends prior free/constant counterexample to entire bounded class. Constructively,same supplied operators admit genuine pair D=Dref+V: common square-form domain gives D²>=.5Dref²-||V||² as form bound; minmax yields Tr exp(-tD²)<=exp(t||V||²)Tr exp(-(t/2)Dref²)<∞. Whole pair heat exp(-tD²)-exp(-tDref²) is trace class for every t>0,without heat factorization or fixed square domain.",
      "scopeEN": "No all-profile/all-P1 exclusion. Newer originals allow any declared f and separately a relative pair. Pair reader is not algebraic rewriting of F((D-Dref)²),original selection of profile/normalization or physical completion. Singular profiles require actual functional calculus and integrable heat mixture. Local symbol-preserving reflection may yield bounded V; other Pin/anticommuting or nonlocal reflections are outside inference. Exponential bound compares eigenvalues/traces,not Loewner exponentials. Existing coupled sources and Seed time retained.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:bounded-relative-operator-positive-laplace-and-compact-source-pair",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1e7810d1a3b37a40ecd7a3d3",
        "source:9329e2e416e2490900da43e0",
        "source:b54c34c09388e6044a7dd009",
        "source:28adffa8f2c767cca19b7efa"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:normal-clutch-orbit-index-equivariantly-recovers-given-weak-module",
      "titleEN": "Normal orbit-index family equivariantly recovers the supplied weak module",
      "statementEN": "Global Pw clutch exists without global Hopf section. Split vertical spin realization gives kerD_N,+=L=O_W(-1),coker0; family Chern character ∫N ÂchE=chL,c1E=x,c2E=xy. Actual U2 action makes H0(W,L*) canonically V* with Y−1/2; its outer dual is canonically V with Y+1/2,and dual evaluation exactly Lw⊂V. This repairs raw doublet identification without fitted charge. Actual q=(Htilde,H) has first columnY−1/2,secondY+1/2;q parametrizes an already degree-one clutch despite zero winding of det(qM). E8 half-root reproduces(0,0,0,1,0) on marked j6. But whole root quarter has248 character(134,56,2,56),while nativeκ/Jhat has(60,64,60,64). No full field conjugacy; separate D5 endpointκ remains correct. Actual oriented64 and fixed carrier marks corrected in review. Projector form I+(z-1)P itself already appears in September30 Bott proof; newly reviewed here is its differently typed normal-equator/weak-orbit family,index and full charge diagram.",
      "scopeEN": "Constructive conditional comparison of supplied weak representation,not derivation of its rank or additional orbit/dual-section rule from P1. Other horizontal connections may retain K class while kernel/cokernel jump; longitudinal holonomy,state,boundary correlations and physical time are not fixed. Root-quarter test applies already complete native toral classification,not new clock existence problem. Freely moving familyj gives12D8+8halfRoots; fixedj6 only8+4. The reviewed64 grades label conjugate64 in original exterior-even chart. 1+3 generator grades and2+2 third-clock phases of distinct operators are no contradiction. Existing natural joint spin/family lifts retained. Old Bott map uses seam circle and normal sphere; current family uses normal equator clutch and separate weak orbit. Those variables are not identified. No reinvention of old projector form.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-normal-spin-clutch-weak-orbit-family-and-u2-linearization",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029",
        "contract:e-series-source-reconstruction-20261024",
        "contract:source-rule-search-20260930"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:4727da241f0a77603f31d69e",
        "source:4a87c7986a63700ed538cb37",
        "source:8d8dd85af67d318088180259",
        "source:fc1bab35d4aeb23add0d2714",
        "source:041a5617773b732d8e3c2540",
        "source:e23fb8064f4d6061d70ed158",
        "source:ec4f2b07704032568f2c0602",
        "source:20ba7d005ffba64df6121ea0",
        "source:5970e5bafb9733ab2ef5a910",
        "source:73e9ccfb54e8a82fb969907c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:normal-orbit-spin-family-index-and-signed-charge-balance",
      "titleEN": "Normal spin lift and fermion response obey the same signed charge balance",
      "statementEN": "Same supplied orbit family and existing September22 lift yield chW_m=64+(32+16Σm)x−16xy. For Σm=−2 normal family index has rank0 and ch=−16y. Split mA kernels are K+=2[Rodd⊗L+Reven⊗detV],K−=2[Reven+Rodd⊗Q],16modes each. Fully SM-equivariant Q is detV⊗L*,Y+.5; bare L* would haveY−.5. For commuting Spin10 charges q,signed quadratic mode sum is A_q=(Σm+2)Tr16q². Per-copy coefficients are Y:5/3+10m/3,T3:1+2m,SU3:1+2m and gravity8+16m. Same condition thus links algebraic natural lift to normal charge balance. Mathematical product index is−16d and weighted I_B=I_L=−4d. Conversely new origin identification of τ|winddet| with Dirichlet minimization fails exactly:gε=diag(exp(i[φ+εsinφ]),1) always costsτ but E=1+ε²/2. True HS loop energy has full Fourier equality class h exp(i sign(k)φP),but is an additional functional. Even one fixed hemisphere leaves all projector directions equivalent under unrestricted smooth other-disk gauges.",
      "scopeEN": "New conditional common corollary of supplied family/lift,not P1 selection. Numbers become anomaly coefficients only under actual chiral1+1D field quantization; not an original Ward insertion calculation. Four A3 carriers are not four physical generations or a contradiction to original three-family construction. N×W index proves neither physical4D theory nor ΔB/L transitions. Dual-bundle formula Wm*=ΛoddE⊗⊕D^(−1−m) holds but supplies no actual OS domain/phase/RP map. Whole ordinary genuine heat pair of pure gauge conjugates Dg=MgD0Mg* is exactly zero; not transferred to Padm,marked insertions or unidentified original reflection-pair convention. Native clock,old Clifford/boundary states and whole positive sources retained. No stochastic rescan of settled loop classes. Local retention of the Yukawa seed in finite qM does not refute an upstream TFPT flavor derivation. Originals contain the hard holonomy formula; archived faulty D/P puncture display and existing analytic v117 C4/A4/S4 repair are already reviewed and reused,without claiming new D4 rigidity.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-normal-orbit-and-four-copy-natural-spin-family",
        "premise:given-normal-spin-clutch-weak-orbit-family-and-u2-linearization",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d4c05d62c3b148af8d59b6c5",
        "source:6c41507ab823a2394bbd666b",
        "source:2e8f249fb5e4eff1dc8c7327",
        "source:4ea74630c7805cb6f5a1d0a8",
        "source:0b6a34e08216429530800b2e",
        "source:33b603a93d93f24fd36ecb4c",
        "source:7bb98421226ad6090801d9ca",
        "source:9d7bce2c2de624ade6f65470"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-flavor-cartan-sign-cover-and-root-lift-parity",
      "titleEN": "Fixed Cartan test couples S4 sign to sector parity and already admits an intermediate cover",
      "statementEN": "Under extra fixed orthogonal Cartan identification c(x,y,z)=(-y,x,z),exactly1920of3840 D5 signed permutations preserve full E8 roots,all exchanging the two marked64 sectors. Exactly12 preserve color/weak root blocks and unorientedX line,all X→−X; none preserve orientedX. Even total E8 half-root parity analytically forces odd signs in both blocks. Generally exchange parity is sign:S4→C2. Existing C4 descent t=z⁴ has local signs(−,+,−); intermediate cover s²=t,s=z² already has A4 monodromy and preserves marked64. Full C4 cover is stronger than needed for this grading alone.",
      "scopeEN": "Independent exact census and analytic review of The reviewed candidate,not original selection of Cartan identification. std⊗sign rotation representation was already proved. No physical spacetime chirality,charge conjugation,OS reflection,Yukawa equality or identification with original C12/48 cover. Twelve X-inverting maps differ by color/weak Weyl actions. Candidate general impossibility claim is therefore too broad. Actual family-vector action is separated in companion finding.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-v117-orthogonal-d3-cartan-identification",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:75575d6f41beea4d59f6bcfe",
        "source:d3915fc4a1abb08587601a35",
        "source:f053500aabea9bfdfa519e22",
        "source:0366ac2bc33ad41e384d6a2a",
        "source:7bb98421226ad6090801d9ca"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-family-vector-action-is-not-cartan-rotation-or-spinlift-selection",
      "titleEN": "Original family-vector action differs from Cartan rotation and does not select a spin lift",
      "statementEN": "Original explicitly contains SU3⊂SU4 via4=3+1. For supplied90degree family-vector rotation R,U=diag(R,1) preserves each of (16,4) and(bar16,bar4). Actual five E8 branches yield248 multiplicities(134,56,2,56) for(1,i,−1,−i),trace132,the already known root-quarter type. In fixed four-basis U induces only h1↔h2 on traceless Cartan,spectrum(1,1,−1),order2; this is not order4R on family vectors. Native glue clock has(60,64,60,64),trace0. Claimed spinlift selection m=(k,k,k,−2−3k),minimal mF/dual,was already proved exactly on22September under extra fixed irreducible parallelity; general covariance does not supply it. Actual mixed output is(E⊕E*)⊗D^(mi+mj+1),with dual pairing of complementary SU4-six indices. Candidate general single-Higgs exclusion ofmA therefore lacks actual physical field map. Later The reviewed dual exclusion from charged-triplet determinant also does not follow from SU3 flavor:forB_k=A+k a I3,tracefree part remainsA for everyk;fullSU4 beta part stays traceless for both natural duals.",
      "scopeEN": "Source-reviewed reuse and concrete representation distinction. Different original clocks need not be identical or incompatible from multiplicities alone. Whole native C12 conjugacy and supplied parallel representatives remain solved. FixedM preservation needs actual transitions,connection and domain; free M↦HMH⁻¹ is not automatic fixed-bundle automorphism for unequal D powers. Fourth-slot anomaly compensation is existing conditional index arithmetic,not a physical fourth generation. Bare E8-bracket/Weyl single-anchor class remains settled in its statistics scope. No original common source,state/R/time derived from this representation comparison. The reviewed I_mu4 identification of normal sphere with flavor base and four equal logarithmic poles is new expressly underived geometry. Conditional uniqueness for fixedO1/simple-pole data holds,but is not origin. Fuchs degree and monodromy need same∇d±a convention:res−1/4 for∇d+a gives+i;ODE+a gives−i withdegree−1. Explicit horizontal point map in original iA(iz)=UA(z)U^-1 convention usesU,notU^-1. Anti-linear coefficient symmetry proves neitherOS norunchanged singularL2 normal index. ActualC3/q-cover alternatives retained.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-original-su3-to-su4-family-vector-action",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:0c672faf61777b23af10c925",
        "source:4934dc25ec23359d68149b3f",
        "source:d10ecf5cc3afc75d886c269e",
        "source:d8680d3b81ed43e0bfb3e822",
        "source:f4fc3910ba7909f4630fd82c",
        "source:4d90158c3db8a3738c636cb5",
        "source:178782d3ed0e25abf5795b79"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-genus-two-sign-family-closes-common-parallel-k-connection",
      "titleEN": "Actual genus-two sign family closes common parallel K connection on cover",
      "statementEN": "Already proved v117 splittingπ*F=L0⊕L1⊕L2 onC plus trivial line gives genuine flat SU4 sign bundle. Transitionsdiag(l0,l1,l2,1),product1,commute with existing natural Spin/family lift. For mA=(0,0,−1,−1)this gives global K=(Spin10×SU4)/Z4 cocycle with(16,4) branchW=ΛevenE⊗[L0⊕L1⊕D^-1L2⊕D^-1]. Half-determinant signs cancel in quotient. Whole associated E8 algebra and Lie products are global. Actual combined connection isA_W=ρ(A_E)⊗I+I⊗(Ma+A_L). Diagonal flatA_L commutes withM and nativeR=diag(ω,ω²,ω²,ω). Along with color center,κ,σ0 andκσ0 are thus global parallel automorphisms on all E8 branches. Irreducible lower A4 holonomy becomes abelianV4 upstairs; lower Schur/mF conclusion cannot be applied unchanged onC. Original ternary deck instead cycles three distinct lines. Unchanged parallelM andR marks require equal triplet values/phases. mA andR2+2 fail this fixed-mark condition and each has three-element transported-mark orbit.",
      "scopeEN": "Constructive new combination of two solved source components,not new cover or repeated monodromy proof. Data and alignment remain explicit. Clock is adapted representative of whole native class; unchanged originally marked clock needs actual mark/connection map. No automatic descent of local matrix between unequal D powers. Triplet equality is necessary fixed-mark condition; coarse descent across branches also needs actual linearization/isotropy. Whole D/Phi/domain action,charged CAR products,original state,OS and physical time do not follow from connection identity alone. Full existing operational Seed retains its state/time. Old bare μ12 cover does not automatically contain q lines by existing ramification proof; no identity with original Fermat source.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:377ad460b55785022829446a",
        "source:c1ff3dffc1d1a7f7e0ebc182",
        "source:cd145ed443ec2bad0d2b15a5",
        "source:a4618db4d6dc9c6b502ff110",
        "source:2e6cd258eeb727b1faaf28cc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-q-quarter-extends-common-k-connection-and-real-coefficient-lifts",
      "titleEN": "Actual quarter preserves K bundle;Kummer cover admits separate Real lifts",
      "statementEN": "In actual q frame,m=(0,−1,0,−1),R=diag(ω²,ω,ω²,ω) are preserved by oldAq. Its parallel line maps extend to whole K cocycle,connection and all associated E8 products;four iterations are identity. Adapted nativeκ,σ0,c0 commute withQ. Of six existing toral norm minima,exactly thism anddual(−1,0,−1,0) areQ invariant. Explicit global Kummer lifts Qh_a=r_a/h_(−a−1),Th_a=1/barh_(−a−1),r=(ω,−ω,−ω) obeyQ⁴=T²=1,TQT=Q⁻¹. E0=QT sends h_a→r_a barh_a and squares1. Same line permutation does not fix lift square:D_sT for s=(−1,−1,+1) squaresD_(−,+,−).",
      "scopeEN": "Supplied split carrier/connection and explicit oldF/native-family frame assignment. Not original P1 selection or minimization of original topological cost. EarliermA assignment is not silently replaced. Q is notκ;fundamental spectrum onW is1,1,i,−i. Fixed-mark C3 descent remains distinct from allowed transported-mark orbit. Kummer frames and Real type must be specified;coefficient lift proves neitherOS/Pin/Clifford nor physical time. Existing minimal48 common cover with inverted ROOT C12 deck is reused;that deck is not equated with verticalc0. Correction:explicit Kummer-function lifts differ from calibrated meromorphic-line/flat-coefficient-fiber lifts. Their h_a signs are not additional relativeAq² signs. WholeK quarter uses original calibrated coefficient lift.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b5f1f684b6f918326958b9ac",
        "source:536949c647444a3050ab56a5",
        "source:ba2e3cf072f3c6c8a083e8ba",
        "source:c1ff3dffc1d1a7f7e0ebc182",
        "source:fcbb77ba05b45d7fe89218f5"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:real-source-reflection-is-not-linear-duality-or-compact-clock-inversion",
      "titleEN": "Antilinear Real structure is not linear duality and compact conjugation does not invert clocks",
      "statementEN": "The reviewed LemmaP is refuted within same existing carrier type:E=O(1)⊕O⁴ onCP1 hasE≅σ*barE forσz=barz,since base reversal and conjugation each reversec1. Exterior/determinant functors give involutivej_W for every integerm withoutm4=−1/2. Compatible split/Chevalley conjugation extends over whole complex E8 bundle preserving brackets. Compact conjugationsigma_c instead commutes withAdg for compactg∈K,exchanges both64 branches and compensates conjugate phases. Alreadyκv=−iv gives sigma_cκsigma_c⁻¹v=−iv,not+i v. Thus general normal-reflection prohibition,compact clock-inversion claim and trivial-slot exclusion of commuting variant are false.",
      "scopeEN": "Exact first-type-error review of external candidate;neitherP1 no-go nor selection of physical Real form/reflection. Linear dual formulaWm*=ΛoddE⊗D^(−1−m) remains valid in its own type. E0 and involutive global Kummer lift retained. Fixed0,1,∞ forcesbar t only under assumed passport preservation. No unique whole-field lift orOS positivity. Oval holonomy alone proves no fermionic boundary zero-mode count;already selectedS0 must be retained. Whole operational Seed retains state/time.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:ff880dad3a7a337ba2c109aa",
        "source:5b25a08ae9aed73c0aeebc02",
        "source:536949c647444a3050ab56a5",
        "source:9d81f6ac292497c87f9d872d",
        "source:a4618db4d6dc9c6b502ff110"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-selected-spin-and-q-signs-have-three-explicit-global-kernels",
      "titleEN": "Existing selected spin and actual q lines yield three explicit global kernel sections",
      "statementEN": "Already source-selectedS0=O(Σq−K),actualLa=O(qa−q(a+1)),2qa~K giveTa=S0⊗La≅O(q(a+2)),eachh0=h1=1. Whole oldFq=L0⊕L1⊕L2⊕O has(h0,h1)=(3,3),index0,trivialslot0. f_a=1/(w+ωa) explicitly spansTa in stated divisorframe;common quadratization isψa²=(w+ω(a+2))dw/η. Actualc/Q classes transporta→a−1,a→−a−1. IMPORTANT LIFT CORRECTION:oldAq²=(-,+,-) are fiber eigenvalues atQ-fixedq0,already carried by canonical divisor linearization;not additional relative meromorphic signs. Correctly calibrated tensor hyperelliptic lift therefore acts UNIFORMLY−i on all3kernels;Q_kernel⁴=−I retained. Earlier Kummerε-based meromorphic matrix instead had(i,−i,i) and is not original coefficient lift. Its simultaneous matrix comparison and normline continuation are identities of that different lift only. Closed Dolbeault has3kernel/3cokernel and no ordinary two-sided Szego inverse. Corrected quarter hasv_a=δa ξω^(1−a),δ=(1,−1,1),ξ=e^(−iπ/4),spectrum{ξ,−ξ,−ξ};lineQ maps require no global scalar roots.",
      "scopeEN": "Deduplicated new application of old data,not new general theta mathematics. SOURCE-SPIN-ZERO-SECTIONS sections1–3 retained;its section4 phase/original-lift assignment corrected byThe reviewed-SZEGO-FIRST-REVIEW section5. SOURCE-SPIN-JOINT-CLOCK-TEST compares matrices for wrongly assigned lift,not an original intertwiner. Uniform−i halfturn is fixed by original fiber linearization,not freeσ convention or equality withQΓ. Complex cohomology,not chiralindex3 or generation selection. Kernel-volume/oldNq comparison must use corrected lift,not earlier uncalibrated calculation. Complete Seed retains state/time. Closed curve,originalP1/APS domain,reflection,physicaltime and charged field products need actual source map. Existing normline/theta/native module proof retained;original one-copy insertion not proved here. Kernel volume is now positively compared in corrected lift as generated-group line representation:finding:actual-spin-kernel-determinant-has-inverse-q-norm-character;not original insertion rule.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:83d690d46f254a9b0a57505a",
        "source:47dfe786c27ddb33dc3ad2d0",
        "source:e907433847678b37e901d588",
        "source:c1ff3dffc1d1a7f7e0ebc182",
        "source:ba2e3cf072f3c6c8a083e8ba",
        "source:fcbb77ba05b45d7fe89218f5",
        "source:1a289db99bbcd6b63d8745c4",
        "source:8c8e689e26e0d3c5e9d3b5b5",
        "source:29fd3ea3b47d5ab152a92650"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-s0-szego-point-legs-generate-q-kernels-with-typed-products",
      "titleEN": "Existing S0 Szego kernel generates actual q kernels as marked point legs",
      "statementEN": "Foru=(w³+1)/η and meromorphic spin sectionsΦ=√(u dw),Χ=Φ/u,S(x,y)=[ΦxΧy+ΧxΦy]/[2(wx−wy)] is unique normalizedS0 Szego kernel. Diagonal residue1,noother poles including opposite sheets/infinities. S(qb,qa)=S(pb,pa)=0 fordistinctpoints;mixedq/p≠0. S(.,qa)∝Φ/(w+ωa) hasS0 divisor−qa+q(a+1)+q(a+2);withactualLa factor it spansH0(Ta). Thus3kernels arise explicitly as old marked propagator legs. For{a,b,c}={0,1,2},actual products lie in1dimensionalH0(KLc),zero divisorqc+q(c+1);bareS0 product(w+ωc)dw/η instead has2qc. Elementary modificationS−S(.,p)S(q,.)/S(q,p) has simple pole atq-dipole with rank1 kernel/cokernel residue. Finite Laurent part is notcanonical without transport:gε=exp(εf) changesG0 toG0+[f,P],retaining same residueP andη point split.",
      "scopeEN": "Exact specialization of established hyperellipticSzego method toactual selectedS0/q packet;primaryfulltext D'Hoker/Hidding/Schlotterer JHEP05(2023)073 section2.3/equation2.26 checked. Not new general propagator formula. Valid point-leg/typedV4 product bridge supplies no originalP1/APS operator/domain map or physical field quantization,state/R/time. Twisted zeros differ from baremeromorphicframe. Additional bijective3point saturation has2nonzero assignments butis not original source rule. Canonical reduced inverse fromηalone is refuted;actual familytransport/normalization and Hermitian projections may define specific reduction. Retain corrected spin/fiber lift,notfreeσchoice orautomaticQΓbridge.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:fcbb77ba05b45d7fe89218f5",
        "source:a99148d073d072bbd5088f6a",
        "source:7ea6e89c350f078c5ea41b0a",
        "source:e907433847678b37e901d588",
        "source:c1ff3dffc1d1a7f7e0ebc182"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-spin-kernel-determinant-has-inverse-q-norm-character",
      "titleEN": "Actual fermionic kernel-volume line carries precisely the inverse q-norm action",
      "statementEN": "For actualold coefficient lift calibrated atq0,Q_kernel²=−iI3,δ=(1,−1,1),ξ=e^(−iπ/4). Q actsbyξ³ onΔ=det⊕aH0(Ta),by−ξ³ onunordered tensorZ. Independent norm test:αq0=iξ,product of exchangedq1/q2 spinmaps=βq1=+i,soQ_Nq=−ξ,Q_Nq^-1=ξ³,Q_Bq^-1=−ξ³. Orderthreec cycle acts1 onall compared lines;three nontrivial actualdeckV4 characters multiply1;spincenter−I acts−1. HenceΔ≅Nq(S0)^−1 andZ≅Bq(S0)^−1 as full line representations of group generated by these c/Q/deckV4/spincenter lifts,upnonzero scalar. Fermionic permutation sign distinguishes matching determinant line fromunordered tensor.",
      "scopeEN": "Independently twice-checked actual line-representation bridge onall generators,not beta-phase match alone. EarlierεKummer-to-flat-fiber transfer andcommonU comparison corrected;cover identities retained. Character equality gives equivariant isomorphism upscalar,not functorially canonical total residue map orphysical norm. Individual legs arelinear,butclaimed individualQ/deck equivariance doesnotfollow. NoJac[2] tensor-translation/N64 equivalence;these changeh0 and differfromdeckV4. No originalP1/APS source map,selectionH0ratherthanH1,single insertion orBerezin dual choice. Whole detRΓ also containsH1 and loses uniform scalarweight sinceχ0. OldNq/theta/native module proof reused;newactual kernel-volume supplies matching linear factor,itsphysical use remains specific origintest.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8c8e689e26e0d3c5e9d3b5b5",
        "source:29fd3ea3b47d5ab152a92650",
        "source:9ae0bbde81665d64252bf3ec",
        "source:e907433847678b37e901d588",
        "source:ba2e3cf072f3c6c8a083e8ba",
        "source:32205af6df86a95044851e5f",
        "source:7ac63ae4aa67a1f471894281",
        "source:a0033640d135c41489de134a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:closed-source-flavor-spin-has-functorial-pfaffline-with-charged-type-limit",
      "titleEN": "Closed spin/flavor source has a functorial Pfaffian line with charged type limits",
      "statementEN": "For supplied V=S0⊗Fq,the orthogonal coefficient form and S0²=K give a symmetric K-valued pairing. Integration by parts makes the closed Dolbeault operator bilinearly skew;its Pfaffian superline exists functorially. With Δ=detH0 and Serre duality,the fixed conventions are λ_coh=Δ²,Det_F=Δ^-2,Pf_F=Δ^-1. Pf_F has reviewed Nq line character and odd parity. This does not identify actual charged W=(16,4):its vertical κ phase−i forbids invariant scalar W⊗W→K. Existing full selfdual W⊕W* source has Pf=±det of its charged block.",
      "scopeEN": "Closed curve with specified orthogonal spin source;no transfer to original P1/F5 operator,APS domain or physical action. No freely choosing a dual to fit target phase. Character comparison only for reviewed c/Q/deckV4/spin-center,not full Jac[2] zero-mode functor. Odd line exists;unsaturated section vanishes at this singular operator. Three geometric Real forms or complex normal index1 do not determine physical Majorana count or parity cancellation. One complex CAR mode has two Majorana directions yet odd relative vacuum parity;odd transition amplitude is not a positive state. Reuse old primitive seam defect and solved same-spin unit quotient. No general origin no-go or physical completion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:56675ee423e0f63d2ae21bc9",
        "source:932193dc1d7b6db6d45dc350",
        "source:294903a96d4c8ec322f7fb3d",
        "source:7ac63ae4aa67a1f471894281"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-relative-seam-has-explicit-whole-graph-fredholm-mismatch",
      "titleEN": "Original relative seam has an explicit Fredholm mismatch on whole given two-face graph",
      "statementEN": "On existing full normalized Cauchy graph V=(sqrtA,sqrt(1−A))^t,A=(1+R²)^-1,R=e^-ell h,the relative boundary mismatch F_U=[−U,I]V=sqrt(1−A)−U sqrtA is bounded. In existing scalar quarter block it normalizes T=R−U on DomR. T is closed Fredholm,index−1,kernel0,with exactly one Gaussian cokernel y_n∝exp(−ell[n(n−1)/2+αn]). Proof uses trace-class perturbation of P_-−U P_+,no truncation or new Hardy projection. Full two-face compression G(U⊕U)G is instead invertible bilateral weighted shift,index0,weights≥sech(ell/2). One-face compression G(I⊕U)G has index+1 in same orientation and leaves G11 unchanged. Circle time covariantly transports matching into U_t=e^it U family.",
      "scopeEN": "Concrete original type of relative boundary operation on given whole collar;explicit index/Gaussian cokernel concern its actual scalar block. No selecting this block instead of whole charged source or physical three-copy count. Whole h=Aγ_F−iγ_FΦ with both principal-symbol directions and C0 completion remains to test. Original fullv21 has four boundary pieces;Γ± are not automatically two F5 faces. No closed operator intertwiner to branched S0 Hardy domain or q evaluation fibers. Index/Fredholm class are not exact operator identity. Time covariance is moving-seam family,not fixed-clutch physical time or new time choice. Old same-spin once norm remains solved;classical matching does not select new state.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:given-relative-unit-seam-on-specified-collar-faces"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3b0d3c2fd07005685c1431b4",
        "source:c28689a70a92eb66f26a9173",
        "source:b2b5718679e4631efad0d832",
        "source:cf1956e1880c77301ab425df",
        "source:294903a96d4c8ec322f7fb3d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-constant-coupled-clutch-defects-are-exact-internal-kernels",
      "titleEN": "Whole constant seam defect follows exactly from actual internal kernel",
      "statementEN": "On unchanged scalar unit-clutch domain,LΦ=∂r+Aγ_F−iγ_FΦ is closed Fredholm. Whole energy identity ||LΦψ||²=||L0ψ||²+||Φψ||² also holds for adjoint. Extra boundary term vanishes by U*VU=V;nonzero massless A/U boundary term remains in ||L0ψ||². Kernel/cokernel of existing whole boundary mismatch are precisely kerΦ∩Fminus and kerΦ∩Fplus. Whole index−Trγ_F=0 for48+48. Previously exactly checked v252 controls immediately give(0,0),(2,2),(1,1),without rerun. Constant original δΦ acts between surviving Gaussian defects as−i Pker,+ δΦ Pker,−. Reuse primitive NS clutch u_cov from solved quarter dictionary.",
      "scopeEN": "Entire supplied constant coefficient class with explicitly retained closed scalar clutch domain. No arbitrary single channel or physical three-copy choice. Invertible Φ removes both defects;index0 alone does not trivialize every determinant action. Controls are not derived Yukawa values. Variable Φ retains−i[A,Φ],normal-dependent V another derivative,and noncommuting U a boundary form. No exclusion of all P1 sources or variable interactions. Original face assignment,branched spin-domain map,physical source selection and time remain actual maps. Scalar unit defect and old same-spin once norm retain valid scope.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:whole-constant-odd-coefficient-on-scalar-unit-clutch-domain",
        "premise:actual-product-collar-two-face-data",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:actual-full-v252-unimodular-p2-gauge-lift"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d37fa9d00a5182547e55945b",
        "source:3d01c23a9174710808bad869",
        "source:4aeac9c461cf7d32a75b7b1f",
        "source:02a45b61c44bd61d15ef2453",
        "source:054e763500be2aab6476a2e4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:old-complex-scalar-clutch-separates-c0-and-product-reflection",
      "titleEN": "Old scalar clutch separates bulk C0,boundary adjoint and product reflection",
      "statementEN": "Actual C0=i_old N is old-complex-linear and commutes with U=e^{i_oldθ}I. New antilinearity for Ical does not allow C0UC0=U*. Whole T chart clutch is diag(U,barU). Oriented T_faces conditions are v1=Uv0,w1=−Uw0. Bulk C0 preserves this closed kinetic domain;C_faces maps unitary clutch subspace to orthogonal complement. Actual theta-fixed product reflection instead transports whole domain to U^-1. SF+1 alone does not assign four original boundary pieces to F5 faces. Reuse old NS/quarter dictionary;The reviewed mixed1/4,3/4 mass toy does not replace actual same-Aα source.",
      "scopeEN": "Actual old product collar with specified complex structures and theta-fixed R_geo. No general reflection no-go;additional original base pullbacks/fiber lifts can give different common operation and must be transported explicitly. Existing open-source reflection positivity,whole Cauchy graph and source state/time remain intact. Bulk adjoint,boundary CAR and geometric reflection are not interchangeable names. Correction rejects The reviewed first C0/U inference,not every physical P1 Real structure.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:given-relative-unit-seam-on-specified-collar-faces",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:57f0173e4bda3879c77bf56d",
        "source:7f31071f51f9e5b0debab6f2",
        "source:d524584442118cdae34ed370",
        "source:4aeac9c461cf7d32a75b7b1f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:scalar-defect-circle-character-does-not-select-projector-holonomy",
      "titleEN": "Quarter circle character does not select Gaussian defect connection",
      "statementEN": "Existing scalar defect family Tφ=R−e^{iφ}U has periodic frame eφ,n=e^{iφn}y_n/||y||. Given circle action satisfies e^{itB}y(φ)=e^{itα}y(φ+t). Natural orthogonal-projector connection instead has〈eφ,∂φeφ〉=iμ and holonomy e^{-2πiμ},μ=〈n〉. Old allowed diagnostic control α=1/4,ell=4log2 gives μ=0.1855335532291087 and holonomy0.3940689714−0.9190808701i,not quarter phase. Exact rational partial sums and geometric tail bounds certify difference. Separately specified flat orbit transport still has circle phase+i;family equation does not select it as projector connection.",
      "scopeEN": "Given free scalar Gaussian defect line,fixed positive ell and constant α. Width4log2 is diagnostic,not physical scale. Projector connection is not asserted compulsory physical choice;no new time or exclusion of other originally specified connections. Original circle character remains correct. Whole coupled h time gives U_t=e^{ith}Ue^{-ith},not generally scalar2π closed clutch family. No native clock intertwiner or missing time in full operational Seed inferred.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-relative-unit-seam-on-specified-collar-faces",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:dc598645ab74df039c80b618",
        "source:7f31071f51f9e5b0debab6f2",
        "source:3b0d3c2fd07005685c1431b4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-spin-is-canonical-ramified-base-spin-pullback",
      "titleEN": "Existing source spin is the canonical ramified sphere-spin pullback",
      "statementEN": "For actual original triple map π:C→P1_z,w³=(z²−1)/(z²+1),all four ramification indices are3. With Rhalf=Rπ/2 and K=Iplus+Iminus,Rhalf∼2K and2Dq∼3K. Canonical ramified pullback of unique sphere spin is S_can=π*O(-1)⊗O(Rhalf)≃O(Dq−K)=S0. Explicit square-compatible map is e_can=√3·w/(w³+1)·Φ0 for Φ0²=μ0=(w³+1)dw/η,with e_can²=π*(dz/z²) and √dz=√3·w/η·Φ0. Actual old lifts satisfy c e_can=e_can,Q e_can=ξ e_can,Q√dz=barξ√dz. Contravariant E0=Qτ0 anti-pullback has J_E√dz=ξ√dz,J_E²=1. S0 is not an additional spin choice on this source.",
      "scopeEN": "Exact spin-line origin and square/lift map on already reconstructed original π source. Common spin sign is ordinary frame sign,not new relative quarter fit. Meromorphic coefficients at poles are not nonvanishing fiber values. No identification of physical BΣ with freely selected pullback operator:actual metric,connection,weighted Sobolev/trace domain at four ramification vertices,whole coefficient system and Γ± face assignment must transport. Spin Real map is not CAR C0 or OS reflection. Triple coefficient pullback is not physical generation count. Preserve old once norm and Kummer/fiber-lift corrections.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:19314c92ba69ef1b40ce6440",
        "source:40e85fb76be3078e8b1a9a34",
        "source:ff111708d69c02bc8034883a",
        "source:46fa09d681f7c9fdd66b09f4",
        "source:323f23e73e4582ded26a0758"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-v117-has-explicit-algebraic-q-cover-fundamental-frame",
      "titleEN": "Original v117 equation has a full explicit algebraic fundamental frame",
      "statementEN": "For unchanged plus-sign equation Ψ'=A(z)Ψ with original A0 and U=diag(1,i,−i),an algebraic3×3 G is constructed on actual negative q Kummer cover. A column is g=(h0 p1/(ab),h0 z p2/b,h0 z p3),a=2√2/3,b=√5/3,with explicit rational p1,p2,p3 overw inQ(ω). Its two c images give detG=−27√2(2ω+1)(z4−1)/10. Ψ=G Gbase^-1 has Ψ(0)=I,detΨ=1−z4. All three original equations independently checked by exact direct substitution. V4 acts on right bydiag(ε0,ε2,ε1),c by3cycle. Actual calibrated Kummer Qh=(ω/h2,−ω/h1,−ω/h0) gives entrywise checked G(Qy)=UG(y)KQ,KQ=[[0,1,0],[-1,0,0],[0,0,1]],hence Ψ(Qy)=UΨ(y)U^-1. This is an explicit differential gauge,not only monodromy or point counting. Positive flat coefficient metric is G^-daggerG^-1. Independent metric calculation gives Gbase Gbase†=diag(27/10,9√3/5,3√3). Canonical spin yields explicit weighted trace Wψ=3^-1/2√π' G^-1ψ∘π. With given inner NS continuation,B_H=−i(∂θ−izA)=G(−i∂θ)G^-1 onD_H=G H1_NS inL2_H is closed selfadjoint;no new extension between four marks.",
      "scopeEN": "Full algebraic frame for given v117 connection on original Yq;actual spin-line origin separately derived. RR justifies finite two-coefficient search,no numerical fit. Initial negative was corrected solver restriction:constants belong toQ(ω),d=ωc;not old-source counterevidence. Meromorphic functions are not flat fiber values. Makes old group-averaged positive coefficient metric explicit,not a CAR state. Three columns are coefficient directions,not physical generation derivation. Does not derive A0 itself from P1 or full96 field/Phi/Γ± domains/state/reflection/physical time. No exhaustive historical novelty claim. Original ledger/proof statuses unchanged. Trace/domain result explicitly uses analytic original inner z disk and its existing NS continuation. This is an input condition,not new physical BΣ selection. Image is C3-equivariant pullback subspace,not arbitrary rank9 space.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:73ae95c7c1370f70953bf30d",
        "source:87f40fcf1ce8856e860384fa",
        "source:65a9d30cd8f808ea6141ef6f",
        "source:794dd09c1365e659935d6cf6",
        "source:486f478e5743ef095e041b66",
        "source:a8805cab869e0f70bee9bed9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:double-circle-reflection-does-not-fix-entire-cubic-cable-seam",
      "titleEN": "Circle-fixing base reflection does not fix entire cubic cable seam pointwise",
      "statementEN": "Actual lift τ_C(w,η)=(−barw,barη) of z→1/barz is antiinvolution,sendingq_a→p_-a,but does not fix wholeπ^-1(|z|=1). Exact regular fiber:z=e^(iπ/4),η=√2,w=(√3+i)/2,(−√3+i)/2,−i. First two are exchanged,only third fixed. Each other global cubic deck liftc^kτ_C likewise fixes only one of three. Literal identification Fixτ_C=entire cable seam fails away from every vertex. Valid half-form relationJτ√dz=±iz^-1√dz determines spin transition in specified reflected inner/outer frame,not original physical Γ± normal-frame identification. Complete marked-circle class:16Mobius/antiMobius sphere mapsi^kz,i^k/z,i^kbarz,i^k/barz give8D4circle actions. Amongq-compatibleanti-cuts,σ1=ibarz ANDσ3=−ibarz avoidmarks and areQ-conjugate. Data giveone mark-freeorbit,not absolute representative. Spinξanti-frame phase is not a newlinearΓ±clutch proof.",
      "scopeEN": "Only literal pointwise fixed-locus identification on actual C and specified circle map excluded. Sheet-permuting reflection,different original cut or reflected-source transport remain possible. Retain valid q/p point map,spin formula and previous open-source reflection. No global P1 impossibility or ban of geometric doubles. Choosingπ*|dz|² is not forced by canonical spin-line identity. the reviewed source global G calibration question now solved by explicit G,not another gap. Orbit fact doesnot introduce artificialnew physicalchoice:iforiginalQuarterisSeedmorphism,thetwo representativescanbeequivalent. Must checkactualsidemarks. For explicitpointmapσk fiberisU^k;oppositeU^-kframeidentity remainsvalidunderpropercontravariantconvention.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:dd1dd57a26132527df2ca0cf",
        "source:ea8b831af329d0d210018d29",
        "source:603a77b74bf9a1ac1f6b85aa"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-fuchs-real-map-transports-whole-given-finite-source-state-and-time",
      "titleEN": "Actual Fuchs Real map transports whole supplied field source,state and time",
      "statementEN": "Original realA equation gives fullE0 field map J_E^rowψ=U_Fbarψ(ibarz). In actual constructedG frame,D_E=Gbase^-1U_FbarGbase=ω²S,S=diag(1,−1,1),unitary,D_EbarD_E=I;independent exact matrix substitution verified. Canonical spinξ cancels against half-form boundary factor in NS coefficients. Under declared v252 generation alignment KE=DcalκP_E has D_E on particles,barD_E on antiparticles,commutesγ_F,J_F andsquares1. Exact coupling images:Y_f^E=SbarY_fS,MR^E=ωSbarMR S,with requiredMajorana transpose. ExistingIcal makes𝒥=IcalKE NEW-complex-antilinear involution transportingC0,C_faces andallfourT_faces slots. Exact𝒥GΦ𝒥^-1=GΦE includesbothcrossblocks;givenprojectorCARstate andallwordstransportwithnonewstate. Givenunitarytime has parameterreversal j_Ee^(ithΦ)j_E^-1=e^(-ithΦE). Realconstructorcontrols return tosameΦviaW_E=VωL_S=Dcal^-1;actualtridiagonalMRrequiresbothfactors.",
      "scopeEN": "Exact whole operator/state/time FAMILY covariance of givenF5/96 source under explicitq/generation alignment. D_E alone is not generic sameΦ symmetry;complexY/MR are reflected. Numerical countercontrol is diagnostic;block identity is proof. W_E is algebra-preserving commutant unitary basis equivalence,not innerSMgauge;nativeK/clock/reference admissibility not proved. A sharedG frame change transformsΦ andJ jointly,different from additionalW_E source action. No universalMajorana/OS obstruction fromω. Circle parameter is not derived physicalOS time. No physicalE0cut or antiξ-to-linear seam deduction. Source001/002 already supply boundary operator,Seedstate/time;old local-source embedding on cyclic image suffices,no unnecessary global presentation equivalence. No universal rank6q+p requirement for all doubles. FullP1generation andT1–T8 remain unclosed. Update: abstractparallelK/E8coverextensionisnowproved. Itsactualchiral96restrictiondiffersfromthisearlierparticlewisehypothesis. Adaptednativeclocksfixed,flavorQtransportedandnotuniversalSeedrequirement.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-q-column-to-v252-generation-slot-comparison",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:actual-product-collar-two-face-data",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1fe2790a789a7b672f75021b",
        "source:4e7e61bc077fadf0e545ce38",
        "source:cee9058a283b5b1d70c60332",
        "source:5981c9f06e52090de6c46ce3",
        "source:fab79d87c34193ae37fe0ddd",
        "source:4aeac9c461cf7d32a75b7b1f",
        "source:41778305ae4a0d4fc6f84f70",
        "source:a9e0479abeec3c6a6739d295"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-e0-compensator-extends-whole-k-e8-with-transported-quarter",
      "titleEN": "Actual E0 compensator extends to whole K/E8 bundle with precise quarter transport",
      "statementEN": "Actual G order(L0,L2,L1) givesW=omega diag(1,-1,1),extendedbyFq=diag(omega,omega,-omega,-1)inSU4. This sameglobalparallelKautomorphism onC preserves allE8branches,Lieproducts andadaptednativekappa,sigma,c. ItconjugatesKQtoinverse whilefullbase remainsQ;nonzero[S,Pc] preventsparallelzdescent. Candidateiota_mq(-I5)hasdifferentGsign. FullE0 obeysinverseQrelation;leftcompensationleavesverticalDQ. Seedopdoesnotseparatelyfixv117Q. Simultaneouswholetransportdiffersfromleftcomposition;localQimagecanforgetDQonlyifAdDQtrivial,andwholeevenfamilyCARdetectit.",
      "scopeEN": "Existing declared jointK/family comparison onC. Positivebundlelift is not automatic microscopic96/E8 orinnerA_Fgaugeidentity. Qisnotkappa orphysicaltime. No universal fixedQSeedcondition/P1veto. Actual localalgebra,seam,collar,reference,state/time stillrequirecommonidentification;givenSeeddataretained.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:db0e4e44a15b21467370ed0f",
        "source:0807ba6743943ee8abc124ed",
        "source:dfa4652da39c79e996eab6ee",
        "source:4401477573eac1abe7b98beb",
        "source:b5f1f684b6f918326958b9ac",
        "source:6ebfcec3dce985bf660507cf"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-v252-entire-real-basis-has-signed-p2-dual-dictionary",
      "titleEN": "Whole v252 real basis has signed P2 and dual dictionary",
      "statementEN": "ReusepositiveSM/P2wedgeintertwiner;completeoppositegradebyWminus(JFv)=CcompWplus(v),Ccomp=P_Nstar. Whole realsigned96unitary intertwinesgrading,JFcompactconjugation andseparate splitcoefficientconjugation. FiveCartanandfortyD5rootexactsignchecks pass. FullSM/charges andinducedCARstarisomorphism retained. Globaldual retains determinantpowersD^(-1-m). Independentsmall96replaypassed.",
      "scopeEN": "Wholeactualfiber/globalSMcomparison;notglobaltrivialization. ExtraSpin10/Kactionistransportedcomparison,notimplementedphysicalE8source. Fourthfamily/otherKbranchesneededforE8brackets. CARmapisnotE8_1currentalgebraorP1selection. ReuseoldpositiveP2/level4results.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:oriented-p2-exterior-carrier",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:822041ef062c54771297462c",
        "source:fd313f493cdd0a0bbbdbd523",
        "source:fab79d87c34193ae37fe0ddd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:chiral-fuchs-source-transport-has-distinct-majorana-phase-and-torus-absorption",
      "titleEN": "Chiral Fuchs transport carries whole source with corrected Majorana phase",
      "statementEN": "AlternativechiralP2actionDEongammaplus,barDEonminusgivesexactYprime=omegaSbarYS,MRprime=omega²SbarMRS. SharedomegaMajoranaformula isfalse. FullKO/F5/faces/graph/timefamilycovarianceholds. ActualSpin10torusplusA3shiftactsYbyomega²,MRbyomega,soafterScompensationtargetisPhi(barY,barMR). Spin10partalonegivesminusoneboth. Correctedq4diagisglobalKbutchangesmarkedquarter.",
      "scopeEN": "Separatealternative,notreplacementofearlierparticlewisehypothesis. Givenwholeconstructor/state transported. Notgeneric samePhi,CP/OSobstructionorphysicaltimeidentity. OriginalhardholonomyisHomtyped;bilinearselfdualitylegmustbeaccountedforinphysicalcomparison.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-q-column-to-v252-chiral-slot-comparison",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-product-collar-two-face-data",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:babba8b530e6d8f28b962696",
        "source:a31a44702117b70a467b57c5",
        "source:822041ef062c54771297462c",
        "source:fd313f493cdd0a0bbbdbd523",
        "source:4401477573eac1abe7b98beb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-theta-composition-retains-conjugate-source-and-parity-square",
      "titleEN": "Native Theta composition retains conjugate target and parity square",
      "statementEN": "NativeRgeo preserveseachfixedsourcegraph. ComposingwithchiralE0givesNEWcomplexlinearBogoliubovmapstilltargetingPhiK,orbarPhi aftertoruscompensation. NativeTheta doesnotconjugateexternalcouplingsagain. Composition squaresminusoneoneparticle,fermionparityonCAR,identityonlyonevenobservables. Linearcircletransporthastargettime-t;nativeHSantiunitaryalonepreservessameparameter. Fullactualmatrixcontrolrejectsgeneric samePhi.",
      "scopeEN": "Wholegivenfamilyincludingcrossblocks;notCPTidentity,universalCP/OSimpossibilityororiginalphysicaltimeselection. ExistingHS/RPsourcepreserved.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:declared-q-column-to-v252-chiral-slot-comparison",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-product-collar-two-face-data",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:18e34778bac5365f27d70b33",
        "source:babba8b530e6d8f28b962696"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:single-graph-range-isometry-does-not-give-local-whole-seed-map",
      "titleEN": "Single graph-range isometry does not yield local whole Seed map",
      "statementEN": "PrintedV-onlyCARmapfailsCintertwining;chargedreadingpullsGbacktoI. WholepolarizationrepairVplusCViscorrectandretainssuppliedgraphstate. Nonconstantspectralmultiplierdoesnotpreservecirclesupports. F3tensor96duplicatesgenerationcount. WeightedflatframewithparallelvolumeislegitimateSU3reduction,notfixedrowfiberautomorphism;nonzeroradialtermrequiresactualcovariantnormaltransport.",
      "scopeEN": "ScopedtoC30printedselfdual/local/stateclaim. NotuniversalvetoofCauchynetsorKframechanges. ReuseexistingwholeTfaces/HS/state/reflection/time. GivenSeedneedsnonewstate;compareitsactualnet/operators.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:actual-car-graph-and-oriented-boundary-pairing",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:593f16b31d83e2b44d20be79",
        "source:ad00e5a997d5c63502cd46ea",
        "source:79678282a36be79b5989a47c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:hard-holonomy-selfduality-leg-and-finite-character-phase-separation",
      "titleEN": "Hard holonomy needs typed self-duality leg and separate complex phase readout",
      "statementEN": "All-pathv117E0covarianceholds. OriginalHomYruleandchiralbilinearruleneedtypedselfdualityleg;actualA4hasB=cIwithcω=barc,makingHB^-1transformbilinearly. Existenceisnotoriginalselection. Pureclosedtriangletraceofbarev117hasrealS4/A4charactersandonly0/piargument;directv117identity,purePiandnonrealCKMphasecannotallhold. ActiveRedteamplacesleadingpi/3inZ6phasefiber,selectednotderived. Broaderphysicalconnectionorexplicitadditionalobservablefactorallowed;oldratios/absoluteanchorretained.",
      "scopeEN": "Exacttype/charactertest,notphysicalCPderivationorTFPTrefutation. Asymptoticissketchcontract,notactualboundednumericalprediction. Norepeatedmoduli/GAclassscan. ExistingSeedstate/timepreserved. FrozenPhi negativesdo notexcludegeometricallytransportedsource;physicalconnectionidentitynotassumed.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d749fc311d98824c7dd4ffaa",
        "source:e4c1c0b36af1f3db80fced99",
        "source:bf41e9760c393aebbe15f638",
        "source:79678282a36be79b5989a47c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-z6-positive-structural-kernel-does-not-supply-oriented-phase-observable",
      "titleEN": "Original positive hexagon kernel supplies no oriented phase readout",
      "statementEN": "Actual originalchain usesU6,Dy=yI-deltaU6 andfixedcompressionpositiveKstr. ExactDdaggerDdependsonU6+U6daggerandisorientationeven. UnsquaredresolventhasorientedFourierpowersbutdisplayed36sitematrixelementsarerealpolynomials. UnspecifiedVadmdoesnotderiveorientedresponse. v561suppliesrho;4rho/P2/V5arescalardiagnostics,notE8adjointtrace/sourceoperator. Actualv252/F5callhasnoC6representationororientedinsertion. Existingcommon-rayphaseblindnessanddistinctrelative-sourcequadraturesretained. Clarification30Oct: original A=D_fPstr,H=A†A,Kstr=H^-1/2 is fixed Gram normalization. PolarV=AK is isometric, but originalY uses HolK, not HolV. K as coupling coefficient need not be a CAR field isometry. BareU6=1 norm countertest excludes only that misidentification. K has an exact cubic cosine expression and fixedPstr variation δY=(δHol)K+HolδK with resolvent derivative; actualδD/δHol and endpoint variations must come from source.",
      "scopeEN": "Scopedexplicitbarekernel/fixedPstr/positiveconsumer,nouniversalphaseveto. GivenSeedstate/timealreadyexist;typedinsertionsaremissingbeforeevaluation. Originalcoherentopenlegorbroaderconnectionallowed. AlgebraicrhocharacterisnotmeasuredCPphase. Actual G-metric P/Q-to-U6 path is now positively closed; no further free metric choice. Fullspine/Pstr/original insertion remain distinct.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:fd2f9f1441ac3f49b7041e92",
        "source:dd74e9b5e858e32824313946",
        "source:25e8abd4c9dc6ea0fbaedc22"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-genus-two-hexagonal-rotation-has-concrete-rho-hodge-line",
      "titleEN": "Original hexagonal curve rotation has concrete rho Hodge line",
      "statementEN": "Actualcurveeta²=1-w6hasR=sc²:w→rho w,positiveinverseofoldT=sc,coversz→1/zandexchangesq/p. ReuseoldjointKummermaps. CanonicalspinliftswapsPhi/Chiwithlambda²=rho,order12;pairedpointnormeigenvalues±i. EllipticquotientX=w^-2,Y=eta/w³satisfiesY²=X³-1,andRacts(omega²X,-Y),soR*(dX/Y)=rho dX/Y,pullback-2dw/eta. ThisisactualgeometricrhoHodgelineinthesamesource. Otherlinehasomega,wholeHodgedeterminantminusone. Independentexactrootcheckpassed.",
      "scopeEN": "Constructive realizationofalreadyoriginalhexagonalphaseinexistingcurve;reuseoldclock/cover/spin/norm,limiteddedupenotnoveltyproof. NotfreelyinsertedrhoscalarorautomaticOS/Pinreflection. ActualHodge-to-field/readoutcontractionstillneeded;line-valuedtraceisnotscalarbeforeclosing,andpairedduallegsdo notcreate netcharacter. Spin/norm/fullHodgedeterminantcannotbereplacedbyoneeigenline. NophysicalCP/fullsolutionclaim.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3005823c72de86e6677febf9",
        "source:0459f69285abfa2dda80e25e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-mixed-spin-products-realize-positive-u6-cycle",
      "titleEN": "Original mixed spin products realize the positive U6 cycle",
      "statementEN": "Actual odd spin lines have nonzero global multiplication isomorphisms into the one-dimensional mixed twisted-canonical sectors. Six off-diagonal sectors form a single orbit under actual R=sc²; spin signs cancel after six steps. On the existing sixteenfold Kummer cover, intrinsic Hodge positivity and deck-character orthogonality make the orbit realization unitarily equal to the oriented v231 U6. Its rho projector has rank one although the full trace vanishes. Existing triality/sheet factors U6^4,U6^3 select rho and rho^4 joint character lines.",
      "scopeEN": "Constructive geometric origin of the supplied six-cycle matrix, without selecting a physical character, CP reader, field source, state or time. Keep twist lines and the harmless common orbit phase. The original physical charge assignment of triality and sheet characters still needs its actual operator map. Originals already declare rho/rho^4 as CP readouts. v233 inserts exponents 1/4 rather than evaluating the actual map J from U6^3,U6^4 to color-Casimir sector parity and family center. Geometric q/p names and the old carrier seam tau do not identify quark/lepton sectors. Clarification 30 October: the phase-free orbit basis absorbs partner phases. Raw s pullback is minus transpose, so raw antisymmetry is on the positive U6-cube sheet. Independent full q/p signs plus R have no rank-three projector; see the new complete deck test.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a54c4ddc700d575135bfa060",
        "source:4cc4ac53f7eb68930fa0e966",
        "source:615c519b9ef101b47738dde5",
        "source:2b9e0972cf124c2aaa9cb54b",
        "source:4ea0c1504d44790df081e084",
        "source:7716bbe329e1515f2ff8daaa",
        "source:1b4108bb6a644dae8b587362"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-spin-quadratics-reach-original-hexagonal-hodge-line",
      "titleEN": "Existing spin quadratics reach the original hexagonal Hodge line",
      "statementEN": "The given elliptic quotient supplies Phex=(I+j*)/2. Existing spin quadratics explicitly reach dw/eta, including the projected odd-spin square. The geometric endomorphism Phex R* Phex has scalar trace rho without choosing an evaluation vector. Full Hodge determinant has character minus one and Q exchanges the two Hodge lines.",
      "scopeEN": "This proves a geometric contraction, not its physical insertion into the original generating functional. Retain the explicitly open seam determinant unification contract. It excludes no unrelated Pfaffian line and derives no physical CP or time.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ad706e45e8af77c2559ad14f",
        "source:d9469055fb16e84a297234ff",
        "source:4ea0c1504d44790df081e084"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:spin-pair-car-transport-retains-parity-and-whole-source-types",
      "titleEN": "Spin pair transport retains fermion parity and whole source types",
      "statementEN": "A stipulated unitary spin action defines a full CAR star automorphism whose sixth power is parity. Ordered fermionic pairs carry minus U6 and the alternating diagonal map intertwines it with geometric plus U6. Diagonal orbit-line comparison is unique up to scalar; unrestricted intertwiners include the six-dimensional commutant. Star completion pairs rho with its conjugate. Fixed graph-state preservation is equivalent to preservation of h; explicit source-family covariance remains allowed.",
      "scopeEN": "No new six-mode state is selected. Hodge positivity is not physical covariance or Hamiltonian. Existing q-to-generation comparison supplies no original p map into F5/96; antiparticles, adjoints, holes and second faces are distinct types. Require the actual source map without imposing a universal extra fixed Q symmetry or this optional comparison. A direct iota6 embedding into one fixed source is only a particular comparison. A global q-to-p pullback may instead map whole source objects without that doubling.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-product-collar-two-face-data",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:55f3c668b367c228a8b46a80",
        "source:8538c2841344e6d3490c64b9",
        "source:4ea0c1504d44790df081e084"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:real-total-trace-does-not-exclude-coherent-phase-reader",
      "titleEN": "A real full trace does not exclude coherent phase readers",
      "statementEN": "The reviewed universal inference from real full traces fails: the actual mixed six-cycle has a complex rho partial trace. An independent exact matrix counterexample has Im tr[Hu,Hd]^3=-360sqrt(3). Relative coherent phases can affect invariants while an overall phase remains invisible. Bare open Fuchs frame products still telescope on a cut and finite closed A4/S4 characters remain real.",
      "scopeEN": "The matrix example is a diagnostic counterexample, not a TFPT Yukawa prediction. An actual open source reader still requires original endpoint legs, path classes and field map. Retain the narrower overall-phase and bare closed-character exclusions.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:61033bd05a784ba689161591",
        "source:efb9561007eabd9027c22b9b",
        "source:4cc4ac53f7eb68930fa0e966",
        "source:4ea0c1504d44790df081e084"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:geometric-six-spin-clock-differs-from-marked-native-clock",
      "titleEN": "Geometric six-spin clock differs from the marked native clocks",
      "statementEN": "Actual spin r has characteristic polynomial t6+1, sixth power minus one and geometric C4/C3 factors. Their q/p and family actions differ from marked native kappa and sigma, already at one fixed D5 weight. A linear side exchange in the specified matched carrier needs a D5 chiral flip and inverts central kappa, so it lies outside that fixed K. Coefficient Real and compact JF also have distinct clock relations.",
      "scopeEN": "This is a marked comparison test, not a no-go for outer/Pin or antiunitary transports. The optional q-slot alignment stays a declared premise. Retain determinant twists and actual base/charge transport. Equal clock orders alone do not provide the whole source-family map.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:oriented-p2-exterior-carrier",
        "premise:declared-q-column-to-v252-chiral-slot-comparison"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:454f555918f2888d207e5193",
        "source:4ea0c1504d44790df081e084"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-q-to-p-pullback-transports-given-source-state-and-time",
      "titleEN": "Whole q-to-p pullback transports supplied source state and time",
      "statementEN": "The alternative to a six-mode embedding is positive for the whole supplied source. Actual linear Kswap reverses gamma and conjugates the complete symmetric-Majorana coefficient. T=Kswap Rx transports h(Aq,Phiq) to h(Ap,-barPhiq composed with inversion). Full F5 lift (iN) tensor T preserves total grading, complex structure and C0, intertwines E and carries all face entries, cross graph correlations, state and same-parameter time. Quarter connection/domain holonomy invert; variable spin frames retain derivative and endpoint terms. Two independent actual96 replays confirm the algebra.",
      "scopeEN": "Exact covariance to its calculated image; original naturality already fixes all image p data and no independent Phi_p rule is required. This does not derive the full given Seed from fewer primitive data. Kswap transports pi rather than fixing its old copy. Match the geometric spin pullback to actual global normal/collar domains, local algebra and reflection; annulus inversion also exchanges faces/normals. Existing state/time are carried, with no mandatory iota6 embedding or no-go for appropriate outer/opposite transports.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-product-collar-two-face-data",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e9557e84eb473c28f946ced3",
        "source:2fb1fb7715c9317e8e7d40f8",
        "source:1f47cf2bb9cc1c373c4f5400",
        "source:96ea648aea15dceaf4b32320",
        "source:9c48c1f99614265da6c4ee61"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-fixpoint-evaluation-keeps-coefficient-signs-and-source-type",
      "titleEN": "Actual fixed-point evaluation retains coefficient signs and source type",
      "statementEN": "At the two actual fixed points, all mixed products evaluate nontrivially into distinct twisted fibers and Rfiber=rho P. P-fixed is not a full flavor singlet: an original allowed deck sign already moves the rho line. A zero complete Stokes period or isotropic Cauchy Green form does not erase nonzero source cross correlations. Both q and p sources have two faces. Reversing every pair order is a global minus basis change and leaves the minus U6 action unchanged; the existing alternating orbit map is required.",
      "scopeEN": "Retain The reviewed positive fixed-point geometry. Its inferred full singlet/CP removability, p-as-second-face and pair-order sign claims fail these concrete tests. No universal exclusion of a separately defined time-order reader or source map. Scalar free annulus propagation is not the whole coupled source, and geometric evaluation is not automatically a permitted unsmeared quantum insertion at a Fuchs mark. Retain original time, spin/norm and conditional CP readouts.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:actual-product-collar-two-face-data",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:00f0333b979eda5bab26258b",
        "source:a9a914149c387935917fd86d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-source-naturality-needs-no-second-p-image-background",
      "titleEN": "Original source naturality needs no second p image background",
      "statementEN": "The previous independent-Phi_p requirement is unnecessary for the transported image. Original Seed morphisms intertwine all data and Cseed is declared functorial. Exact conjugation of the original inner-fluctuation generators gives U Omega1_D U^-1=Omega1_Dprime and transports the full fluctuated Dirac operator. Existing Majorana/background data move with the representation rather than being retuned. Thus the whole image-source arrow needs no second p input. The D5 signed Hodge-complement type also matches simultaneous D5/A3 opposition, with minus I8 explicitly in W(D8).",
      "scopeEN": "Corrects an overstrong premise; the image-source result is positive. This transports a given complete Seed rather than deriving its existence from fewer primitives. Do not promote the original definition/proof architecture to a new physical theorem. Fixed pi/Y/clock symmetry is a stronger separate question. Match the geometric spin pullback to the actual normal/collar realization, domains, faces, local algebra and reflection, without inventing a new p-background gate. Root normalizer type does not fix all original cocycle/spin phases.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:oriented-p2-exterior-carrier",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:9c48c1f99614265da6c4ee61",
        "source:a9e0479abeec3c6a6739d295",
        "source:334af098e9b83ab49991ba08"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:canonical-spin2-lift-carries-whole-annulus-source-with-reversed-time",
      "titleEN": "Canonical Spin2 lift carries the whole annulus source with reversed time",
      "statementEN": "The existing collar Clifford product is i_old Z. The pure geometric half-turn, both coordinate inversions and endpoint exchange transport the entire given collar operator, oriented real structure, four field/adjoint slots, full graph covariance and CAR state. In the charged chart its generator relation is T hq T^-1=−hp, so the actual circle parameter reverses. This OLD/NEW linear map squares to minus identity and needs no particle swap or independently fitted p coefficient.",
      "scopeEN": "A complete image-source map for the given original F5 family, without claiming physical P1 selection. Constant-normal graph formulas retain their stated scope; general normal-dependent data are transported as existing Cauchy data. Distinguish this time-reversing linear geometric lift from the earlier linear Kswap plus-time map without face exchange and The reviewed antilinear plus-time face map. No identification of circle, modular and physical time.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:ca68d12c2baac5414b75ab32",
        "source:5f4fa482f6ca93863322b2f2",
        "source:a25c445c1937c13c6245e7da",
        "source:2f5e980ea58566094d1388f3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:geometric-spin-collar-map-closes-weighted-image-domain-with-total-deck-action",
      "titleEN": "Geometric spin collar map closes the weighted image domain with total deck action",
      "statementEN": "The original ramified spin frame converts the global lambda phase to the ordinary collar half-turn ±i, with the known ramification correction. The existing weighted Fuchs spin trace transports the given domain, corner powers and transmission into its genuine C3-equivariant image. The geometric R map carries this q image onto p and agrees with the whole Spin2 collar map. Its total descent operator is delta_c=Pc c*, not bare geometric c*. The canonical descended inversion has order four while the unquotiented global S0 lift has order twelve; sixth-power parity alone does not identify the representations. A geometric omega eigenline needs an actual inverse coefficient character to define an invariant tensor. The required inverse direction is already present in actual Pc; the full Hom result also closes coupled q/p signs without a naked parallel-line condition.",
      "scopeEN": "The transported image domain is closed and needs no independent curve operator, p background or corner choice. Do not equate it with all spin sections, the entire rank-nine pushforward or an independently prescribed maximal domain. Pc channels are not yet a physical insertion reader. No unchanged faithful U6/C12 claim on this descended source and no general exclusion of rho. Original physical source derivation remains distinct from this proved image transport.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:364f665bf55d33badd4c9bb3",
        "source:30e92a06eb031f99c9163c2f",
        "source:a25c445c1937c13c6245e7da",
        "source:2f5e980ea58566094d1388f3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:claude33-annulus-map-is-valid-distinct-type-not-unique-geometric-spin-selection",
      "titleEN": "The reviewed annulus map is a valid distinct type without unique geometric spin selection",
      "statementEN": "The reviewed full face-swapped Z gamma K candidate has correct operator signs with its given minus-conjugate target coefficient. The whole four-slot map exchanges fields and adjoints, is NEW antilinear and carries plus circle time. Normal M proportional to Z is unique only inside the constant separated matrix ansatz. Both the candidate and its old-i multiple preserve oriented face reality but differ in squares and JF parity. Old i equals Ical Gamma and is not a uniform scalar in the new typing. Sixth-power comparison does not establish a unique geometric spin lift.",
      "scopeEN": "Retain the valid algebraic candidate while rejecting its unsupported uniqueness/type inference. No exhaustive global lift classification or physical origin theorem. The older Ucal Kswap map remains NEW linear without face exchange. the reviewed source is archived as unreviewed provenance rather than used as proof.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-full-v252-unimodular-p2-gauge-lift"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:5b0833aa66d46575dfa9f7c9",
        "source:bf58dce32997ba57f1da4973",
        "source:9086f019b50ea18d9f00edbc",
        "source:7ab663de3030baede1c58d79",
        "source:29b19f2bf089e483ed496d35"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-mixed-spin-products-already-have-complete-dual-hom-coefficients",
      "titleEN": "Original mixed spin products already have complete dual Hom coefficients",
      "statementEN": "The inverse cubic character is already in the actual Pc spectral line. Original normalized Kummer square pairings identify the two-torsion sign lines isometrically with their duals. Mixed spin products are therefore already global K-valued Hom(Fq,Fp) sections. Composition with reverse Hom and trace canonically cancels the full q/p signs; no naked parallel one-dimensional leg or fitted character is needed. The actual End coefficient omega-squared channel has dimension three, so Pc alone does not select a unique clock matrix up to scalar.",
      "scopeEN": "A complete positive bundle/coefficient connection, without supplying an arbitrary reverse kernel, selecting a new state or duplicating q/p as independent CAR species. Actual source-kernel endpoints and types must match. The checked original output formulas do not explicitly identify a selected additional Hom/Fourier contraction, which is no universal absence theorem and does not forbid coupled total projections. A one-sided reader is an example rather than a new required architecture. Retain The reviewed positive AdPc channel; Pc-alone uniqueness fails, while a separately fixed diagonal marking gives a narrower uniqueness. No physical CKM or general CP theorem is adopted from its random-profile claims.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:c2008ef6029b31eb9376c6b6",
        "source:6ff6460dd24c0d929d83e020",
        "source:c18d2693978f68b365aa9489",
        "source:a1c06ea7dd38033b6a752d00",
        "source:b98b09e58269c0fe881c9250"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-f5-graph-supplies-canonical-reverse-qp-hom-kernel",
      "titleEN": "Whole F5 graph supplies the canonical reverse q/p Hom kernel",
      "statementEN": "The already proved whole transport J=Swap tensor j gives a uniquely specified reverse comparison B=Gq J*. Its same-face blocks are precisely the original smoothing cross-face coherence Xq followed by geometric return. The entire G/W kernel composition retains endpoints, half-forms, metrics and adjoint slots. No reverse kernel or state is fitted. The q/p field labels refer to the same source with a non-diagonal redundant CAR metric, not independent duplicated species.",
      "scopeEN": "A positive actual source-kernel bridge, without deriving the original physical state from thin P1 or identifying it with the printed Yukawa/CP consumer by name. R can be a symmetry of an existing seam rather than its gluing map; no compulsory R-based endpoint identification is added. Original quotient sewing and bulk-eliminated responses remain allowed.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:actual-full-v252-unimodular-p2-gauge-lift"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:cef717266a13791fd89f2869",
        "source:e9aeb2c31848365a63abbf85",
        "source:c1d6e412db836ede9c520d9f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-spin-product-weight-has-canonical-trace-class-form-pairing",
      "titleEN": "Actual spin-product weight has canonical trace-class form pairing",
      "statementEN": "Original divisors give explicit mixed spin products and their actual Clifford type. Their base boundary coefficient has an integrable but non-L2 power singularity at all four ramification marks; source/target half-densities cancel in the multiplier. The exact surviving-channel L2 criterion retains deweighted jets. The original smoothing cross kernel still yields an absolutely convergent form pairing and canonical two-sided trace-class realization, with no new cutoff or kernel.",
      "scopeEN": "Do not promote the unsandwiched singular multiplier to a bounded L2 operator. Retain full coefficient ends, actual deweighted jets and cancellations. Clifford type alone does not prove admissibility of arbitrary family Hom coefficients as original central one-forms. A finite form trace or derived response operator is not automatically the original full CAR composite or physical P1 selection.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ee3a7ae0812c6156d38f5063",
        "source:cef717266a13791fd89f2869",
        "source:c1d6e412db836ede9c520d9f",
        "source:889f033ccb1d4d2a2d9c54ec"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fully-descended-covariant-reverse-kernel-removes-rho-form-channel",
      "titleEN": "Fully descended covariant reverse kernel removes rho form channel",
      "statementEN": "Original normalized lifts calibrate c=R_V squared to the entire Hom action, not a bare geometric character counted twice. On the fully descended source, a reader covariant for this same total action compresses every nontrivial character to zero. Thus the rho form channel is removed by the canonical equivariant reverse kernel. The invariant ranks are two off-diagonal and three in the full family; the whole source does not vanish.",
      "scopeEN": "Exclude only the specified fully descended covariant rho insertion with this actual kernel. Marked open arcs, actual additional original reader legs or a different sewing consumer change the premise. No automatic identification of native internal Zc with this descent and no general physical CP exclusion. Retain the positive inverse-character/Hom pairing results without counting their factors a second time.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5c0e7a6e34cb84f90c47b1a7",
        "source:c1d6e412db836ede9c520d9f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-a4-linear-quarter-does-not-supply-proposed-scalar-mu3-repair",
      "titleEN": "Original A4 with linear quarter does not supply proposed scalar mu3 repair",
      "statementEN": "The proposed minus-one times omega-squared repair requires a scalar mu3 holonomy on a V4 loop. Every actual A4 scalar character is trivial there, and quarter equivariance further leaves only the trivial character. The entire four-puncture mu3 character class has 27 members and only one cyclic-quarter invariant member. A marked extra line can give the desired value but is additional changed data.",
      "scopeEN": "Only the proposed scalar repair within the stated original class is excluded. No claim against marked lines, projective/antilinear/rank-two structures, actual Higgs/reader legs or physical CP as a whole. Do not infer reality of all structural projectors from real kernel parameters, or identify a bilinear evaluation rule with its argument or with the physical consumer.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b5d73dfa23d6068bcd638a72",
        "source:cdcfbdf436b075d46fcf4dfd",
        "source:1e4abbf435dbd2f05cd13f01",
        "source:4164254eea5ae0d5b798b6ff"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:offdiagonal-hom-matches-a4-family-six-but-not-two-triplet-e8-product",
      "titleEN": "Off-diagonal Hom matches A4 family six; holomorphic triplet wedge has complex rank three",
      "statementEN": "Original s/R lifts and normalized two-torsion products give the explicit unitary A4 bundle map. The direct holomorphic two-triplet wedge has complex family rank three and is not six independent complex holomorphic components. Its fixed-quarter and generic SU4 counterexamples remain valid for that complex-linear map. Compact real completion must instead retain the actual adjoint and simultaneous D5 carrier conjugation, as reviewed in the subsequent correction.",
      "scopeEN": "A genuine restricted bundle connection and product exclusion for these two inputs, not a dimension dictionary. The original full K includes O; no singlet zero mode does not exclude full fields or existing seam/Hardy modes. Their actual spin, twist, mode and statistics must be checked. Do not substitute a bosonic E8 current for a Grassmann matter field. Fixed-quarter failure is not a universal fixed-marking requirement under whole-data transport, and no free singlet is added. Correction: no universal O-fermion gate follows for compact real completion. Family Hodge alone also does not prove full(10,6) with the carrier suppressed: direct C/X triplet inputs give30 real directions, full16xF inputs60. Subsequent carrier and restricted-D8 findings replace the old active O-input gate.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:one-e8-bracket-weyl-pairing-with-single-anchor-dressing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0068a2c28831c6b4e5a3b8dc",
        "source:17aae365999d9ae6a493b4fb",
        "source:1e11b20f07043402efe6a1ee"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:compact-e8-adjoint-completes-family-six-with-carrier-rank-retained",
      "titleEN": "Compact E8 adjoint completes family six with D5 carrier retained",
      "statementEN": "Actual compact adjoint induces canonical anti-linear Hodge reality on the family six and is native-quarter/SU4 covariant. No universal extra O-fermion input is required for real family completion. Dagger simultaneously reverses the D5 vector weight: restricted C/X|F gives15 complex and30 compact real directions, while full16xF inputs supply30 complex and all60 compact real directions. The missing carrier half comes from10xbar5, not family Hodge or10x10 alone.",
      "scopeEN": "Corrects both the universal O gate and the first overstrong full60 reading of family-only Hodge. Retain valid adjoint/SU4 identities. Does not identify geometric mu with complete spinor inputs or a finite Phi block; no physical scalar or whole-origin promotion. The separate D8 finding decides the entire restricted recursive class.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-original-e8-cx-current-cocycle-and-compact-adjoint",
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:80e6d8ca736926e9c2d2b7fa",
        "source:95d81616e78701028f0d8b49",
        "source:e5988acd2e628fe494824870",
        "source:ade5135f6ff4de64bb41eda4",
        "source:a08e09932e0886ce4b2250d2",
        "source:6b8934507f60dcbeb5408b53"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:three-family-cx-recursion-closes-exact-d8-with-minimal-original-escape",
      "titleEN": "Three C/X families recursively close exact D8 with minimal original escape",
      "statementEN": "Only original C/X family labels1,2,3 and adjoints give36 seed roots. Full recursive Chevalley closure is36,92,112, rank8 and exact D8. Missing10xF components remain unreachable;30 of60 target roots occur and30 never do. Depth-two new roots are10xO plus adjoints. Any single omitted original C0 or X_i0 root, with its adjoint for compact input, escapes to E8 with114,170,240. Thus this restricted recursive class is fully decided and its minimal original escape specified.",
      "scopeEN": "Complete finite zero-mode Lie closure and concrete different D8 frame in E8. Not a no-go for higher affine products, other original operations or the full original family four. No new species invented. Geometric mu access to the minimal existing escape current and actual finite consumer remain separate. Algebraic reachability is not state preparation or physical time; independent root-sum and source-cocycle audits agree.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-original-e8-cx-current-cocycle-and-compact-adjoint"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:fee1a1b0427ee8076f5938fd",
        "source:1696e3a30f9ad0b758a9feb7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-weak-current-coefficient-has-explicit-finite-oneform-consumer",
      "titleEN": "Weak current coefficient has explicit original finite one-form consumer",
      "statementEN": "The actual weak bar5 coefficient has an explicit quaternionic Higgs witness in the original finite algebra. Its evaluated one-form has LR=q(H)diag(Yup,Ydown), with correct SU2, hypercharge and grading and explicit nonzero lepton/quark entries. General sums retain a common2x2 matrix Q multiplying the already supplied Yukawas across generations and sectors. The separately evaluated central dz normal reader is finite-identity valued and does not create a family Hom matrix.",
      "scopeEN": "A genuine finite-slot coefficient witness, not a full geometric mu-to-current-to-Higgs identification. General complex-linear span gives Q in M2(C); quaternion conjugation constraints require an explicit real-algebra/reality contract and do not follow merely from self-adjoint completion. Preserve actual color projection and Pati-Salam scopes. Old v258 modular inversion is for a given covariance and records the physical seam compression as conditional, not an independently evaluated mu source. Next test the simultaneous common-Q times given-Y relation at the actual geometric sewing consumer. Crucial goal distinction: the QY test applies to inner fluctuations around a fixed supplied D_F, not to original generation of D_F and its Yukawa matrices themselves. Source reconstruction of the background may change those matrices and must neither be excluded by the fixed-background fluctuation class nor replaced by merely varying it. The reviewed further mandatory family-scalar mu-reader conclusion is unsupported. A bare C3 sum is not A4 invariant, and real D†D does not imply real full Pstr kernel with unchecked complex projectors.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:given-original-e8-cx-current-cocycle-and-compact-adjoint"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:57ff6b841a56821e0b52c67e",
        "source:431c16382b14c2f84678e73f",
        "source:771a87a05ba7095512085759",
        "source:20fc36174d107fcc250f652a",
        "source:dcb0f70ecb4eebfbced8b74b",
        "source:128e8653c093797a33aaf003",
        "source:616c98c770fdd91f28be6703",
        "source:43d18c61835e364a70261329",
        "source:2db938435e7ff93731915d0e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-d5-zero-mode-closes-triplet-carrier-and-fixed-glue-is-minimal-escape",
      "titleEN": "Original D5 zero mode completes triplet carrier; marked glue is exact minimal escape",
      "statementEN": "The restricted D8 contains only20 of40 original D5 roots. An original grade-zero D5 zero mode gives the explicit cocycle-correct word into the missing carrier half, preserving glue grade2. Full original D5 action with the triplet seed closes to all240 roots; its Weyl orbit completes15 to30 complex target directions and adjoints to all60. No new O fermion or freely supplied full16 input is needed. Original marked glue lambda maps in the fixed chart exactly to C0 dagger, with its adjoint the minimal D8 escape pair. The D8 vacuum lattice VOA preserves its coset; distinguish its new Z2 parity from old mu4 grades.",
      "scopeEN": "Positive actual operator connection at the given P2/E8 current level; replaces the extra-carrier/O gate. Not primitive P1 realization, physical zero-mode history, geometric mu-to-current or simultaneous-QY consumer derivation. Original quarter twist still lacks the localized charged glue-vertex identification beyond its conditional neutral eight-copy kernel. Accept The reviewed independently matching D8/D5 step, not its further exchange/CP or normal-carrier-selection conjectures. Do not count existing total Hom character compensation twice.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-original-e8-cx-current-cocycle-and-compact-adjoint",
        "premise:original-d5-base-current-action-on-given-p2-e8-source"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:f33480c737d9fa1ebb7dfc71",
        "source:2037163e734c34d218e17655",
        "source:c41f29a8755937bad128c26f",
        "source:59538771a664b0189d81c0e8",
        "source:00900f1ebb9a9f033532a809",
        "source:ad76b742e8c01f7a0ed5310d",
        "source:c666be8b0d2761f122ac448b",
        "source:4f4836111bbe3ff90aea9134"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:mixed-spin-full-deck-has-no-rank-three-projector",
      "titleEN": "Full deck signs forbid bare triplet projection; original spin transport fixes its sheet",
      "statementEN": "In natural spin frames s*mu_ab=-mu_ba and R*mu_ab=rho^-1 mu_(b+1,a+1); the antisymmetric half is the positive U6-cube sheet after orbit phase calibration. The diagonal-A4 coefficient coisometry and bare positive K3 calculation are exact but do not define a global triplet subsource: six distinct V4q times V4p characters, together with transitive R, have scalar commutant. A displayed sign element exchanges antisymmetric and symmetric pairs. The original base map and v117 pullback already exist.",
      "scopeEN": "Complete finite result only for the bare six global section channels with independent original deck signs and R. Not an obstruction to coupled endpoint kernels, Bmu, diagonal response or P1. A4-only coefficients are a restricted category. Marked S conjugation transports a supplied triplet matrix rather than producing a global triplet subsource; retain canonical-form and endpoint factors. Read the early bridge report only together with its corrected addendum. Completed The reviewed and the reviewed source identify bare mu channels with Gamma paths, but matching labels do not compose their actual q/p endpoint and canonical-form types. The actual Bmu response is the source-supported replacement.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:d97530405822a7441f9e8836",
        "source:889d7333c58d8a864cb5ce62",
        "source:1b4108bb6a644dae8b587362",
        "source:4658bb6c9f1b43710adf17e2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-reverse-hom-diagonal-supplies-global-q-hodge-response",
      "titleEN": "Actual reverse kernel yields global q Hodge response after full composition",
      "statementEN": "The actual B=GqJ* composition T(u,v)=B(u,v)mu(v) cancels the full intermediate p signs and retains q input/output covariance. On existing smoothing same-face diagonals, the original bilinear skew projection and oriented Hodge map yield a global canonical-form-valued Fq response, retaining normal and D5 operators without new line, state or normalization. The given scalar common-quarter collar at Phi=0 already has a nonzero response to original off-diagonal insertions, using its actual positive diagonal Fourier kernel and invertible endpoint factor, without input Yukawas.",
      "scopeEN": "Positive global coefficient/form response of the supplied whole source. No pointwise Hodge at unmatched bilocal endpoints. Its integrable diagonal is not automatically a bounded full L2 composite, holomorphic section or finite Yukawa matrix. Scalar Phi=0 test does not trivialize actual Fuchs monodromy. At D_F=0 the original finite one-form vanishes while this response may not; the actual P1 variation or sewing operation must select and turn it into a background generator. No universal fixed-background QY gate. Wrel alone does not select J* M_mu. In an exact supplied graph block the second CAR cumulant9/25 differs from affine-logdet second derivative−16/25 and mean product16/25; retain actual source coupling. This is not a complete TFPT countermodel.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:66305f20ff5d3784d14af0ae",
        "source:2d90400f0957c27c8cc3523c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:bare-c3-kernel-diagonal-yukawas-have-common-real-frame",
      "titleEN": "Bare C3 kernel class with diagonal readers has a common real frame",
      "statementEN": "The same D=diag(1,omega,omega²) conjugates every positive bare H3 and its inverse square root to real symmetric matrices. Real diagonal left/right readers commute with D, so all such Yukawas are simultaneously real and all weak flavor CP-odd invariants vanish. No parameter or genetic search within this fully classified bare class can change the result.",
      "scopeEN": "Only the specified bare kernel class without additional relative readers or noncommuting actual holonomy words. No general TFPT CP obstruction, Majorana/theta claim or identification with full Pstr. Singular parameters are outside the inverse-square-root domain. Outside the common-real class, twisted contributions in both sectors are not necessary for algebraic CP: invariant Yu and one-sector twisted Yd=I+Pdiag(1,2,i) have Tr([Hu,Hd]^3)=-1440i. This is not an original TFPT mass derivation.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:bare-c3-positive-kernel-with-real-diagonal-yukawa-readers"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c46f2628346301877930126d",
        "source:4658bb6c9f1b43710adf17e2",
        "source:11329f02603048209cd2d63d",
        "source:afce7e1265efce912f472048"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-primitive-action-is-present-highpass-is-not-finite-selector",
      "titleEN": "Original primitive action exists; its high-pass does not select a finite carrier",
      "statementEN": "the reviewed source correctly quoted the original primitive relative-action formula and its bound reference/relative split. Do not reject it by substituting a different relative-trace convention. The actual primitive projector is seam-even times a spectral high-pass and retains infinitely many circle modes, so it does not by itself select finite Hcar or generate Yukawas. The displayed master variables and hypercharge Y are distinct from Yukawa matrices.",
      "scopeEN": "Preserve the original action and supplied full GNS/state/time source. Not an exclusion of every possible variation or renormalization; reuse existing coupled reference/reflection/gap/domain/projector/eta variation results. Old first-order-bound and D4 corrections are not rediscovered. This checks only the claim that primitive projection/stationarity already generated the finite background.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:be83830f5bc40587dcede746"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:atlas-detail-retrieval-recovers-existing-d4-solution",
      "titleEN": "Atlas detail retrieval recovers existing D4 solution after content ranking repair",
      "statementEN": "The actual natural D4 request reached the correct large problem, but full-JSON detail ranking let source metadata hide the existing solution. The small existing Rust retrieval now prioritizes semantic coverage and result text while preserving exact IDs and metadata fallback; bilingual tokens and continuation packing were repaired. Three regressions and all19 research-module tests pass. A fresh actual run.sh mcp request retrieves the existing D4 repair first with seven sources and within budget at the same data revision.",
      "scopeEN": "Retrieval software repair, not a new theory proof or direct graph edit. Existing old MCP processes do not hot-reload; fresh isolated connection was actually verified without stopping other clients. No full server-suite claim. Until normal reconnect, use exact IDs or the existing fresh stdio path rather than interpreting missed retrieval as scientific openness.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:77dac87a6b05d0c9a0fcca2e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-poisson-normal-trace-fixes-whole-calderon-graph",
      "titleEN": "Original Poisson range and boundary metric fix the whole Calderon graph",
      "statementEN": "For the supplied homogeneous selfadjoint collar, its Poisson range graph(exp(-ell h)) and original positive boundary metric uniquely determine the full bounded orthogonal projection G with A=(1+exp(-2ell h))^-1 and X=(2cosh ellh)^-1. Both normal traces of the antiperiodic Green formula give G directly. An invertible periodic realization yields an oblique projection with the same range and thus the same orthogonal G. Functional calculus includes unbounded h; no extra AP-selection gate is needed.",
      "scopeEN": "Exact bridge for the supplied homogeneous source. Bulk Green kernel and boundary projection are related by the proved normal-trace map, not literal equality. No equality of h with longitudinal quarter time. Wrel defines generic source derivatives but does not alone select J_geom* M_mu; the supplied source and specified insertion fix its response.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f32d83074b0964f5ac0c2462",
        "source:a0b9b31cec89e5e65230b28b",
        "source:2d90400f0957c27c8cc3523c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:induced-original-hardy-defect-gives-finite-whole-source-reader",
      "titleEN": "Actual induced Hardy defect gives a finite whole-source reader",
      "statementEN": "Actual signed G columns prove F_v117=Ind_V4^A4 chi0=pi_*L0q. The old spin cable is the correct induced family bundle without extra copies. Its given NS Hardy unit-shift defect has family rank three and transports by V_h into the whole graph, giving M_rs=<JE_r,M_mu E_s>. The actual induced mu01 input at Phi=0 gives nonzero M02=(4X*/pi)I Pgamma+, X*=(2cosh(ell_NS/2))^-1, I=0.1258739334853158906973-0.4697679151157443151336i. Actual q2/p1 open arcs add by their Kummer signs while diagonal pairs cancel. A closed primitive and strict analytic lower bound prove nonvanishing. Independent root checks give zero exact derivative remainder and continuous-branch quadrature residual below3.2e-76.",
      "scopeEN": "Existing mathematical NS Hardy source contract, not a newly proved physical finite P1 selection. The graph-lifted shift differs from both-face diagonal shift and relative matching; the whole-annulus shift has index zero. Graph membership alone does not establish finite time stationarity. The evaluated response is neutral and grading even, retaining all D5/charge slots, not an odd Higgs/Dirac source. NS frequency1/2 and quarter1/4 are related only via the old double-frame map with ell_quarter=2ell_NS and both quarter sectors for the seam shift; no physical scale/time equality is inferred.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:actual-product-collar-two-face-data"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:104905476adc28a485d79b57",
        "source:142e3c6cceee76a86c610628",
        "source:afce7e1265efce912f472048",
        "source:7d660655e5d28a3660d3a3cb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-weak-quartic-action-has-nonzero-nonlinear-response",
      "titleEN": "Original weak quartic action has a genuine nonlinear response",
      "statementEN": "Original Metrology already contains E_rel=-R I48/4-(Phi*Phi)P2+gammaF/2 and the weak E2 potential. Along admissible Phi=s varphi the first E response vanishes, second equals-2(varphi*varphi)P2; the potential has explicit nonzero second and fourth responses and a nonzero radial minimum for positive coefficients. The supplied scalar collar crossblock likewise has zero first but explicit nonzero second variation. No new free quartic ansatz is needed.",
      "scopeEN": "Retains given E2 admissibility and Yukawa seed. Euclidean GammaD4 and stated potential use distinct sign conventions. Zero first X derivative is not a no-go for whole G responses. Bound primitive variation retains reference, gap, reflection, eta and domains. Does not prove that B_mu is the E2 tangent or impose fixed-background QY as a universal origin condition.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-gap-normalized-primitive-relative-action",
        "premise:given-finite-sm-triple-yukawa-inputs"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d278b32ea12139342ba06c5c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:all-common-leading-distance-clutches-fail-original-flavor-lengths",
      "titleEN": "All common leading-distance clutches fail original flavor lengths",
      "statementEN": "Original diagonal TOTAL lengths Lu=(7,3,0),Ld=(7,5,2),Le=(8,5,3) have sorted gap ratios3/4,3/2,2/3; separate numeric left/right lists are not supplied. A common single-leg list requires one ratio. For equal-weight same-list two-leg readers, normalize x=(0,1,t): all six relative S3 permutations are degenerate or give only t-1 and its reciprocal. No arbitrary real triple reproduces all three original rows. Entire class is analytically decided.",
      "scopeEN": "Only shared leading distances with the stated equal weighting. Different q/p spectra, unequal weights, full mode sums and actual sector-dependent original C6 residue packets with additional length-six windings remain outside the exclusion. Frobenius exponents are not a boundary clutch without an actual operator dictionary.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:common-leading-distance-flavor-readers"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f52ec8bca35c4bbfc3153599",
        "source:a3ed41266c161e100026f595"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-hardy-response-has-weak-clifford-odd-and-ko-real-completion",
      "titleEN": "Original weak wedge consumer reads the Hardy response with full KO reality",
      "statementEN": "For the actual nonzero Hardy coefficient and marked original weak P2 creators, the exact commutator gives a nonzero grading-odd color-neutral weak doublet of hypercharge+1/2, rank16 for each component in the declared whole-96 comparison. All45 D5 Clifford bilinears commute with the even Hardy projection. Adjoint completion alone has rank32 and fails finite reality. Full original KO6 completion has rank64, is selfadjoint, grading odd and J_F real, with D_KO^2=|kappa|^2(E00+E22) tensor I32. All four sectors retain the same family matrix but fixed quark/lepton signs and antiparticle conjugations; no Majorana block. Actual checker replays and independent root algebra pass. Crucially, original carrier008 already contains the primitive exterior-volume coupling. Its actual up-quark channel reads the new directed coefficient as+kappa; the fixed signed KO Hilbert convention gives-kappa because compact conjugation reverses the complementary wedge. No phase is fitted. The original weak carrier consumer is therefore present.",
      "scopeEN": "Exact operator and original carrier consumer under the declared family/96 P2 comparison. Original wedge contraction corrects the earlier overly broad claim that no original weak Clifford application exists; read the two earlier operator reports with this addendum. Original family coefficients are already prescribed by Hol(nablaF*)Kstr. It remains to compare the actual Hardy contribution with the relevant entry, actual variation or path summand, without imposing equality to the whole Ybr as a universal condition or treating original Y as arbitrary free v252 inputs. Keep mixed E8 family leg, fixed-background limits, C0 versus J_F, internal versus field CAR parity, and NS versus physical quarter time distinct. A correct finite block is not the complete physical source derivation. General addendum: identical familyM on all96slots yields S=M+M^T. Two directed edges give equal nonzero singular values, not unique polarCKM. Different bare doublet-component coefficients violate fixedSU2. Typed original sector-specific readers remain allowed.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:oriented-p2-exterior-carrier",
        "premise:declared-q-column-to-v252-chiral-slot-comparison",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:original-d5-base-current-action-on-given-p2-e8-source",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2e7fc0417649756ea611d23f",
        "source:1e8c739326dde4163e565b2c",
        "source:146283eadbacba9ccc45e536",
        "source:371560477bfa3559622d6732",
        "source:1d2a8e3a73abac682e458692",
        "source:dd21b249e9fc00cf4b22846c",
        "source:3e2db98277adc36cb9a745bc",
        "source:9c53fb4e7908136bfe6a0999",
        "source:15b12b04c4902b2d70897743",
        "source:25e8abd4c9dc6ea0fbaedc22"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:two-entry-hardy-adjoint-hierarchy-fails-full-ko-and-su2",
      "titleEN": "Two-entry hierarchy fails full KO completion and doublet covariance",
      "statementEN": "For arbitrary complex3x3M identically lifted to actual96family slots, full originalKO6 completion of A=[X,MP+]=MXgamma is D=(M+M^T)Xgamma−(M†+barM)X†gamma. For M=aE02+bE21 the symmetric coefficient has singular values(r,r,0),r²=|a|²+|b|²; fullD has rank64. Independent symbolic characteristic polynomial and actual96replay confirm this. RawM/M† Grams are diagonal; fullKO has a degenerate two-space, not a unique polarCKM prediction. Actual[T+,Xw2]=Xw1 forbids unrelated bare matrices on this fixed doublet.",
      "scopeEN": "Complete stated identical-M lift/two-edge class, independent of uncalibrated second-ray sign. Not a universal restriction on originalYukawas. Typed sector-specificHolK readers,H/conjugateH intertwiners and complete mixed-current family legs remain outside. Originalwedge consumer is present. Rayquadrature is not calibration of actualM21. No physicalmass/CPclosure.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:oriented-p2-exterior-carrier",
        "premise:declared-q-column-to-v252-chiral-slot-comparison",
        "premise:actual-full-v252-unimodular-p2-gauge-lift"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:15b12b04c4902b2d70897743",
        "source:25e8abd4c9dc6ea0fbaedc22",
        "source:03bb3fcb8fc083b53df0bdcb",
        "source:bf61691404c791425923302b",
        "source:fc888525788e5352b7b764a7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-fuchs-halfpath-has-canonical-g-metric-c6-kernel-map",
      "titleEN": "Actual Fuchs halfpath has a canonical G-metric C6 kernel map",
      "statementEN": "Actual originalv117 P/Q integration and separately exact unitarykernel now share a closed frame map using already proved algebraicG. Fixed H=G^-dagG^-1 source metric and actualsigned cycleCs give Cpair^-1TrawCpair=[[0,Cs],[I,0]] with Cpair=diag(Gx,PGx) an isometry. Sourceadjoint equalsinverse. ExplicitB and existingJ connect to originalM/U6. Actualpath,D,metricGram,Green and inverse square root share one isometricfinite map, independently replayed with realP/Q residuals<1.3e−12. EvenwordCs² reads certifiedκE02 contribution; barepositiveK branch weights give v±κ. These are evaluated contributions, not an assertion that the complete originalsource inserted them. Stronger common marked closure: originalGbase/H0 gives H0^1/2Gbase=e^(7pi i/12)Bstar with explicitly fixed unitaryBstar. The sameBstar intertwines both actualCs to originalM0 and inverseKQ to originalU, hence all four markedmeridians. Exactly BstarE02Bstar†=M0P0 and BstarE22Bstar†=P0. CertifiedHardy contribution is thusκM0P0 in the common originalmarked frame with the existing quarter-fixede0 input. Six exact rootidentities and literalGbase normalization replay confirm it. The fixed markedendpoint is explicitly P0=(I+U²)/2; separately reviewed findings continue this same channel through the actualreal delta jet and allfour originalopenpaths. Positive actualspine consumer: originalP/Q fold is realized by P=T3,Q=T0^-1 and fixedC, with sameJ carrying inversefold to originalU6. OriginalD_y/fullGram/positivefunctionalcalculus and every already givenPstr transport isometrically; eight independent rootsymbolic checks pass. Recovered original v118 consumer reads det(I-tM0)=1-t³; native t=1/2 gives16/7,4/3,7/6. Later v121/FLAV.H2.04 uniquely pins recorded R under declared margins anddet8 among17 candidates, independently re-enumerated.",
      "scopeEN": "Positive finite ORIGINALpath with transported endpoints and every already givenPstr. No fitted/free metric or rawEuclideanadjoint identification. Read preliminarytype review with positiveGmetric addendum. Transportfiber pair need not equalF5faces; sheetparity is not automaticallyCalderonpolarization. No equality of geometricR/nativeclock/U6 by order. Wordtraces concern only certifiedcontribution. ActualZadm/blockedT insertion,entireD4spine and originalendpoints/compression remain at their originalconsumer. K is coupling,not a universalCARmap. GivenwholeG/W state/reflection/time remain; fullphysicalorigin/time derivation is not proved. StrongerBstar also retains originalquartermark; a single-M eigenbasis match alone would not. Common scalarphase cancels in endomorphisms. Transport full96J_F/Clifford/marks with the complex basis. κP0 is not identified with entirepositiveKstr, and actual originalsource insertion remains to execute. diag(kappaM0P0,0) is explicitly a comparisonembedding, not a derivedwhole6Hardysource or physicalzero for otherbranches. Any already givenwhole6operator andcross/adjointlegs share the sameEfold. Do not reopen nine free addresses or a new Hitchin PDE. Retain conditional margin provenance, distinguish native1/2 from later delta_ph, and do not turn scalar readout into whole-Yukawa or insertion provenance.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ee481464486cb35a476e4b1e",
        "source:8c4508505617265b852802e2",
        "source:5bfb91acae74f69500054786",
        "source:f20b71d148c8148772da2578",
        "source:73ae95c7c1370f70953bf30d",
        "source:fc8c5ba1817f8fc9ce90037b",
        "source:f1c8f108d524a2c7e31937c1",
        "source:a038de5ecd49e7d396f6c1d5",
        "source:743828407486df7063800a49",
        "source:a2c135a988787be9e1da8d26",
        "source:18bff43dd5b57668ad18ecbc",
        "source:47f0a5f83fed89caccdc8ee4",
        "source:5715e9f5effee72edf9e1f4d",
        "source:ef86b7579666b7a063bd46ac",
        "source:259622fbaa7ca9185b630600",
        "source:93bbdf9a1b12920c1736013b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-real-delta-jet-reads-same-marked-hardy-open-word",
      "titleEN": "Original real delta jet reads the same marked Hardy open word",
      "statementEN": "Actual common original frame identifies certified kappaM0P0 with the marked component of the ORIGINAL delta derivative. The original real-adjoint determinant consumer reads both sign branches and all three cusps. Paired marked-leg current is4delta^5/(y6-delta6), whole family derivative three times it. At exact original nonzero delta_star the full first response is exactlyzero; the same action has positive dimensionless curvature417.71513194757964. Independent symbolic identities and numerical replay confirm it.",
      "scopeEN": "Actual original operator direction and executed real consumer. Does not insert the complex Hardy coefficient into Zadm/Y merely by direction matching. P0 is the marked endpoint, not Pstr or determinant-sector projector. Imaginary kappa is not a free real delta variation. Curvature is not physical mass/time. Preserve the already complete given seed.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract",
        "premise:original-closed-real-delta-transport-action"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:fa16a67953817a9bd3d0cb0a",
        "source:86621e6224bff59d6b013c39",
        "source:2fea462c25e2cee8f5753aa2",
        "source:ec59ddd5eda1895b6f8b954f",
        "source:a038de5ecd49e7d396f6c1d5"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:four-actual-fuchs-spine-edges-recover-marked-meridians-and-nonzero-open-word",
      "titleEN": "Four actual Fuchs paths carry all meridians and a nonzero open-word contribution",
      "statementEN": "Actual algebraicG produces all four original diagonal0-to-infinity transports and fixed endpoint metrics. Their different source/target quarter actions give T_k=V^kT0U^-k and ALL FOUR adjacent return loops recover the exact original markedmeridians in the normalized sourceframe. The covariantly rotated open-word sum is nonzero: -6sqrt30/5 E10 with normalized input and -2sqrt2 E10 with target also normalized, while frozen insertion sums tozero. An initial raw/normalized mix was caught and corrected before registration. Fourteen exact identities and independent root integration of all four genuine original paths confirm it. Positive actualspine consumer: originalP/Q fold is realized by P=T3,Q=T0^-1 and fixedC, with sameJ carrying inversefold to originalU6. OriginalD_y/fullGram/positivefunctionalcalculus and every already givenPstr transport isometrically; eight independent rootsymbolic checks pass. Complete addendum: T_hat,k M_k=T_hat,k-1, so the covariantword sum equals the unweighted edge sum. Actual four-edge tuple retains four nonzero Fourierchannels of ranks(1,2,1,2) and metric squarednorms(1/2,1,1/2,1). Complete inverse transform reconstructs all actualpaths/meridians. Only the invariant linear single-Hom compression is one-dimensional; whole covariant packaging is not automatically this compression.",
      "scopeEN": "Four actual original path classes with typed open endpoint action. Preserve explicit geometric reading when identifying their diagonal theta4 graph with the unnamed original geodesicspine. HolomorphicD4 alone is not the larger real-reflection symmetry. Nonzero four-path expression is an explicit consumer comparison, not a claimed originalsum prescription or nine-address table. Execute originalHol_G packaging/coefficientinsertion without inventing it. Full physical closure and time origin are not proved. diag(kappaM0P0,0) is explicitly a comparisonembedding, not a derivedwhole6Hardysource or physicalzero for otherbranches. Any already givenwhole6operator andcross/adjointlegs share the sameEfold. Rank1 sum is not established as the original complete physical consumer. RawkappaM0P0 also fails nonzeroSU3 holonomy tangency since trace(M0^-1deltaM)=kappa; this is not an obstruction to differently typed field or additiveV_adm responses.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract",
        "premise:four-original-diagonal-paths-and-regularized-endpoints"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:214be057beb34f5e3dd97d07",
        "source:86621e6224bff59d6b013c39",
        "source:c9a6b43aebee9592719c9161",
        "source:65f5136908a0d3e3be4cdad9",
        "source:6cb78875381a9cc5ad6e470c",
        "source:73ae95c7c1370f70953bf30d",
        "source:743828407486df7063800a49",
        "source:a2c135a988787be9e1da8d26",
        "source:18bff43dd5b57668ad18ecbc",
        "source:1ed4f041f80fc8bad7b625e2",
        "source:31ac3289c0795a52fd4ce830",
        "source:90f63d8b54168166b7e5c0b9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-adjoint-quarter-clock-cannot-compensate-hardypair-odd-character",
      "titleEN": "Native adjoint quarter clock does not compensate the odd Hardy character",
      "statementEN": "The reviewed scalar trace/Fourier tables are correct. Its left-vector phase identification fails for the actual endomorphism: native conjugation fixes neutralB and negates weakoddA, character2 rather than the odd quartercharacters. The combined adjointaverage is exactlyzero, confirmed on actual96 and independently replayed.",
      "scopeEN": "Only specified nativeadjoint compensation and scalaraverage class. Not a universalHardy or D4consumer no-go. Preserve positive originalwedge/commonmarkedword. Actual openHom endpoints with different quarter actions can retain nonzero responses, as the four originalpaths explicitly demonstrate. A freely one-sided phase is not an originalderivation.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:oriented-p2-exterior-carrier",
        "premise:declared-q-column-to-v252-chiral-slot-comparison",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:native-clock-adjoint-compensation-for-hardypair"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:0c2ac4ef2499ccdb5e0075b5",
        "source:1b6ba3a25f23a677030bfe57",
        "source:f8abfe21845e5671ebe82636",
        "source:38450c58843b7b63cf323b4a",
        "source:214be057beb34f5e3dd97d07"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-cubic-gram-differential-retains-hardy-phase-and-cross-resonance",
      "titleEN": "Whole cubic Gram differential retains Hardy phase and mixed resonance",
      "statementEN": "The complete inverse-Gram-square-root derivative is given exactly by its two spectral projectors, including cross blocks. For declared V=-kappa M0P0 the fixed-line coefficient is exactly Re(kappa)/(3g²), but mixed operator response diverges as |kappa|/(sqrt6 g), not a bounded remainder. Actual Hardy phase gives rank3, Frobenius17.9916735432 and fixed-line amplitude share0.890301077, squared share0.792636008. The quoted99.3% applies only to an artificially real direction. Independent root two-projector calculation confirms the full eigenvector divided-difference result.",
      "scopeEN": "Exact response of the existing uncompressed cubic block to a declared direction. Original EM5 requires actual Pstr commutation and a gap norm bound; it does not select this V_adm. Conditional length threshold is not a derived physical length. PositiveC6 block is not physical seam projection, nor P0 the structural projector. Finite response differs from its derivative, with22.65% relative control error near the bound. No physical source insertion, CP or time origin is claimed. Preserve prior bareK3 reality and actual wedge consumer.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract",
        "premise:original-closed-real-delta-transport-action",
        "premise:declared-positive-cubic-hardy-direction-for-gram-differential"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:649ff21aa9cfb02877d0f0ed",
        "source:944c66429cee1ddbfea001a2",
        "source:d22036e48dfe799a7579e2bc",
        "source:ddf1e3377848b712318702ee",
        "source:098a73120e0f693310548196",
        "source:d348f45f20858fd1a77e8dbe",
        "source:9680a237d7b3f5c0ae2054e6",
        "source:743828407486df7063800a49"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:complete-original-mu01-hardy-reader-has-two-calibrated-entries",
      "titleEN": "Complete original mu01 Hardy reader has two calibrated entries and seven exact zeros",
      "statementEN": "For the SAME actual inducedmu01 input, complete nine-entry family answer has only E02 and E21, with seven exactsupport/eta cancellations. ActualG/R endpoint calibration fixes the opposite second root and sameCCW orientation. Two genuine atan continuations give EXACT I21=-I02+pi(1-sqrt2)C, not a numerical phasefit. Independent root support/sign/orientation, rational derivative and70digit period replay confirm it. Matrix has rank2, cubezero. Reuse the already complete two-edgeKO theorem: under declared identical96family lift, neutralB rank32, fulloddcompletion rank64 and symmetricfamily singularvalues(r,r,0).",
      "scopeEN": "Whole evaluation of ONE original mu01 reader at the given NS kinetic point, both graphfaces and actualnormal gradingprojection. Not the entirephysicalYukawa or wholejointsource insertion. Other originalmu_ab are separateactualinputs whose formpullbacks, spin/NS/J andendpointmaps must be checked together. KO result uses the already declared G/96dictionary; carryJ_F in complexframe changes. No rawhierarchy/CKM inference, fittedweights, phases, state, time or zeroing of otherphysicalbranches. The actual maps and other five inputs are now closed in finding:whole-six-original-hardy-inputs-generate-full-family-coefficient-algebra; this entry remains the single-mu01 subproof.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:oriented-p2-exterior-carrier",
        "premise:declared-q-column-to-v252-chiral-slot-comparison",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:whole-same-mu01-induced-ns-halfmode-reader"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:44c976081c1e6f349dadaff5",
        "source:5b9de035960441aef7f4c410",
        "source:142e3c6cceee76a86c610628",
        "source:a7ac8b0d43b02599626bdd6a",
        "source:c24f81c3a3226f73901d81f3",
        "source:41e7614e40d0bd10cdb44936",
        "source:15b12b04c4902b2d70897743",
        "source:df9512a1989b1b688a52888b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-six-original-hardy-inputs-generate-full-family-coefficient-algebra",
      "titleEN": "All six original Hardy inputs generate the full family coefficient algebra",
      "statementEN": "Actual G columns and original R lift force G_a=G Pc^(-a) and the two-leg map Common=P^(1-b)ScalarP^a, preserving the stated kinetic NS/Hardy domain, metric, spin and full graph. All54 entries are computed:42 exact support/eta zeros and12 continuous-root periods. The two oriented triples are (1,omega²,omega)F and (1,omega²,omega)N, F=alphaE02+betaE21,N=-i(alphaE12+betaE20), with actual normal projector. Reverse phase follows exactly from the calibrated period. Independent65digit replay and source review confirm all inputs. F and N together generate all nine matrix units of M3(C), even without separately adjoining identity, with scalar common commutant. In the SAME originally marked Bstar frame, Fhat=alphaM0P0-betaP0M0 and Nhat=-Dsign Fhat Dsign, hence Fhat is the original delta jet at both marked endpoints with actual period weights. The finite moment reader intertwines rawR with Ad(W), W²=-I, retaining only its ±1 moment lines. Actual fixed-D resolvent traces are exactly (alpha-beta)delta²/(y³-delta³) forFhat and i(alpha-beta)y delta/(y³-delta³) forNhat. Twenty-one additional exact root checks confirm these identities. Actual fixed-cusp tangent test gives d(M³)[Fhat]=(alpha-beta)I nonzero. At the same time its cyclic centralization is ((alpha-beta)/3)M0 and original scalar resolvent trace is (alpha-beta)t²/(1-t³), with determinant linear response -delta²(alpha-beta). Independently verified exactly.",
      "scopeEN": "Complete six-input alphabet in the given kinetic NS/Hardy reader; global twist sectors remain distinct. Squares alone only generate an embedded two-by-two block. Coefficient accessibility does not identify physical field/CAR products or select whole Yukawa, coupling mix, state or time. Equal-weight sum cancels by cubic phases, not a universal source no-go. Existing wedge/Clifford/KO consumer applies linearly. Continue original common use without imposing this route as a universal P1 gate. The linear finite R moment image does not replace the global spin/R action or source state. Two jet orderings do not select physical V_adm or reduce the entire origin to endpoint placement. Do not replace original provenance with another conditional Gram comparison. Only labeling Fhat as fixed-cusp deltaHol fails; genuine coupling or insertion remains eligible. Scalar response does not establish original source selection.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:whole-six-original-induced-inputs-at-fixed-kinetic-ns-reader",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract",
        "premise:original-closed-real-delta-transport-action"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:df9512a1989b1b688a52888b",
        "source:87315b8b3a6ddfeb06fe8f97",
        "source:9ec47f89199e3c223d06dc37",
        "source:78978fdbfe23d54742894f98",
        "source:d0b554b37f013fc5ce606a18",
        "source:439a94209f4e65d0ed5f0c7a",
        "source:d2ebddda30d6fcfa1ffc5bc7",
        "source:94b7e09d335f078dc5e78dd3",
        "source:278efb3e3d5897d48b790218",
        "source:b24886853a5b0d2cb72588be",
        "source:2de89d39680e2a82bca21df0",
        "source:3268891002ecd26070450dd2",
        "source:7eb93107297b62c11a409ee5",
        "source:44c976081c1e6f349dadaff5",
        "source:b36d65ccd93460c2fcf52d0a",
        "source:a7193cbf1304eda81cedc11b",
        "source:f1c8f108d524a2c7e31937c1",
        "source:fa16a67953817a9bd3d0cb0a",
        "source:62cc9b9e25c6714ed2d9d4f2",
        "source:390265a486efb462640559b8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-whole-hardy-alphabet-has-finite-particle-hole-wick-block",
      "titleEN": "The original whole Hardy alphabet has a finite joint particle-hole Wick block",
      "statementEN": "Actual retained face/normal maps give pp=sech(ell/2)L,ph=hp=tanh(ell/2)L,hh=-pp for all six inputs. Finite joint connected CAR block equals g Tr(m_mu m_nu), g=16(2/pi)^2tanh²(ell/2), with actual carrier multiplicity correcting The reviewed. Unstarred same-orientation squares vanish but adjoint norms equal positive gh. Four ordinary real quadratures have the explicitly recorded covariance with strictly positive eigenvalues g(|I02|±|I21|)^2 each twice. Independent symbolic64-dimensional CAR replay checks eleven identities, independently confirmed analytically. A pp-only traceless compression annihilates the filled corner, not the whole operator.",
      "scopeEN": "Exactly the canonical finite E/Eh corner of the GIVEN kinetic reader. No whole unsmoothed limit, whole J_F/KO field, P1 selection, CP or CKM claim. Any global selfdual half-trace is separate and does not erase sixteen internal components. Preserve existing positive finite-reader/WEDGE path.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:whole-six-original-induced-inputs-at-fixed-kinetic-ns-reader",
        "premise:canonical-finite-particle-hole-corner-of-given-kinetic-graph"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:c91935b40ad15df71f82d57c",
        "source:d1c37220290e279525f172fa",
        "source:eb4d47ed7de4f4d355e47f34",
        "source:1040d143a71174dcff616c25",
        "source:08947fae48a6adc1a9b0c2fe",
        "source:d8b74259d37284dd1f56020d",
        "source:d60a520e9eb698ea12e3ab8f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:bare-unsmeared-mu-crossface-quadratic-fails-vacuum-domain",
      "titleEN": "Bare unsmoothed geometric cross-face quadratic fails its vacuum domain",
      "statementEN": "Actual multiplier retains nonzero |theta-theta_j|^(-2/3) jet after given maps, L1 but notL2. On one original occupied n=0 column, the bare T produces nonsquare-summable Fourier coefficients, while actual hole projections retain positive limiting c²/d² factors. Connected cutoff CAR variance therefore diverges. Original fixed Zref[0] denominator drops out of positive source derivatives and does not remove a source contact term or select the finite PH block as the whole regular part. Independently source/domain reviewed.",
      "scopeEN": "Only the explicitly bare unsmoothed equal-time caller. No P1 no-go or exclusion of sewn/relative/renormalized insertions or existing finite WEDGE→D_F/Sadm path. Separate reflected HS midpoint remains scoped finite and distinct. Original selection of this bare caller is not established; do not impose universal regularization or a free smoothing choice as provenance.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:whole-six-original-induced-inputs-at-fixed-kinetic-ns-reader",
        "premise:bare-unsmoothed-crossface-quadratic-on-given-graph-vacuum"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:35a0b681221b35a5f7017970",
        "source:d8b74259d37284dd1f56020d",
        "source:6f9164749447e775ce6079be",
        "source:a4424871611c71642a9067f2",
        "source:e7108f13bf1f0e2ac9098834",
        "source:d99de6a860b134446668e889",
        "source:bf2a41e22166dd7304b84756"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:linear-spectral-centralization-does-not-replace-full-marked-hardy-source",
      "titleEN": "Linear spectral centralization does not replace the full marked Hardy source",
      "statementEN": "Centralizations cM0 and icM0^-1 reproduce first scalar traces, but actual full marked determinant differs from the centralized two-sided replacement already at quadratic order. Exact recorded full polynomial and difference hold for actual periods, with nonzero1+r+r² at real period ratio. The full adjoint relation has a nonzero marked residual; only its centralization agrees. Original delta is real, so the complex analytic saddle is not an admissible original descent. Inverse legs already exist in original Gram/Green/Kstr. Ten exact root identities and independent source/matrix review confirm.",
      "scopeEN": "Only replacement of this whole marked F/N family by its linear central quotient as a full nonlinear source and the claimed original complex instability. Formal probe variables are not new physical couplings. Preserve positive linear readout, genuine later inverse insertions, endpoint marks and existing source/state/time consumers. No universal source no-go or CP claim.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:whole-six-original-induced-inputs-at-fixed-kinetic-ns-reader",
        "premise:original-closed-real-delta-transport-action"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:fc1406241b6dc884f374886a",
        "source:77a33a8b0778c325f2ce49a8",
        "source:ab9a39fe652c6decacbbca01",
        "source:eb99e3ec886ace8113ce74f2",
        "source:a5c879df9b0b198f59ef273b",
        "source:c2052d33fddf157d2d5e6083"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-admissibility-projector-is-explicit-penalties-do-not-read-retained-amplitudes",
      "titleEN": "Original admissibility projector is explicit; its penalties do not read retained amplitudes",
      "statementEN": "Original QFT2 explicitly produces P_adm as the joint zero-penalty Hodge sector. Positivity gives K_rP_adm=0; every unital penalty polynomial and joint bounded functional calculus restricts to its zero value times identity, with exp(-betaDelta)=I. Such penalty-only weights cannot separate a retained basis of dimension at least two. Actual QFT4 explicitly names additional transport counts, carrier labels and retained selector weights. Reviewed Source45/Paper42 passages do not provide numerical d_r(w) or ordered whole-T_V contraction. Existing v330/v175/origin_transfer are different concrete consumers, not silently identified with this producer.",
      "scopeEN": "Necessary original type separation between selection and label-dependent amplitudes within the selected sector. Preserve explicit projector and given full operational seed. Bounded source coverage is not universal absence. Rank-one separation is trivial. Do not impose a new d_r program as a universal gate; actual original action-to-transfer or sewing constructions remain eligible. No new free state, smoothing or Hardy=wholeY assumption.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-original-two-stage-admissibility-complex-and-blocked-weight-caller"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b5a0a83bd5cbf3f42575e2ac",
        "source:fc1406241b6dc884f374886a",
        "source:75554c5535c27abac436633f",
        "source:06fcf18192979abfc5223edd",
        "source:29a6b485f10379ecc3c34ec6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-original-inner-fluctuation-has-whole-noncommuting-two-face-response",
      "titleEN": "Original inner fluctuation has a whole noncommuting two-face response",
      "statementEN": "The existing real Higgs direction gives Phi_s=(1+s)D_Y+D_MR with Majorana fixed. The new result is the full coupled-background response using the Frechet derivatives of q(u)=tanh(ell sqrt(u))/sqrt(u) and x(u)=1/(2cosh(ell sqrt(u))). The actual neutrino block has commutator norm squared4M^6m², so a commuting derivative is invalid. Finite tanh differentiation is injective and forces nonzero diagonal response for nonzero D_Y. The all-quarter-mode graph derivative is Hilbert Schmidt and its crossing derivative trace class, determining all finite smeared CAR word derivatives of this given source.",
      "scopeEN": "The inner form is reused prior work; Yukawa values remain given. Injectivity is before additional projectors or readouts. This is the source side of the requested comparison, not a mixed boundary-source response derived from S_prim, bosonic averaging or physical-time closure. Preserve the existing full Clifford functor premise and actual B_Sigma identification for the primitive gap; do not identify reflection types.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a98b976eed56f3891f2474a0",
        "source:2716a2190874629fe659a5ee",
        "source:6719e74cfa8dd14b381f7d11",
        "source:4221e26e3bad9be144286153"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fiber-only-primitive-split-and-frozen-gap-miss-original-action",
      "titleEN": "Fiber-only reflection and frozen gap miss the original action",
      "statementEN": "The reviewed fiber-only identification fails on central coordinate multiplication, before domain completion. Restoring normal pullback preserves the full constant product Dirac expression and gives D_rel=0, reusing the prior product-lift result. A field-independent unscaled K does not make Tr f(K/chi) field-independent when chi is bound to the boundary gap; a constant Dirac-block heat contribution has an explicit nonzero derivative. the reviewed source's scalar first variation, without two source insertions and their mixed derivative, is not a mixed boundary term.",
      "scopeEN": "Narrow rejection of these concrete origin identifications, not a universal P1/action no-go. The full product lift is not thereby selected as primitive. The heat control only tests alleged field independence, not a physical profile. Retain actual bundle transition, closed domain, reference, gap and eta. A joint S_bos+S_ferm is allowed without requiring bosonic action equal to a fermion determinant or Hessian equal to Dirac. Preserve the given whole-source response and OS reconstruction.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-geometric-dirac-deck-lift",
        "premise:original-admissibility-and-graded-source-interfaces"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:510aaa8dfd987e78cbf9cde4",
        "source:7daf45f331cc0da0d4be0fc7",
        "source:f793d86527e9098ba3f15448"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:oriented-resolvent-weights-do-not-identify-original-reflection-producer",
      "titleEN": "Oriented resolvent weights do not identify the original producer",
      "statementEN": "The resolvent coefficients are correct, but the additional diagonal-weight construction fails abstract word-reversal invariance, with an exact rational diagonal difference2600/3969. QFT2 does not identify that reversal with OS Theta or Q_Theta; only Q_Theta=R forces the even projector and word pairing. Symmetry does not refute Perron primitivity. These coefficients alone do not derive the actual retained-basis action and original weight call.",
      "scopeEN": "The reflection failure excludes the candidate only where R stability is actually required. No general exclusion of oriented weights, no missing inverse C6 leg and no original-selector claim; preserve positive Gram/Green/Kstr kernels and P_adm.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-admissibility-and-graded-source-interfaces"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:24418edd2a780e4d79b6785d",
        "source:bf23311e0015cc49ccc18223"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:current-odd-carrier-reader-is-lossless-on-whole-coupled-source",
      "titleEN": "Original odd carrier reader is lossless on the whole coupled source",
      "statementEN": "The complete original v258 mu_geo Pi_odd log-odds reader composes with the existing reducing E chart and actual second face to R=2ell mu_geo U_gamma Phi U_gamma*. It retains the full96 coefficient, Majorana and Yukawa jet while removingcircle momentum without a new Fourier projection. The smooth H1 identity remains valid for noncommuting even connection and odd coefficient. Retaining known A,ell andmu gives a lossless reconstruction of the whole graph; the full covariance recovers both A andPhi. The comparison unitary preserves actual antiunitary charge and even algebra. Direct unrotated feedback is only cPhi: all coefficients fixed at c=1, otherwise only zero; exact inverse feedback is identity and selects no Yukawa pattern.",
      "scopeEN": "Positive composition in the given source class, not provenance of supplied Yukawas or bosonic source. E has96 fiber rank but infinite circle rank; face compression does not reduce G. The named physical P_F is not identified with E/face in the read current passages and v258 call path. Keep2ellmu explicit and physical time open. Current modular D_rel and archived geometric split are distinct displayed calls; current UV chi is not automatically archived inverse gap. WholeG is not a strict log-odds input. Actual-constructor diagnostics are not physical parameter derivations. No universal generation no-go or requirement of noncommuting compression.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-full-v252-unimodular-p2-gauge-lift"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ba1c42a41992c73070a8cfb7",
        "source:59dc78be6ccd2e22cab708cc",
        "source:3ffe99e909e6766edb2eedf6",
        "source:fe22e53861054cd4c6848f02",
        "source:868268b931c4fcfc70f73d5b",
        "source:327a34bf933d5eceddd1a9b8",
        "source:4f81d02d0b090fec785258f2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:ap-spectral-formulas-do-not-force-normal-domain-or-complete-source",
      "titleEN": "AP spectral formulas force neither normal domain nor whole source",
      "statementEN": "The reviewed AP resolvent sum and scalar second-order determinant X^-2 are correct. They do not force AP closure from the orthogonal Cauchy projector, also obtained from a periodic realization with the same image. Correct D=N(partial+B); whole Pfaffian identification retains charge legs,multiplicity,reference and phase. One scalar directional jet does not reconstruct an operator, whereas full first variation over all probes may identify a gradient. the reviewed source's scalar/operator comparison is not a pair of complete sources and proves no nonidentifiability. C59's AP bulk/gluing split is correct with its regulator. Gluing variation is a scalar consumer of X_E, not the whole cross kernel; retain matching mu and joint zero-spectrum limits.",
      "scopeEN": "Only these forced identifications are excluded. Preserve the named elliptic NS source with given AP holonomy, correct sums, full coupled response and stronger operational seed. APS and AP are distinct domain data. No whole-TFPT no-go or claim that only noncommuting compression can select couplings. New explicit standard Clifford gluing derives AP from stronger common domain data; distinguish it from the excluded inference from G alone.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:closed-antiperiodic-scalar-wall-with-fixed-hermitian-coefficient"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:505ec9f8e384c79ae0060b0b",
        "source:27a09c11f2e93f55e35a5253",
        "source:745221db9959f6f23d735769",
        "source:d85291a83bedd7f286f9ae8a",
        "source:fd25c8f02fd19231b53f9aaf"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-weak-connection-transmits-family-orientation-to-both-faces",
      "titleEN": "Actual weak connection transmits family orientation into the joint boundary source",
      "statementEN": "In the given v252 source the actual real weak lift Q=-i(T+J_F T J_F^-1) has the required antiparticle minus sign. For h=(pI+tQ)gamma-i gamma D_F the commutator term in h² is retained. Two constant diagnostic quark backgrounds with equal separate singular spectra give DeltaTrh²=DeltaTrh⁴=0 but DeltaTrh⁶=5760t² at p=1/4, with all96 slots and identical nonzero lepton/Majorana data. Independent block calculation yields36 DeltaTr(HdHu). Thus for every nonzero t and every given positive width the actual cross-face X eigenvalue multisets differ. Finite small-width trace and logdet differences begin at -244ell⁶t² and -128ell⁶t². The actual coupled source retains mixing information at constant Higgs through its existing weak connection. Under the whole unitary polar formula Y_f=T_f K_f, Tr(LuLd)=Tr(Ku² V Kd² V*) with V=T_u* T_d; a common T gives V=I. Retain original lambda dressing and path-reader typing.",
      "scopeEN": "Actual full96 source operation in one existing quarter mode; no selection of Yukawas,weak background,width or physical time. Unlabelled fullG projection spectra remain0/1; labelled cross blocks differ. No interchange with infinite mode sums and no established coefficient in the original full action/Gamma. Refutes extending frozen separate-spectrum blindness to the existing coupled operator, not every particular functional. A new seam derivative is not required for this capability.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-full-v252-unimodular-p2-gauge-lift"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b983d0ec62222b4a59b1524d",
        "source:8fb82370f8343ac321dbd70f",
        "source:ffda9190aa02e95780df325d",
        "source:1f29f45338673d3826b34cdc",
        "source:dc02afcd83796c982b412d64",
        "source:cb0356aa541e1622b0b8d0e0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-higgs-variation-is-not-independent-yukawa-stationarity",
      "titleEN": "Original Higgs variation gives the full radial tadpole at fixed Yukawas",
      "statementEN": "The original v252/v254 call varies q(H)M with supplied Yukawas. Its displayed local target quartic yields the Higgs tadpole, not independent matrix-Y stationarity. The whole96 radial family with Majorana retained has exact quadratic/quartic trace identities, including4Tr(DY²DMR²)t², and the corresponding contracted radial tadpole. Bound coefficients,gap,reference andeta retain chain terms. The reviewed further identification of the original APS generator with a function of h² is absent from the cited definition; only the already known pure PF<=G branch is settled. The reviewed original master already contains relative Z and determinant terms; The reviewed separate extra Gamma_H is not specified there and may double count. Differentiate the actual shared field dependence in the existing expression. The explicit logdet coefficient alone is not the derivative of the whole master: the relative Z contribution can change it already at first field order. An exact scalar Gaussian control refutes that inference without replacing the original TFPT source.",
      "scopeEN": "Evaluation of the displayed local target action and actual field direction, not derivation of its coefficients or whole renormalized functional. Existing flavor/Spine outputs are not replaced by a new Yukawa fit. Explicitly declared Dirac-modulus variations remain allowed, including fixed-shape Majorana amplitude and the existing sigma branch. No complete primitive dichotomy or physical completion. The reviewed claimed exact H=0 decoupling and H!=0 failure are not proved by its determinant-only coefficient. Permutation extrema of a single linear mixing invariant do not classify stationary points of the whole master.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-global-quaternionic-sm-mass-loop-with-fixed-yukawas",
        "premise:original-gap-normalized-primitive-relative-action",
        "premise:original-admissibility-and-graded-source-interfaces"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:dc02afcd83796c982b412d64",
        "source:d297d1f5eb7dfe7d3e763d12",
        "source:9ba286e3b1ff48f12e749ed3",
        "source:cb0356aa541e1622b0b8d0e0",
        "source:9ad523276c45201fd157c860",
        "source:de07c877240108437bdc0404"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-weak-cap-converges-on-whole-quarter-circle",
      "titleEN": "Whole weak cap converges across polarization changes",
      "statementEN": "For the actual constant weak source, Zp=exp(ell E_p)det_RanP0(P0 exp(-ell h_p)P0) is the old Slater expectation of exp(-ell H_exc,p), with0<Zp<=1. For v=||V|| and g=|p|>2v, negative eigenvectors yield Tr(Ph P_wrong)<=48v²/(2g-v)². Ground overlap and spectral resolution give the same bound for1-Zp uniformly inell. Thus the product over all quarter modes is strictly positive and finite at every finite ell>0. Finitely many crossings or overlap zeros do not destroy the finite-time cap. Zero-mode occupations leave E_p and H_exc,p unchanged and do not affect the cap at fixedP0; only a particular ground vector/Thouless chart needs them. ConstantQ preserves Fourier modes but not the old scalar-pair reduction. The actual free-reference ratio retains exp[-ell(E_p-E_ref,p)]Zp. Full96 numerical controls confirm that factor and recover the t0 scalar formula; convergence is analytic.",
      "scopeEN": "Complete stated constant weak cap comparison in coupled ground-energy normal ordering. No derivation of original P0,fields,normalization,Zrel or physicaltime and no nonconstant-source theorem. Large-time limit can vanish; strict positivity is finite-time. HS equivalence gives a common Fock vector, not an automatic original positive-time OS insertion or global Thouless chart. Orthogonal-line control refutes only that universal chart inference, not a pair of full TFPT sources. Original reference/bulk/phase prescriptions remain required.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-constant-weak-quarter-cap-with-coupled-normal-energy"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e7c47fc8bdd3d4a176eff69b",
        "source:2309476458c95327666f3251",
        "source:b3a991703736cc50d3346496",
        "source:eb56309a7bf438a9f0eb1a7c",
        "source:9e6f9811c25d1e8af38fae53"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:canonical-clifford-double-derives-normal-ap-and-typed-deck",
      "titleEN": "Canonical Clifford clutch derives normal antiperiodicity and common cross kernel",
      "statementEN": "Opposite normal Clifford transitions unfold D union(-D) into the same D on circumference2ell with antiperiodic closure. L=-ND=partial+B gives S_AP(ell,0)=(2cosh(ell B))^-1, the existing whole charged cross kernel without matching a target. D²=-partial²+B². At finite tangential cutoff logdet_zeta(D²+mu²)=Tr[2ell E_mu+2log(1+e^(-2ell E_mu))]. Full-circle gluing Fredholm factor exists, while bulk retains original renormalization. Natural T=NP_r has square -I and reverses D. Involutive R_odd=i_old NP_r reverses D; R_even=Gamma_tot NP_r preserves D. Both anticommute with Gamma_tot and fail the older [inv,Gamma]=0 if the old grading maps to this Gamma_tot. The actual old grading/real-structure map is unresolved. Actual v252 full192 control confirms15 exact identities.",
      "scopeEN": "Complete geometric operator result for the stated whole product class and standard clutch, stronger than the Cauchy projector alone. No identification with original TFPT tau*,i_C,OS Theta, no universal inconsistency or pair of complete TFPT countermodels. Scalar determinant derivative is not the whole cross operator; retain matching mu regulators. Original reference,Pfaffian phase,source selection,EM readout and physical time remain unproved. C60 reference and Taylor stability arguments do not select R_odd: external-source independence is not background independence, f(0)I is not trace class in infinite dimension, and a negative quartic Taylor truncation does not imply unbounded full heat functional. Unitary D-anticommutation conditionally gives eta_D=0, not boundary eta0.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:whole-product-dirac-with-standard-normal-clifford-double"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:76392203b22774e0c42e1809",
        "source:d1822a0e70032ef4b3572941",
        "source:d261b09db93c7e1e52d8d544",
        "source:90a3e9cc6d068dd3ffabd9b0",
        "source:1c963fb9a386c810c4ddc99f",
        "source:24f2d3e1ce5f07f347c82009"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:universal-graded-source-reducing-images-do-not-fix-carrier-frame",
      "titleEN": "Universal graded reducing images do not fix the carrier frame",
      "statementEN": "For the full independent graded matrix class the common commutant is span{I,Z⊗gamma}, giving exactly two nontrivial reducing projections of rank dimF. Frames retain unitary freedom; every phase chart E_theta has the same image. The intrinsic odd reader is independent of that chart. Reduction does not select its phase.",
      "scopeEN": "Analytic finite classification with exact dimension4,6,8 and symbolic phase controls. Fibre reduction retains the circle; no physical PF, clock identification or new Lean proof, and no transfer to a smaller SM coefficient class.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:full-independent-even-odd-matrix-coefficient-class"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f34056a15de779599a25c0cd",
        "source:da2fc8d50d1298331623950a",
        "source:be527dbdfd6555e64d98364c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-two-face-compression-projector-defect-detects-hidden-source-loss",
      "titleEN": "Whole two-face projector defect detects hidden source loss",
      "statementEN": "At one positive scale K−K²=(QwGW)*(QwGW); K is a projection exactly when VV* reduces H, in which case K=G(V*HV). Single-face equality at every scale is insufficient: symmetric ±a compressed by (1,1)/sqrt2 gives1/2. At a=log2 and ell1 the full compressed cross block is2/5 instead of1/2 with exact defect9/100 I.",
      "scopeEN": "Complete finite proof and rational counterexample. The bounded projector identity extends to infinite spaces but unbounded H retains domain requirements. This is a criterion for closed lossless reduction, not a universal physical PF condition.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:whole-fermi-two-face-projection-and-diagonal-isometric-compression"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f34056a15de779599a25c0cd",
        "source:da2fc8d50d1298331623950a",
        "source:be527dbdfd6555e64d98364c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-v252-quark-lepton-split-prevents-weak-grading-uniqueness-inference",
      "titleEN": "Actual quark-lepton split prevents weak grading uniqueness inference",
      "statementEN": "Actual v252 preserves quarks(rank72) and leptons(rank24) for all its Yukawa, Majorana and SM algebra blocks and internal J. gamma(2q−I) is another internal KO6-compatible grading, distinct from ±gamma, and yields an additional B-reducing rank96 fibre image when A preserves q. Full M96 irreducibility cannot be inferred from this smaller source class.",
      "scopeEN": "Original block proof plus integer coefficient and all24 real SM basis controls. Does not change the original gamma, construct a physical countermodel or test the full normal J or Hochschild orientation. Further original orientation data may select the grading.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-v252-sm-coefficients-and-internal-ko6-without-extra-mixing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f34056a15de779599a25c0cd",
        "source:da2fc8d50d1298331623950a",
        "source:be527dbdfd6555e64d98364c",
        "source:6ab318441602c4a6f1d69a17"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-graded-hypercharge-trace-rejects-quark-lepton-sign-intertwiner",
      "titleEN": "Original graded hypercharge rejects the sector-sign intertwiner",
      "statementEN": "The actual real unimodular v252 gauge lift gives Tr(gammaY³)=0, quark−9/2 and lepton+9/2. gamma_prime=gamma(2q−I) gives−9, excluding every unitary simultaneously preserving Y and intertwining those two fixed gradings. Weak KO6/operator signs alone allow gamma_prime, while the original fixed graded charge tuple is not equivalent. The complete four sector-sign choices have distinct cubic/fifth graded trace pairs: (0,10/3),(-9,-95/12),(9,95/12),(0,-10/3). Only the original (+,+) preserves the fixed joint dictionary.",
      "scopeEN": "Finite trace proof and actual rational96 gauge-lift computation with ten controls. Excludes only the specified simultaneous dictionary intertwiner. Does not derive physical PF or reject every other intrinsic grading on the same normal fibre image, extra sectors or inflow; anomaly cancellation is not treated as sufficient source selection.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:actual-v252-sm-coefficients-and-internal-ko6-without-extra-mixing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f2775d98b36cc2335eecc7f2",
        "source:5c4814e527439cd6e425695c",
        "source:00786f5741af311cc998abe7",
        "source:593bbe3c22290c4f0eb887c2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:separable-normal-real-maps-compose-to-given-deck-and-quarter-image",
      "titleEN": "Separable normal real maps yield existing deck and typed quarter transport",
      "statementEN": "Exactly four normal real types in the stated separable product ansatz. Their product JS JR is the existing Clifford deck, old linear and new antilinear. Scalar quarter shifts violate J-oddness and map to the existing inverse-holonomy source rather than an endomorphism of the same periodic bundle.",
      "scopeEN": "Analytic coefficient/domain result with46 actual controls. Not every96 antiunitary, physical OS reflection or archived inv/Gamma dictionary is classified.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:separable-normal-real-map-with-actual-jodd-gauge-and-typed-quarter-image"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:304267a7124f8ea9afedb48e",
        "source:b20dd96c888a57d172defd54",
        "source:5ede282f1c000796a400b349"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-gauge-real-frames-leave-carrier-phase-as-coordinate-freedom",
      "titleEN": "Actual gauge-real frames leave carrier phase as coordinate freedom",
      "statementEN": "All rephased Etheta intertwine the fixed JS and JF. The fixed P2 gauge/grading/real dictionary admits constant U(3)^6 frame freedom, real dimension54, with negative-grade action determined by J. Actual-slot generators preserve all24 left algebra basis elements and therefore the opposite action. These are coordinate equivalences, not additional physical couplings.",
      "scopeEN": "Completeness uses the six original inequivalent irreps and Schur. Extra fixed Phi, connection or clocks require intersecting their stabilizers. Does not derive physical PF.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:separable-normal-real-map-with-actual-jodd-gauge-and-typed-quarter-image",
        "premise:actual-p2-six-multiplet-gauge-real-coordinate-frame-class"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:304267a7124f8ea9afedb48e",
        "source:b20dd96c888a57d172defd54",
        "source:5ede282f1c000796a400b349",
        "source:a6c008124c2f24a9d53061da"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-higgs-family-has-one-complex-kk-class-but-different-whole-sources",
      "titleEN": "Original Higgs family shares one complex K class but has different full sources",
      "statementEN": "The original bounded radial Higgs perturbation preserves complex graded K-homology on the common compact product domain, while inverse Fermi functional calculus distinguishes every actual h_r and whole source. trPhi_r² distinguishes amplitudes1 and2 from fixed-dictionary frame changes. The boundary reader is not gamma-odd.",
      "scopeEN": "Analytic bounded homotopy with actual96 controls. Does not reconstruct K_car representation/connection, assert realKO without quarter-domain data or vary free Yukawa parameters.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-higgs-radial-family-on-common-compact-product-domain"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9e65081849e2184886ad9e6d",
        "source:404c6751611e6e7995e6af25",
        "source:598de0c3c7e2e305c377866a",
        "source:a98b976eed56f3891f2474a0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:signed-one-particle-modular-weight-is-not-the-positive-even-heat-operator",
      "titleEN": "Signed one-particle modular weight differs from positive even heat operator",
      "statementEN": "The given two-sided signed circle generator has positive unbounded exp(-k), whereas even heat operators are bounded. A two-level exact test separates them. Finite Fock and GNS modular densities act on different spaces. Valid v259 moment arithmetic is retained, while literal untransported operator equality cannot derive the heat profile.",
      "scopeEN": "Only the literal operator comparison, not every correctly defined source transport or the supplied KMS theorem. Exponential domain controls the negative tail and is neither simply H1 nor a subset of all Sobolev domains.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9e65081849e2184886ad9e6d",
        "source:404c6751611e6e7995e6af25",
        "source:598de0c3c7e2e305c377866a",
        "source:d82c5530b43974236da8b89a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:three-moments-select-one-exponential-exactly-in-positive-laplace-class",
      "titleEN": "Three moments uniquely select exponential within positive Laplace cone",
      "statementEN": "Across the entire positive Laplace cone, the moment determinant is nonnegative and vanishes exactly for one point measure, selecting the exponential for moments1,1,1. Variance supplies an automatic concentration bound. General smooth positivity alone is insufficient, as the exact same-moment polynomial counterprofile demonstrates; it is not completely monotone.",
      "scopeEN": "Complete analytic class/equality proof with shared27 controls. Original Bernstein and current action variables still require identification and independently derived moment values. v259 computes moments after inserting exp(-u), so its outputs are not independent selection premises. No new UV kernel or physical state is postulated.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:positive-laplace-profile-finite-three-moment-comparison"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9e65081849e2184886ad9e6d",
        "source:404c6751611e6e7995e6af25",
        "source:598de0c3c7e2e305c377866a",
        "source:b8194634347b132f3be0dff4",
        "source:d2816691788c0acb67faaf49",
        "source:2f59f5cb2a51f488327e1080"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:existing-ap-positive-source-factor-has-oriented-poisson-heat-bridge",
      "titleEN": "Existing positive AP source has an oriented Poisson-to-heat bridge",
      "statementEN": "The existing source is exactly reconstructed from its signR and positive AP factorQ, including the crossing block. Q alone loses orientation. In the explicitly squared argument, this same factor is the diffuse positive subordinated profile exp(-sqrt(u)), with moments1,2,12 and amplitude/scale invariant shape ratio3, whereas every pure exponential has ratio1.",
      "scopeEN": "Analytic whole-spectrum result with18 new exact and actual96 controls. Constructs a bridge for a supplied source without selecting a new source/action. Physical action argument, K_car origin, reference and eta remain required. Does not impose Sbos=fermion logdet or exclude whole TFPT; linear-energy arguments require their own moment convention.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:existing-ap-positive-source-factor-and-declared-squared-energy-comparison",
        "premise:positive-laplace-profile-finite-three-moment-comparison"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7c51024130522c334bc9f3df",
        "source:233bca69b53b793b0287fdc5",
        "source:91bfcfc0fe6b350c3e2d93a5",
        "source:51067aacb72d2ac9448ce55e",
        "source:21d3dd91374387221a9f1e99"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-v252-entire-compatibility-family-has-generic31-dimensional-quotient",
      "titleEN": "Entire original compatibility family leaves generic31 parameters",
      "statementEN": "At actual v252 all84 independent real directions and their whole real family pass the specified compatibility equations. Actual54 U(3)^6 Lie generators have generic orbit rank53, certified by a nonzero exact53 minor and universal baryonic U(1). Generic quotient dimension31. Enumerating the same compatibility predicate cannot select a unique source. This checks the known31 dimensional finite NCG moduli on the implementation.",
      "scopeEN": "Entire family within the specified finite v252 form; basis plus linearity, Gaussian integers and exact rational rank;15 controls passed. Does not impose whole TFPT source/action selection or exclude original provenance; no new Lean theorem/ledger status. Binary2^84 subfamily is covered, not individually enumerated.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-v252-entire-yukawa-majorana-family-with-compatibility-only"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c34e6f407d845cd55b613d30",
        "source:bc7779ba4359db232f61d3db",
        "source:fd0f5d3685c41206086aa5be"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-memory-schur-reconstruction-preserves-every-ordered-word-under-nesting",
      "titleEN": "Full memory reconstruction preserves every ordered word under nesting",
      "statementEN": "For M=I-sum x_a A_a in formal free variables, F_P(F_R(M))=F_P(M) exactly for P<=R with identical variables and order. All block inverses have identity constant term. Full exterior feedback and input/output legs preserve every word coefficient. Gram positivity follows from actual word-vector norms. Minimal representation can be structurally fixed while responses change; stationarity or physical time does not follow.",
      "scopeEN": "Coefficientwise theorem on supplied domain; familiar Schur/Feshbach mathematics. No physical source selection, general analytic UV closure or noncommutative determinant. Whole original Z and unobservable factors are not inferred from a single boundary response; reuse completed F1.M1-M3.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-invariant-word-domain-with-nested-readouts"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b52e3ed67ae75eed66eb87cb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-return-and-native-j-have-minimal68-dimensional-all-word-memory",
      "titleEN": "Original return and native J have a minimal68 dimensional word realization",
      "statementEN": "Exact original Fock polynomials close under L,J,Jdagger in dimension68. Actual positive metric and adjoint closure prove reachability, observability and minimality for all word lengths in this alphabet. Code5 needs memory63 with J multiplicities18,14,17,14 at1,i,-1,-i. Positive original forms F_w give both old defect Delta=sum F_w and new rank5 clock defect sum(w-1)F_w=-2(F_-1+F_i), with F_i=F_-i and ranks4,5,5,5. Original unit f4 has L² response6144 and LJL response0; bare repeated code compression gives1024. Full nested Schur reconstruction through10 equals direct reduction to5 exactly.",
      "scopeEN": "Complete linear realization for specified original single-beta L/J alphabet on neutral grade4:204 exact original-vector identities, positive metric,15 source controls and6 structure controls.68 is neither spacetime dimension nor whole E8 source. Values are response amplitudes, not event probabilities. No new Lean formalization, ledger promotion or full physical origin. Old rank10 was only a lower bound.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:specified-original-pair-ordered-response-composition",
        "premise:original-single-beta-return-with-native-cartan-j-word-alphabet"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:205c404a0498273fd2011515",
        "source:b2b801974284d0791d25a9ee",
        "source:783a0010d91697bbfc715146",
        "source:b6aa00feb0d01f7ee26a44e3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-full-source-regulator-flow-retains-normalized-kernel-and-vacuum-factor",
      "titleEN": "Original full scale flow retains field kernel and null-source factor together",
      "statementEN": "Original v42 integral gives partial_t Z=-D_dotR Z. For q=Z/Z[0],ell=logZ[0],a=(D_dotR q)[0], partial_t q=-D_dotR q+a q and partial_t ell=-a. Exact reweighting and conditional factors retain all original field responses and reference normalization through actual fibers without Gaussianizing. Keep mixed exterior legs. Gamma=Gamma_norm-ell retains geometric scalar response; at J=0, Gamma[phi_bar]+V_R[phi_bar]=-ell, not generally Gamma[0]=-ell. Reuses prior null-source result in the actual v42 flow.",
      "scopeEN": "Whole functional identities for supplied original integral; no existence proof of complete physical source. All8 even-density and6 bilinear-regulator Grassmann coefficients checked exactly; bosonic inverse heat series requires convergence. Retain geometry,reference,eta and original given time. Native68 state space is not configuration field space. No Lean or ledger promotion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:original-regulated-full-source-with-actual-measure-and-legs"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7816b374a7515b08d57a537b",
        "source:11363fc8655cdd14c912d9ce",
        "source:0f0877c5b4346959c8f074a7",
        "source:15ba296fa366878a2b8513c9",
        "source:085e01bec9934e9e368c7f12",
        "source:a183d1e53c635a8c97bda462"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-reflected-quadratic-regulator-cone-preserves-every-rp-source",
      "titleEN": "Entire reflected quadratic regulator class decided by negative cross matrix",
      "statementEN": "In specified finite class exp(-phi R phi/2) preserves every original positive RP measure iff C is negative semidefinite. Bounded reflected feature expansion gives sufficiency; RP product Gaussian with Gcross=((I+A+C)^-1-(I+A-C)^-1)/2 and inversion order gives necessity, without simultaneous diagonalization. Cone closed under addition; R_k to zero recovers original source by finite dominated convergence. Exact RP baseline C0=[[1,1/2],[1/2,1]],R=ones,P_adm=I gives reflected response-1/16 despite ordinary positivity and structural commutation. Existing generic spectral-weight exclusion is reused, not recounted as new proof.",
      "scopeEN": "Complete universal preservation theorem only for specified bosonic two-half class. Known RP-cone mathematics specialized to original IR caller. Not necessary for every regulator of one fixed source, not full P1 countermodel or proof of original S_adm RP.18 controls together with source flow; analytic class proof separate. No new physical model optimization.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:finite-reflected-positive-quadratic-ir-regulator-class"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:232072059a5a50cff9e334fd",
        "source:085e01bec9934e9e368c7f12",
        "source:a183d1e53c635a8c97bda462"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-shared-higgs-source-induces-fixed-yukawa-mixed-matter-words",
      "titleEN": "Shared original Higgs source induces coupled matter words with supplied Yukawas",
      "statementEN": "All288 real coefficient basis images of actual full96 one-form consumer match four H derivatives exactly with adjoints,grading and JF. Same supplied H fiber gives exact affine Z_H[J-j|A],all cumulants and absolute factor. Induced ordered nu/up four-fermion action coefficient is -G_h2barh2 Ynu_ab conjugate(Yu_dc),no factor2; third/fourth boson cumulants give6/8 fermion terms. Retain all extra H dependent fermion vertices,which can also alter four-fermion coefficient. Fermion-first evaluation uses actual det/Pf weighted full source polynomials,with minors at singular fibers rather than inverse division.",
      "scopeEN": "Actual original field consumer and whole finite source identity for supplied boson moments. Reuses old one-form and kinetic Pfaffian/determinant bridges. No new physical H measure,naive96 independent fermion integrations,full connected/1PI amplitude or universal nonzero coefficient at degenerate G/Y.17 controls including288 original identities; general proof analytic. Preserve Yukawa/Flavor/Alpha and free g+ results.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:37d8b3d9fa0981776fabedf6",
        "source:2ffecdf78624207cfe526587",
        "source:b300a5432b979c720fcb5622",
        "source:75bd3bb3e391dd0b100c78af",
        "source:848fceac6437e957e974b7d0",
        "source:ca675dd4ab18367e438db2c1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:local-even-yukawa-sewing-preserves-given-joint-graded-rp",
      "titleEN": "Local even Yukawa sewing preserves supplied joint graded RP",
      "statementEN": "Original v42 mixed RP inference does not follow from commutation and separately positive marginals. Strictly positive reflection-invariant logical control p=(1-r xminus xplus yminus yplus)/16 has RP product marginals and mixed reflected form-r. Constructive full replacement: for actual joint graded RP reference and even local half action B=exp(-Vplus), omegaY(ThetaF circ F)=omega0(Theta(BF) circ BF)/omega0(ThetaB B)>=0 with positive normalization and integrability. Handles whole supplied Yukawa class with adjoint partner wherever same actual reflection intertwines H/matter density. No pointwise positive determinant required.",
      "scopeEN": "Specialization of known RP half-action mathematics to actual Yukawa consumer,not new general RP theorem. Finite Euclidean graded path or proved integrable limit. Internal JF reality does not prove common spacetime reflection. No unchecked spectral/eta/gauge weights,fixed-plane/cross insertions. Logical marginal control is no TFPT countermodel. Old negative-cross criterion applies to regulator R,not Higgs propagator G. No original boson source selection or3+1D completion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber",
        "premise:original-graded-rp-reference-and-even-local-reflected-half-action"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:683f130dd1e649b7652fda11",
        "source:b300a5432b979c720fcb5622",
        "source:75bd3bb3e391dd0b100c78af",
        "source:03658bf5209de73b65042022"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-original-constant-higgs-orbit-has-reduced-majorana-spectral-response",
      "titleEN": "Whole original constant Higgs fiber has reduced Majorana spectral response",
      "statementEN": "For all H and supplied Y,Phi(H)=V(q/r)(rDY+DMR)V*,weak left rotation with same JF/gamma and unchanged MR.84 real Y/MR basis images on actual original96 confirm block proof. det96(z+Phi²) reduces exactly to charged3x3 powers12,12,4 and squared6x6 neutrino determinant Bnu=[[rYnu,0],[MR*,rYnu^T]]. First u jet is4/z Tr(3Yu*Yu+3Yd*Yd+Ye*Ye)+4Tr[(z+MR MR*)^-1Ynu*Ynu],retaining necessary Majorana cross-resolvent term. On supplied quarter circle the whole absolutely convergent mode sum is evaluated by s_alpha(v)=pi/sqrt(v)sinh(2pi sqrt(v))/(cosh(2pi sqrt(v))-cos2pi alpha).26 controls pass.",
      "scopeEN": "Whole constant original coefficient class and named1D product circle,no new physical parameter choice. Internal96 spectral multiplicity is not96 independent fermion integrations. No free Yukawa search,whole4D Z master or full dynamic H covariance. Nonconstant H,fixed nontrivial A and global projections retain original connection,domain and source transport. Existing weak-connection mixing response remains valid.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber",
        "premise:original-constant-higgs-fiber-and-symmetric-majorana-spectral-consumer"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:52608b081ed7625fa0968069",
        "source:e34295c925b018a46b5612c8",
        "source:7e8d08bf014e8242271cd92a",
        "source:848fceac6437e957e974b7d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:archived-geometric-higgs-residue-bulk-needs-coefficient-identification-repair",
      "titleEN": "Archived geometric Higgs residue requires concrete coefficient identification repair",
      "statementEN": "Printed -6chi²ED+GammaD4 gives bulk +chi²u/(8pi²)+u²/(16pi²) at R0. Equal quadratic/quartic signs match neither printed target potential -mu²u+lambda u² nor its -V reading. Positive canonical/sheet normalization and common action/Wick sign cannot repair relative sign. For same u,+V requires original remainder -chi0²(1+wH²)u/(8pi²),-V requires chi0²(wH²-1)u/(8pi²)-u²/(8pi²). Required source responses,not permitted new addends. H-independent U(chi) or constant source denominator at fixed chi do not help. Keep FPzeta(0) distinct from -zetaPrime(0),and M(xi) distinct from H-source/Legendre/bare actions.",
      "scopeEN": "Exact failure of a literal identification of specifically named archived local formulas. No TFPT countermodel,physical vacuum-instability claim or exclusion of existing Yukawa/Flavor/Alpha. Full relative source,reference,eta,scale and continuation can carry further H contributions and must be evaluated. Existing local target quartic and its conditional responses remain; direct derivation from this printed bulk is not established. No new Lean theorem or ledger status.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:literal-archived-geometric-residue-and-common-higgs-field-comparison"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:83b13a1d2fde0a18b70650a4",
        "source:e34295c925b018a46b5612c8",
        "source:7e8d08bf014e8242271cd92a",
        "source:4a3c63393512886758ffbf49",
        "source:6a4bd14f00c55e7a56c8e286",
        "source:2bd56469aa61e8a26caac5bc",
        "source:78829ccc5fc409d7c3e4ce81",
        "source:4a1ae0e9abbb2d11e22e448e",
        "source:0097eebe93ca2397e6289977"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-local-higgs-residue-linear-coefficients-fail-same-trace-heat-ratio",
      "titleEN": "Original local Higgs residues fail common linear heat ratio",
      "statementEN": "Literal local Erel=-R/4-X gives coeff_ED(u)=-12 coeff_Gamma4(Ru),independent of rank/common linear trace weighting,including subtraction of two same-type Dirac producers. Named archived printed values -1/(48pi²),+1/(96pi²) give-2,a factor6 mismatch. With ordinary48 trace and rank2,whole printed ED bulk equals a2/6 while quartic/Ru match a4;conditional normalization diagnosis,not new original definition. If displayed E is complete and connection H-independent,integrated a4 gives no Higgs kinetic term;Delta u is a total derivative. Fixed boundary/reference data and s-independent iEta cannot repair real ED jet. Actual bound-reference variation is deck-even part of operator jet and may be frozen only upon established deck-oddness.",
      "scopeEN": "Excludes specifically named literal local heat identification,not whole TFPT or existing target action,Yukawas/gravity. Nonlocal Padm,different symbol,moving domain or additional original curvature terms require their actual producer. R029 sign problem is separate;+6 alone does not repair ratio.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:literal-archived-geometric-residue-and-common-higgs-field-comparison",
        "premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ca92db3e2acc99fce053d868",
        "source:b71e83cc555cb5aee24d8ab6",
        "source:9cea7949cb863edb29fb265b",
        "source:14d4e0f7ffa1a9459c41f89d",
        "source:78829ccc5fc409d7c3e4ce81",
        "source:e52e69eb286468b9df3ae67e",
        "source:6a4bd14f00c55e7a56c8e286",
        "source:b1ca5668b0b8866c58449189"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-original-higgs-moments-fix-conditional-local-kinetic-mass-quartic",
      "titleEN": "Whole original Higgs moments jointly fix conditional local kinetic mass and quartic",
      "statementEN": "Whole original96 family satisfies Tr(Phi²-DM²)=Au,Tr(Phi⁴-DM⁴)=Bu²+4Cu,Tr(dPhi)²=Akin,A=4Y2,B=4Y4,C=2Tr(Ynu*Ynu MR MR*)>=0. Generic block proof and unchanged v252 consumer confirm identities including four-real derivative Gram matrix. Explicitly conditional standard4D product Dirac with separate spin trace gives a2H=-Au/(4pi²),a4H=Akin/(8pi²)+Bu²/(8pi²)+Cu/(2pi²)+ARu/(48pi²).For cchi²a2+da4,Z=dA/(8pi²),mu_can²=2(c/d)chi²-4C/A-R/6,lambda_can=8pi²B/(dA²). At R0 negative quadratic requires cchi²A>2dC;c=-6,d=1 gives positive quadratic for all supplied Y/MR.28 direct controls pass;control numbers are not new physical parameters.",
      "scopeEN": "Whole original finite coefficient class and named conditional local consumer. No new Y choice,96 extra physical fermion integrations,derived original boson measure,physical pole mass or full H covariance. Finite96 trace,geometric48 E and compact P2 require actual common map;printed scalar quartic must not be renamed.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-constant-higgs-fiber-and-symmetric-majorana-spectral-consumer",
        "premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ca92db3e2acc99fce053d868",
        "source:b71e83cc555cb5aee24d8ab6",
        "source:9cea7949cb863edb29fb265b",
        "source:14d4e0f7ffa1a9459c41f89d",
        "source:848fceac6437e957e974b7d0",
        "source:52608b081ed7625fa0968069",
        "source:b1ca5668b0b8866c58449189"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-variable-original-higgs-bound-reference-response-and-forced-clifford-factor",
      "titleEN": "Whole variable original Higgs bound-reference response and forced Clifford factor",
      "statementEN": "Fixed spin4 Clifford contract forces {gamma_mu,W}=0 hence W=gamma5 L(H),with gamma5=Z in given collar chart;H derivative in E follows by squaring. Put p=(H+Htau)/2,m=(H-Htau)/2,P=|p|²,M=|m|²,v=Re p*m,QS=P²+2PM+4v²,QT=M²+2PM+4v². Bound original references L(m),L(p)+DM give after H0 baseline:a2S=-A intP/(4pi²),a4S=int[A|Dp|²+BQS+4C(P+M)]/(8pi²)+A intRP/(48pi²);a2T=-A intM/(4pi²),a4T=int[A|Dm|²+BQT+4CM]/(8pi²)+A intRM/(48pi²). Normal derivative parity transported. Only reflected-pair quartic mean is nonnegative;raw local difference can be negative. S cannot repair R0 mass sign or ratio-12 in -6chi²a2+a4. T cancels entire unscaled same-geometry pair response for purely even H at every spectral order.",
      "scopeEN": "Whole variable fields and supplied finite coefficients in named local product/reference contract. No primitive lift selection,derived spacetime origin,deck/RP identification,RP proof from positive integrated action,or exclusion of separate original fermion source/full TFPT.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer",
        "premise:whole-variable-higgs-bound-reference-and-conformal-dirac-map"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:039eb8d38b194a51c6147af4",
        "source:f76af118431de9a886f088be",
        "source:d596995b98ba7991b5c1b9c5",
        "source:ca8672e219b410b47a6163e0",
        "source:848fceac6437e957e974b7d0",
        "source:c97f5e1ef7056d4b9bea3274",
        "source:b6282f43d19905759fe14fa9",
        "source:20271554929f9198008f7754",
        "source:e52e69eb286468b9df3ae67e",
        "source:6a4bd14f00c55e7a56c8e286",
        "source:b1ca5668b0b8866c58449189"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-symmetric-scale-map-fails-simultaneous-higgs-einstein-repair",
      "titleEN": "Original symmetric scale map fails simultaneous Higgs and Einstein repair",
      "statementEN": "Given4D spin realization gives Dsigma=fDf unitarily equivalent to Dirac_ghat+gamma5 exp(-sigma)Phi,ghat=exp(2sigma)g,U=exp(2sigma)F^-1. H and DM scale together. H-dependent a2=-A int exp(2sigma)|H|²/(4pi²);integrated a4H invariant up to divergence,including Majorana term. For deck-even sigma,UNSCALED bound reference,t=exp(2sigma):a2SrelH=-A int[tP+(t-1)M]/(4pi²),a2TrelH=-A int[tM+(t-1)P]/(4pi²),a4 as R032. t-1 not always positive. Constant sigma,pure even H,S branch gives H²/RH² ratio-12t. t=1/6 alone would match printed-2,but same ordinary positive trace/same bundle gives Einstein a2relR=-N(t-1)intR/(192pi²),POSITIVE at1/6 versus printed NEGATIVE for all N>0. Jointly scaled reference cancels pure Einstein response. Variable sigma adds -N int6t|dsigma|²/(192pi²). Complete Ksigma=fDgeof+Brel is not resolved by B0 test. Dsigma² differs from exp(-sigma)D²exp(-sigma).",
      "scopeEN": "Executed original scale map within named product realization/two explicit reference conventions. Not general exclusion of different original Brel/symbol/trace/domain data,no free Psi coupling,joint sigma backreaction,or whole H source integration. Read metrology owner names Brel without evaluating its H component there;not corpus-wide absence claim.29 direct controls,exact generic proofs,and actual The reviewed/Gemini/the reviewed source review.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:literal-archived-geometric-residue-and-common-higgs-field-comparison",
        "premise:whole-variable-higgs-bound-reference-and-conformal-dirac-map"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:039eb8d38b194a51c6147af4",
        "source:f76af118431de9a886f088be",
        "source:d596995b98ba7991b5c1b9c5",
        "source:ca8672e219b410b47a6163e0",
        "source:848fceac6437e957e974b7d0",
        "source:c97f5e1ef7056d4b9bea3274",
        "source:b6282f43d19905759fe14fa9",
        "source:20271554929f9198008f7754",
        "source:e52e69eb286468b9df3ae67e",
        "source:6a4bd14f00c55e7a56c8e286",
        "source:b1ca5668b0b8866c58449189"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-original-higgs-inner-scale-and-affine-full-source-transport",
      "titleEN": "Whole original Higgs producer scales jointly and has exact affine full-source map",
      "statementEN": "Exactly [fDf,b]=f[D,b]f,hence A_sigma=fAf including real completion,also for variable sigma without omitted df commutator. Actual inner change is V(H)=gamma5[L(H)-DY],not entirePhi again. K_in=fDstarf+qV(H)=fD_Hf,q=f²=e^-sigma. Same unscaled outside change gives K_out(H)=K_in(Hstar+q^-1(H-Hstar)). InverseH=qh+(1-q)Hstar;H0 does not map to0. Whole finite source:Zout[j]=(prod q^4)exp(sum(1-q)j.Hstar)Ztilde[qj],with actual pulled-back action,all extra vertices and reference;other measures by pushforward. Higher cumulants retain external q factors,mean shifts,absoluteZ0 retains measure factor. Whole same inner fluctuation thus falls under R033;mere relocation with full coordinate transport is no new physical repair.",
      "scopeEN": "Whole original H/Y coefficient class and named finite source contract. Does not prove packaged originalBrel equals this vertex. Same named H with unchanged action/reference is another comparison;no general exclusion of different original producers. No continuum anomaly exclusion,new state,or joint sigma backreaction.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber",
        "premise:original-inner-higgs-central-scale-and-finite-affine-source-map"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5da18e093f0b30ca805ce420",
        "source:01f538f254f5a549c832c64d",
        "source:12e5e737d5148d94efb4ccda",
        "source:5372f60dc934dbebcc4200c5",
        "source:848fceac6437e957e974b7d0",
        "source:6d284944db8757876c1537a2",
        "source:20ba7d005ffba64df6121ea0",
        "source:85d9d4e9d4a2e67bc8280371",
        "source:a162b449a911d408b1591593",
        "source:ca675dd4ab18367e438db2c1",
        "source:2c030511ad7371b889126645",
        "source:2bd56469aa61e8a26caac5bc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:normal-higgs-mode-type-and-exact-kernel-metric-require-actual-relative-operator-map",
      "titleEN": "Normal Higgs mode type and exact kernel metric fix required original Brel bridge",
      "statementEN": "Hom_G^R(H,End_C(C3+C2))=0:color center removes cross blocks,weak center is even on diagonal endomorphisms and odd on H. Original whole96 wedge/Yukawa consumer remains valid. Normal B_Ea has different first symbol and is not its zero mode or coupling. BP0=0 impliesP0BP0=0,not vanishing Higgs vertex. For actually given B_sigma=fBf,S*S=I,rangeS=kerB:kerB_sigma=f^-1kerB,G=S*f^-2S>0,T=f^-1S G^-1/2. T*(fXf)T=G^-1/2 S*XS G^-1/2;unscaledX needsf^-1Xf^-1 inside. G can be nonscalar. For q constant on normal fiber,T=S;normalization does not select vertex placement. Two-complex-mode d4Hraw=(det_CG)^-1d4Hnorm differs from q^4 Jacobian of other affine map.",
      "scopeEN": "Excludes only bare5-slot mass insertion;exact full given normal kernel map under explicit scale/domain. No new normal space,physical spin/gauge identification,retraction of original Higgs/Yukawa results,or absence of field algebra claim. Actual original B_Ea/bosonic-relative reduction to Brel and same Tr_rel with normal metric/insertion remain needed;names/index alone insufficient.33 controls and independent generic proofs.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-normal-higgs-mode-realization-and-distinct-module-types"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5da18e093f0b30ca805ce420",
        "source:01f538f254f5a549c832c64d",
        "source:12e5e737d5148d94efb4ccda",
        "source:5372f60dc934dbebcc4200c5",
        "source:848fceac6437e957e974b7d0",
        "source:6d284944db8757876c1537a2",
        "source:20ba7d005ffba64df6121ea0",
        "source:85d9d4e9d4a2e67bc8280371",
        "source:a162b449a911d408b1591593",
        "source:ca675dd4ab18367e438db2c1",
        "source:2c030511ad7371b889126645",
        "source:2bd56469aa61e8a26caac5bc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-superconnection-grades-and-weighted-heat-retain-higgs-kinetic-excursions",
      "titleEN": "Whole superconnection and weighted heat retain Higgs kinetics through exterior components",
      "statementEN": "Quillen A² splits by form degree into F,DPhi,Phi². In given full product square i gamma^mu gamma5 DmuPhi has spin degree3,orthogonal to every ordinary internal gamma^munuFmunu;no hidden ordinary two-form derivative. A compressed endomorphism can still exactly contain mass without Hkinetics:for parallel spin-compatibleP,a4[TrP exp(-tL)]−a4[Tr_PH exp(-tPLP)]=(32pi²)^-1 int tr(P E Q E P). Actual internalP+=(I+GammaF)/2 with oddPhi gives compressedE−P Phi²P without derivative;full weighted heat retains A/(16pi²)int|DH|² difference. Mass/RH² also halved,ratio−12 unchanged,so this alone does not fix printed factor6.",
      "scopeEN": "Concrete algebraic alternative to globally declaring printedE incomplete. Does not establish originalTr_rel reader or printedI48/P2=internalP+=normalP. WholeY/MR-weighted P Phi²P is notu times rank2projection. Clifford-valuedF needs actual dictionary. No physical spacetime origin,new coupling or globalno-go.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-product-clifford-grades-parallel-projection-and-complete-relative-block-reader",
        "premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c108aa1ab95c0445a592d857",
        "source:eb1f2e6b0227ba0ae14ca9b3",
        "source:2fb53547b0c3b574ae83fc4d",
        "source:035682bd18b6773db7d3b0ac",
        "source:848fceac6437e957e974b7d0",
        "source:417053dba23fdd907e310aff",
        "source:e52e69eb286468b9df3ae67e",
        "source:6a4bd14f00c55e7a56c8e286",
        "source:bd619cc4b84c83f2c90238ef",
        "source:a162b449a911d408b1591593",
        "source:ca675dd4ab18367e438db2c1",
        "source:411120cbda538239f28969b7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-normal-reduction-preserves-relative-spectral-reader-and-higgs-jets",
      "titleEN": "Whole normal reduction preserves relative spectral trace and first Higgs responses",
      "statementEN": "PK²P−(PKP)²=PKQKP=(QKP)*QKP≥0;for[P,K0]=0 andK0+tV defectt²PVQVP. Original96P+hasP+PhiP+=0 whileTrP+L(H)²=A|H|²/2. K−z=[[A,B],[C,E]],R=E^-1,S=A−BRC full inverse retains all4blocks. Unweightedfulltrace=TrR−Tr(S^-1 dzS),dzS=−I−BR²C;apply actual weightedtrace to allblocks. (K²+omega²)^-1 uses both K±iomega resolvents;retain same reference/eta and original continuation. Full finite source keepsdetEdetS,two shifted legs and directQterm. Complete affineHjet recursion andlogdetH²/H⁴ with nonzeroB0/C0 andnoncommutingblocks executed.",
      "scopeEN": "Extends existingSchur/memory results with same geometric spectralreader,rather than relabeling them new.36controls andgeneric algebra. No numericnormalblocks,physicalgap ornewmetric chosen. Finite logdetjets are notFPzeta0 orautomatica2/a4;no multiplicativity of separatezetadets. IndefiniteR gives no universalSchursign. Distinguish parallel/nonparallelP andmovingframes. OriginalB_Ea→Brel/Tr_rel mapnotderived;F1remainsopen.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-product-clifford-grades-parallel-projection-and-complete-relative-block-reader",
        "premise:given-normal-higgs-mode-realization-and-distinct-module-types"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c108aa1ab95c0445a592d857",
        "source:eb1f2e6b0227ba0ae14ca9b3",
        "source:2fb53547b0c3b574ae83fc4d",
        "source:035682bd18b6773db7d3b0ac",
        "source:848fceac6437e957e974b7d0",
        "source:417053dba23fdd907e310aff",
        "source:e52e69eb286468b9df3ae67e",
        "source:6a4bd14f00c55e7a56c8e286",
        "source:bd619cc4b84c83f2c90238ef",
        "source:a162b449a911d408b1591593",
        "source:ca675dd4ab18367e438db2c1",
        "source:411120cbda538239f28969b7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-admissibility-own-spectral-reader-has-no-free-low-mode-residue-repair",
      "titleEN": "Original admissibility reader reduces its own operator without a free residue correction",
      "statementEN": "The original Padm spectrally reduces its own positive Ladm, so whole weighted heat and restricted heat coincide. Original local-net observables reduce the admissible space when both the operator and adjoint preserve it; this does not cover every source or Ksigma. Removing finitely many low modes subtracts an entire function from zero-excluded zeta: all residues remain unchanged and FP0 shifts by minus the positive removed count. Heat also counts removed zero modes. The full low count is constant without threshold crossings; the positive count additionally requires constant nullity. Zero-appearance jumps cancel in cut FP0. No continuous Higgs or Einstein correction follows, whereas logdet can carry Higgs responses. Transport the original spectral projection with its operator.",
      "scopeEN": "Reuses established high-pass, zero-penalty and kernel results; new result is the whole spectral, FP and residue consequence. Does not derive the original domain/reference map from Ladm to Ksigma² or equate a normal Higgs kernel with the same kernel. Infinite low bands and other traces or continuations are outside scope. No global TFPT refutation.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-positive-admissibility-reader-and-given-total-chiral-product"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:de0206aa98c05d15dd3b8a04",
        "source:a3cb4484c95cb19bc4b54f5e",
        "source:f85d19ca6c19f0b3077d08e2",
        "source:e12690961262150833f4c8cd",
        "source:75554c5535c27abac436633f",
        "source:325d54d6b6a2a3ab8e24ade1",
        "source:574d3f21bd2b578cf95cdd8f",
        "source:417053dba23fdd907e310aff",
        "source:e52e69eb286468b9df3ae67e",
        "source:6a4bd14f00c55e7a56c8e286",
        "source:a162b449a911d408b1591593",
        "source:ca675dd4ab18367e438db2c1",
        "source:848fceac6437e957e974b7d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-total-chiral-positive-spectrum-retains-higgs-kinetics-and-common-half-trace",
      "titleEN": "Whole total-chiral positive spectral reader retains Higgs kinetics and common halving",
      "statementEN": "In the given Spin4×96 product, total Gamma=gamma5⊗GammaF anticommutes with D_H. Pc is parallel but does not commute with individual gammaMu. The Higgs derivative is spin odd and internally odd, hence total even: Pc retains it and reduces D_H², unlike the internal half in R036. Equal rank does not identify these projections. Every selfadjoint odd K with grading-stable domain pairs all positive spectra of T*T and TT* including multiplicities. Thus every allowed summable zero-excluded Pc spectral trace is exactly half; heat including zero modes adds half the index. A common positive high-pass of the same K² removes this index remainder. Scalar f preserves oddness; a bound reference requires its actual domain and tauGamma tau^-1=±Gamma. H-dependent a2/a4 supertraces vanish in this product: H²,RH²,kinetics,H⁴ share the same half and the ratio remains −12.",
      "scopeEN": "No physical chirality origin or identification with Padm, printed I48/P2 or normal Higgs projection. Retains local H-independent index density, absolute zero modes, boundary eta, reference, Z0 and phases. Half an action is not an ignorable normalization and proves no equal H moments, Pfaffian, mixed sources or RP. Actual Brel and domain/reference realization remain to evaluate; do not double count the existing H insertion.43 direct controls, no new Lean formalization.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-positive-admissibility-reader-and-given-total-chiral-product",
        "premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:de0206aa98c05d15dd3b8a04",
        "source:a3cb4484c95cb19bc4b54f5e",
        "source:f85d19ca6c19f0b3077d08e2",
        "source:e12690961262150833f4c8cd",
        "source:75554c5535c27abac436633f",
        "source:325d54d6b6a2a3ab8e24ade1",
        "source:574d3f21bd2b578cf95cdd8f",
        "source:417053dba23fdd907e310aff",
        "source:e52e69eb286468b9df3ae67e",
        "source:6a4bd14f00c55e7a56c8e286",
        "source:a162b449a911d408b1591593",
        "source:ca675dd4ab18367e438db2c1",
        "source:848fceac6437e957e974b7d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-scale-energy-response-uniquely-reconstructs-normal-profile",
      "titleEN": "Whole energy response uniquely reconstructs the normal scale profile",
      "statementEN": "Whole K=fK0f has kernel f^-1kerK0 and identical correctly transported zero-energy Cauchy space,including full variable Phi=L(H)+DM. Actual energy resolvent retains exp(sigma):G(z)=f^-1(K0−z exp(sigma))^-1f^-1 and (K²+omega²)^-1=f^-1Rplus exp(sigma)Rminus f^-1. Existing homogeneous collar gives first-energy moments M_n=int0ell exp(sigma(r))exp(-2rE_n)dr,where E_n=sqrt((n+alpha)²+mu²) is from one unchanged fullPhi² branch. Muntz density of lambda_n=E_n−E0 proves uniqueness of the entire continuous normal profile from ALL moments. Explicit positive Gram gives convergent L² recovery;existing flat source gives exactly w=1.",
      "scopeEN": "Extends existing massless Cauchy transport using existing normal source without choosing it anew. No finite/noisy stability theorem,no angular sigma recovery or physical scale origin. Original whole Dplus/continuation must actually supply Tprime(0);P(0) alone does not. No Ladm=Ksigma² identity,no invariant absoluteZ0 or full dynamicHiggs measure. ExteriorBrel may change the inner operator itself.15controls are algebraic/numerical diagnostics,not physical proof.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:whole-original-scale-congruence-and-specified-normal-energy-data"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:41769106603ac7daae415b1c",
        "source:cf2e8846aa9fe28dba9d7a82",
        "source:1aff3dea755c86a75bcc75e7",
        "source:29819559d46551b3d0414760",
        "source:3295e28477ad21a4fb0dd36a",
        "source:f25f7118e958734c09c55693",
        "source:666f49c8dea3f8819e27c103",
        "source:75554c5535c27abac436633f",
        "source:a3bdadfcea9b1004b36c0503",
        "source:565dab148497fbe612c65eae",
        "source:a3cb4484c95cb19bc4b54f5e",
        "source:e52e69eb286468b9df3ae67e",
        "source:4cf1b24f3ae484ba7d29ce89"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-relative-scale-flow-separates-residue-finite-part-and-local-anomaly",
      "titleEN": "Original relative scale flow separates residue,finite part and local anomaly",
      "statementEN": "Interior h=delta sigma gives deltaK=−{h,K}/2 and deltaZeta(s)=2sTr(hL^-s). If inserted zeta is regular at0,FP0 is invariant while delta logdetL=−2FP0Tr(hL^-s);with simple poles deltaED=2Res1Tr(hL^-s). Original ordinary product a4H additionally contains divergence−(2A/3)Delta|H|²/(16pi²),which cannot be discarded under local h. Actual exteriorBrel gives Wext=deltaBrel+{h,Brel}/2(+fdeltaDgeof) and deltaZeta=2s[TrhL^-s−Tr(Wext K L^-s-1)]. Retain reference,eta,zero modes,domain and trace response. PcK=KQc,not commutation:given odd-family chiral variation is half the whole,not naive inserted Pc trace.",
      "scopeEN": "No anomaly term invented to repair originalFP0,no identification of logdet with original action/Z0. No arbitrary weighted trace assumed cyclic. Wext=0 is sufficient,not necessary for vanishing residue. Preserves prior wholeH/Einstein results and factor6. Primary method comparison hep-th/0306138 Section7.1. Cauchy equality determines neither action measure nor operator origin. No new Lean formalization or ledger promotion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:whole-original-scale-congruence-and-specified-normal-energy-data",
        "premise:original-positive-admissibility-reader-and-given-total-chiral-product"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:41769106603ac7daae415b1c",
        "source:cf2e8846aa9fe28dba9d7a82",
        "source:1aff3dea755c86a75bcc75e7",
        "source:29819559d46551b3d0414760",
        "source:3295e28477ad21a4fb0dd36a",
        "source:f25f7118e958734c09c55693",
        "source:666f49c8dea3f8819e27c103",
        "source:75554c5535c27abac436633f",
        "source:a3bdadfcea9b1004b36c0503",
        "source:565dab148497fbe612c65eae",
        "source:a3cb4484c95cb19bc4b54f5e",
        "source:e52e69eb286468b9df3ae67e",
        "source:4cf1b24f3ae484ba7d29ce89"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-whole-green-produces-energy-response-with-correct-orthogonal-trace",
      "titleEN": "Original whole Green kernel produces energy response with correct orthogonal trace",
      "statementEN": "Energy insertion in same source forcesA_z=B+zN. ExistingAP Green/Poisson call givesC_z=[[a,Ta],[Ta,T²a]],a=(I+T²)^-1. For realz it is oblique;actual orthogonal graph projection is[I;T](I+T*T)^-1[I,T*]. At0 and both±iomega,C=Q. Exact whole±E block formulas giveQprime0=[Cprime0,C0] with normtanh(ellE)/(2E)≤2 uniformly over ALL quarter modes. Same original fixedAPS source with BOTH endpoint columns gives same Cauchygraph without vacuum identification. Singlecrosskernel has derivative0 on adapted block despite nonzeroTprime. Actual whole energy response givesR040 flat moments(1-exp(-2ellEn))/(2En);existing flat source is now read from its given producer.",
      "scopeEN": "No physical scale origin or Ladm=Ksigma². Real orthogonalQ is not holomorphic,transfer quotient only modewise,no globally boundedQ11inverse. No rescan ofR040 normal profile class. No movingAPS(H)replacement.31controls diagnostic,wholecircle analytic;no newLean formalization.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-whole-green-energy-source-and-conditional-scale-response",
        "premise:whole-original-scale-congruence-and-specified-normal-energy-data"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d7370097d2e0ac2cd87782b7",
        "source:b24140fc363b06213210515d",
        "source:50f76e194e262be8dbb50279",
        "source:e25ec3e969dd17307d2b15b6",
        "source:a3bdadfcea9b1004b36c0503",
        "source:dc4025fcf9e58b9ccf8cca94",
        "source:4f19a83cddbf837f24ff3aff",
        "source:555a2cf54a211a87baae422c",
        "source:3295e28477ad21a4fb0dd36a",
        "source:a162b449a911d408b1591593",
        "source:2c030511ad7371b889126645"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-mixed-scale-source-reads-bosonic-insertion-before-higgs-average",
      "titleEN": "Whole mixed scale source reads bosonic insertion before Higgs averaging",
      "statementEN": "For actual conditionalG=(K−z)^-1 anddeltaK=−{h,K}/2+W,deltaG={h,G}/2+zGhG−GWG. Whole original scale response determinesW as operator form throughGWG without trace/residue information loss. Existing inner96vertexf gamma5L(deltaH)f givesdeltaH W=0;rigidouter insertion gives{h,I}/2,without choosing either as originalBrel. DynamicH obeysdelta<O>=<deltaO>+Cov(O,delta log rho),delta logZ0=<delta log rho>. Rho retains boson measure,absolute fermionic factor,reference and phases. Inverting averagedG does not replace this whole conditional/mixed source map.",
      "scopeEN": "Direct check,not a proved originalB_Ea→Brel/Tr_rel reduction. Original normal index operator and existingWedge→96H consumer remain distinct. No free overlap weight,no secondPhi,noFP0=logdet/Z0 or anomaly term. Commonphysicalorigin and factor6 remain toresolve.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-whole-green-energy-source-and-conditional-scale-response"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d7370097d2e0ac2cd87782b7",
        "source:b24140fc363b06213210515d",
        "source:50f76e194e262be8dbb50279",
        "source:e25ec3e969dd17307d2b15b6",
        "source:a3bdadfcea9b1004b36c0503",
        "source:dc4025fcf9e58b9ccf8cca94",
        "source:4f19a83cddbf837f24ff3aff",
        "source:555a2cf54a211a87baae422c",
        "source:3295e28477ad21a4fb0dd36a",
        "source:a162b449a911d408b1591593",
        "source:2c030511ad7371b889126645"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:current-original-spectral-action-triplet-fails-positive-laplace-class-unless-leading-relative-term-cancels",
      "titleEN": "Current full coefficient triplet fails positive Laplace class with stated relative exception",
      "statementEN": "Current master isTrf((Drel+AΣ)/chi)−Trf(Dref/chi)+iπDeltaeta/2,not archived−6Res1+FP0. Sameordinary heat coefficients giveheat(1,1,1),Poisson(12,2,1). Actualv255/v259combination prints(2,2,1),mixing moment variables and2prefactors. Applying existingR017 theorem requires(m0,m1,m2)=(1,2,2),determinant−2;no profile inENTIREpositiveLaplace class realizes fulltriplet,even after common positiveamplitude/scale. If actualboundreference exactly subtractsa0,thistriplet exclusion doesNOTexclude surviving relativeaction;weights2,1fitPoisson without selectingit. Unscaledreference with scaledvolume can leavea0visible.",
      "scopeEN": "New application toactualcurrentfulltriplet,not reclassification ofR016/R017/R019,no universalexclusion ofallpositiveprofiles orTFPT. Sameordinarycoefficients and actualreference essential;no physicalPoissonselection,newBrel/trace/fieldmap or repair ofdistinctR030factor6.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:current-original-spectral-action-and-fixed-ordinary-moment-dictionary",
        "premise:positive-laplace-profile-finite-three-moment-comparison",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d58b761d8c1bee3c1145045b",
        "source:e8863a82d623d012c19635a6",
        "source:407674b75e7564e81997f4a5",
        "source:65c861d14cdba0b8fc7dcbb6",
        "source:3d32c655f4d90e07f32b044c",
        "source:942af3ad1feb4d35f65992b1",
        "source:d82c5530b43974236da8b89a",
        "source:5d52ec597926c790dd39c828",
        "source:9e65081849e2184886ad9e6d",
        "source:7c51024130522c334bc9f3df",
        "source:07c70a41376f2cfa103b2063"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:correct-current-argument-weights-link-whole-higgs-threshold-and-same-einstein-response",
      "titleEN": "Correct current argument weights link whole Higgs threshold and same Einstein response",
      "statementEN": "Independent exactflat4Dmasseigenvaluetest givesI_P=exp(−m/chi)(6chi4+6mchi3+2m²chi²),I_H=chi4exp(−m²/chi²)/2,confirming12,2,1versus1,1,1. Poisson hasremainder−2m5/(15chi),not blanketheatOchi−2. ExistingwholeR031consumer withA=Tr96DY²,B=Tr96DY4,C=Tr96DY²DM²>=0andINNERchangeL(H)−DYgives,forproposedweights2,1,mu_can²=4chi²−4C/A−R/6,lambda_can=8π²B/A². Negativewholequadratic requireschi²>C/A+R/24forA>0. Samea2weight appliesEinstein. Sameoriginalrank/geometryreference can subtractpureEinsteinaswellasa0;freeNrelcannotrestoreit.",
      "scopeEN": "Existingconditional4Dconsumer,no spacetimeorigin ornewHiggsmass/vacuumprediction. EvaluateotheractualHreferencejets/traces. KnownboundaryQprovesneitherwholebosonicactionnorlogdet. RetainallY/MR/Chi,H0,Eta,Z0,clocks,E8,words,R035G/T,R037blocks.25directcontrols,analyticclassproof,no newLeanformalization.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:current-original-spectral-action-and-fixed-ordinary-moment-dictionary",
        "premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer",
        "premise:existing-ap-positive-source-factor-and-declared-squared-energy-comparison",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d58b761d8c1bee3c1145045b",
        "source:e8863a82d623d012c19635a6",
        "source:407674b75e7564e81997f4a5",
        "source:65c861d14cdba0b8fc7dcbb6",
        "source:3d32c655f4d90e07f32b044c",
        "source:942af3ad1feb4d35f65992b1",
        "source:d82c5530b43974236da8b89a",
        "source:5d52ec597926c790dd39c828",
        "source:9e65081849e2184886ad9e6d",
        "source:7c51024130522c334bc9f3df",
        "source:07c70a41376f2cfa103b2063"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-original-spinor-curvature-a4-has-no-independent-scalaron-r-squared",
      "titleEN": "Whole original spinor curvature has no independent scalaron R-squared",
      "statementEN": "FullordinarySpin4xNheat givesa4_grav=N/(5760pi²)int(11Euler−18Weyl²−12DeltaR). IndependentR²coefficient0. Thusv255directWeyl²plusR²→scalarondoesnotfollowinthisconsumer. Whole20dimensionalalgebraiccurvaturespaceand400polarizedcouplingscheckedexactly. Samegeometry/rankreferencesubtractswholepurea4gravity;conformalfDfdoesnotchangeitsintegratedvalueonclosedtopologyorinteriorvariation. NoordinaryconformalcovarianceofD²claimed.",
      "scopeEN": "Scoped exact original-consumer calculation with the German record scope;no completephysicalsource,geometry,RP,measure,polemassorTFPTclosure. No newfreecouplingorprofile.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-whole-spinor-and-entropic-curvature-consumers-with-given-higgs-response",
        "premise:typed-source-structures",
        "premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d96806f43a772e98dc6e2a93",
        "source:e2a00d3ee6fe29fc84478936",
        "source:a8dcc5d4aca0f02081ae0648",
        "source:942af3ad1feb4d35f65992b1",
        "source:6b23b85b2d0b5f3277dba3a5",
        "source:65c861d14cdba0b8fc7dcbb6",
        "source:40839ae99ea0e7cd4d004e3f",
        "source:07c70a41376f2cfa103b2063",
        "source:ac915e3ee438ffe58bb8341a",
        "source:555a2cf54a211a87baae422c",
        "source:8c544f610fb293fdeb4cb994"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-original-entropic-curvature-corrects-max-symmetric-scalar-scale",
      "titleEN": "Whole original entropic curvature corrects the max-symmetric scalar scale",
      "statementEN": "Samev475consumer withoriginalX0=R,X1=Ric,X2=2RiemhasTrX=3R,TrX²=R²+Ric²+Riem². Quadraticbeta²(5R²/6+5Weyl²/4−3Euler/4). Maxsym17/24remainscorrectbutincludesEulerandisnotindependentR²coefficient. WholetensorspaceandindependentconformalFourierresponseconfirm5/6. Samebeta=1/(384pi²Mbar²)andEinsteinpingive,underusualquadraticmetricmatching,m0raw²=1152pi²Mbar²/5,17/20ofold4608pi²Mbar²/17. MismatchtoexistingTFPTtargetremains(18/5)(8pi)^9≈1.4403e13inmass². Noscalefit;retainWeylchannel.",
      "scopeEN": "Scoped exact original-consumer calculation with the German record scope;no completephysicalsource,geometry,RP,measure,polemassorTFPTclosure. No newfreecouplingorprofile.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-whole-spinor-and-entropic-curvature-consumers-with-given-higgs-response",
        "premise:typed-source-structures",
        "premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d96806f43a772e98dc6e2a93",
        "source:e2a00d3ee6fe29fc84478936",
        "source:a8dcc5d4aca0f02081ae0648",
        "source:942af3ad1feb4d35f65992b1",
        "source:6b23b85b2d0b5f3277dba3a5",
        "source:65c861d14cdba0b8fc7dcbb6",
        "source:40839ae99ea0e7cd4d004e3f",
        "source:07c70a41376f2cfa103b2063",
        "source:ac915e3ee438ffe58bb8341a",
        "source:555a2cf54a211a87baae422c",
        "source:8c544f610fb293fdeb4cb994"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:given-whole-higgs-source-fixes-radial-curvature-susceptibility-without-extra-scalar",
      "titleEN": "Given whole Higgs source fixes radial curvature susceptibility without a new scalar",
      "statementEN": "R031/R045Higgs withxi=1/6,lambda=8pi²B/(dA²),mu0²=2(c2/d)chi²−4C/Agives on specifiedflatbrokenbranchv²=mu0²/(2lambda),mrad²=4lambda v²,g=sqrt2xi v. WholefixedbackgroundquadraticK_R=−Delta+mrad²+xiRgivesdetK_R^-1/2exp[1/2(J−gR)K_R^-1(J−gR)]. Treeresponse−xi²v²RK0^-1R,lowmomentum−dA²/(1152pi²B)R²,withEinsteinshiftxi v²R. SamepoleisfixedbackgroundHiggsradialresponse;integrationaddsnoindependentnewscalar. AllhigherH/gauge/fermionvertices,reference,Z0remaininwholefunctional.",
      "scopeEN": "Scoped exact original-consumer calculation with the German record scope;no completephysicalsource,geometry,RP,measure,polemassorTFPTclosure. No newfreecouplingorprofile.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-whole-spinor-and-entropic-curvature-consumers-with-given-higgs-response",
        "premise:typed-source-structures",
        "premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d96806f43a772e98dc6e2a93",
        "source:e2a00d3ee6fe29fc84478936",
        "source:a8dcc5d4aca0f02081ae0648",
        "source:942af3ad1feb4d35f65992b1",
        "source:6b23b85b2d0b5f3277dba3a5",
        "source:65c861d14cdba0b8fc7dcbb6",
        "source:40839ae99ea0e7cd4d004e3f",
        "source:07c70a41376f2cfa103b2063",
        "source:ac915e3ee438ffe58bb8341a",
        "source:555a2cf54a211a87baae422c",
        "source:8c544f610fb293fdeb4cb994"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-original-four-ghost-complex-preserves-base-selector-with-full-cohomology-and-distinct-traces",
      "titleEN": "Actual original four-ghost complex preserves base selector with whole cohomology and distinct traces",
      "statementEN": "Whole actual Qadm gives Delta=Kadm tensor I16,Kadm=sum lambda_j Pi_j bounded and at least minlambda on its positive complement. PkerDelta=Pbase tensor I16,H^p=PbaseH tensor Lambda^p(C4);h=Qdagger K^-1(1-Pbase) contracts the whole positive branch. Partial ghost trace is (1+u)^4 exp(-tK):ordinary16,alternating0,degree0 recovers original base selector. All positive penalty weights preserve that selector;no free physical normalization16. Exact whole class of the original commuting projections.",
      "scopeEN": "Original algebraic complex under its stated commuting-projection premises. No normal S2 index or existing Higgs/flavor finding is revoked. Partial supertrace0 is not a physical Berezin measure or RP proof. Base selector stays valid;do not automatically divide the whole ghost source or Z0 by16.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-four-ghost-commuting-projection-admissibility-complex",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d32c52e372e93798380b7de1",
        "source:7abc2bfe14d302000d3fc64a",
        "source:5118e4b7ce2f2881fc4e15c0",
        "source:f91d7c570a7e2b8fae26a33a",
        "source:0b60ee63c1c3eb971fd5c8cd",
        "source:a162b449a911d408b1591593",
        "source:417053dba23fdd907e310aff",
        "source:166429197e5a39761c5c2015",
        "source:7db376a0de143cc44e3bafdd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-original-admissibility-energy-source-recovers-constraints-but-cannot-replace-geometric-operator",
      "titleEN": "Whole original admissibility energy source reads constraints without replacing geometry",
      "statementEN": "Actual DQ=Q+Qdagger has whole Rz=(DQ+z)(K-z²)^-1,R00=z(K-z²)^-1,Rj0=Kj(K-z²)^-1;for nonzeroz these recover Kj=zRj0R00^-1. Retain whole mixed sources and exact commuting-penalty variations. This bounded finite-spectrum penalty operator is not a unitary replacement for unbounded elliptic normal B_Ea. On infinite baseH exp(-tK) is not trace class;the parity block is Fredholm for finite base kernel and has index0. Normal Fredholm/Hodge alone does not fix independent4D R²/scalaron. v36 incomplete curvature part and target-moment assignment are provenance for already resolved R046,not another curvature discovery.",
      "scopeEN": "First original type comparison and exact algebraic source reader,not a general no-go for geometric reductions. No claim that bounded operators cannot be Fredholm,no physical ghost integration or4D spacetime derivation. Actual B_Ea to Brel symbol/domain/trace/reference map remains to calculate;retain established Wedge to96H coupling.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-four-ghost-commuting-projection-admissibility-complex",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d32c52e372e93798380b7de1",
        "source:7abc2bfe14d302000d3fc64a",
        "source:5118e4b7ce2f2881fc4e15c0",
        "source:f91d7c570a7e2b8fae26a33a",
        "source:0b60ee63c1c3eb971fd5c8cd",
        "source:a162b449a911d408b1591593",
        "source:417053dba23fdd907e310aff",
        "source:166429197e5a39761c5c2015",
        "source:7db376a0de143cc44e3bafdd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-moving-normal-kernel-fixes-induced-connection-and-full-scale-covariance",
      "titleEN": "Original moving normal kernel fixes induced connection and whole scale covariance",
      "statementEN": "Differentiate actual R035 T/G:A=Tdagger nablaT,C=Q nablaT,U=gmunu Cmu dagger Cnu>=0 and F_A=Tdagger FambientT+Cdagger wedgeC. BT=0 forces Cmu=-R_N(nabla_muB)T and the whole Tdagger(nabla_muB)R_N²(nabla_nuB)T including all paired normal modes. Full matrix square-root derivative uses Sylvester equation. In parallel scalar subclass A=[G^-1/2,dG^1/2]/2 and exact ordered normal covariance follows. Whole block Gram is positive,individual mixed blocks need not be. Only compressed ambient curvature vanishes via [W,[Fambient,W]]=0;FambientT=0 is unnecessary. Uniform normal rescaling cancels in T;G=gI givesA0 but need notU0. Whole Th+q form keeps both cross terms and R037 Schur/sources/determinants/Z0.",
      "scopeEN": "Exact derivative of supplied moving normal family and restriction of its actual quadratic form. Apply known Berry/Kato structure to original T;reuse old Kato classification and horizontal flat-line freedom without recounting. No selection of original horizontal rule/normal family,no dynamical decoupling,new physical weak gauge channel,4D origin or extra Higgs action. Whole measure/reference/source transport can cancel partial scale effects. No new Lean or ledger promotion. F1 remains in progress.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-smooth-normal-family-with-supplied-unitary-horizontal-connection",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:64617af4b295e8111923b6a4",
        "source:8c00026c8435806174140b39",
        "source:a7520d32cffa72bba1f57075",
        "source:1d47ba11550e82802ef559f1",
        "source:6e55b0e212595556faea182e",
        "source:2a47d64c9d19beb71a6fa333",
        "source:e9ebb5c16ae25bbb520bc5a7",
        "source:a162b449a911d408b1591593",
        "source:417053dba23fdd907e310aff"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-original-o1-source-rejects-nonconstant-normal-multiplier-and-fixes-placement-test",
      "titleEN": "Fixed original O1 source rejects nonconstant normal multipliers and fixes placement test",
      "statementEN": "On whole original H0(O1)=span(z0,z1),WV is contained inV iffW is constant on each normal fiber. Polynomial coefficient comparison decides whole positive profile class without a metric choice. With actual kerB0=V,unchanged B0T_sigma=[B0,W]SR^-1=c(d_NW)SR^-1 vanishes iffW is fiber constant. Actual fB0f annihilatesT_sigma;its ordered derivative reproducesR051 rather than another finding. Whole K=f(Dgeo+WBrelW)f;genuine first-order normal WBrelW retains symbol/drift commutator. Actual producer nabla_muB=(nabla_muc^a)nabla_a+c^a[nabla_mu,nabla_a]+nabla_muPhi;only fixed compatible product gives cF_mu,a+nabla_muPhi. Index does not select that producer.",
      "scopeEN": "Close fixed original O1 multiplier class and shared-domain normal identities. Retain R035/R051 under actual fBf premise;do not exclude changed holomorphic structures/operator families or TFPT. Distinguish norm from kernel movement,global SdaggerS from pointwise injectivity. Exterior B may itself beBrel(sigma,H);C(Brel)=0 does not imply zero wholeK response. Retain R034 zero-order map,R037Schur,R043GWG and Z0/reference/Eta/H0. No free connection/Phi/Y/profile/gap/4D choice,newLean or ledger promotion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-original-o1-section-consumer-and-actual-normal-first-order-placement",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2a8c02a061763563e71fb6a4",
        "source:575463d84424b121c700612b",
        "source:33389e654837feb29822cc8f",
        "source:1d47ba11550e82802ef559f1",
        "source:64617af4b295e8111923b6a4",
        "source:c416daab5702d1a4bc5e00f5",
        "source:417053dba23fdd907e310aff",
        "source:2c030511ad7371b889126645",
        "source:2a47d64c9d19beb71a6fa333"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-master-variation-keeps-spin-weight-and-active-source-route-typed",
      "titleEN": "Keep original spin holonomy weight and active source call typed",
      "statementEN": "Original wspin is varpi_spin, explicitly a spin holonomy weight, not an assigned normal or spin connection variation. Brel may depend implicitly on original e/chi fields; missing formulas do not imply zero mixed response. Active compressed covariance logarithm is a separate original call, not obliged to follow archived normal reduction. Supplied whole H source with Yukawa input is not independently identified primitive C_Sigma. Reuse existing M(xi),seed and v258 scope rather than count new resolutions.",
      "scopeEN": "Source clarification and corrected direction; no new physical origin derivation,corpus-wide absence theorem,general impossibility or additional completed F1 subtask. Retain existing Higgs/Yukawa/Flavor/Alpha and whole source results in their scopes.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4f168b718350ace3f95c32d0",
        "source:ae5cae97f7a886f66ac758e1",
        "source:f586b520face59aff68388c8",
        "source:d0d2d4b97ab82dd0478a1b11",
        "source:68f23ec0d0b1aec0ca3695c2",
        "source:2c030511ad7371b889126645",
        "source:3295e28477ad21a4fb0dd36a",
        "source:b2e5cc82888fa744942ad173",
        "source:ba1c42a41992c73070a8cfb7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:shared-original-higgs-mixture-has-invariant-color-fourpoint-wick-defect",
      "titleEN": "Shared original Higgs fluctuation has an invariant four-field witness",
      "statementEN": "O=3N²−sum_cd E_cd E_dc with E_cd=sum_i a_icdagger a_id is pure quartic and invariant under constant internal colorU3 and commonU6 frames. Any A_H tensor I3 gives <N²>=9m²+3tau,<Q>=3m²+9tau,<O>=24m². On original q(H) quark block,m(u)=3−p/2 sum_y tanh(ell sqrt(p²+y²u))/sqrt(p²+y²u) is strictly monotone for any supplied nonzero quarkY,independent of H direction. Thus full positive nonconstant-radial mixture class has exact defect24Var_mu(m(u))>0 from the Gaussian state with identical full two-point data. Covariance log remains an exact two-point reader,but not a whole H-mixture reconstruction.",
      "scopeEN": "Analytic theorem in supplied constant-quarter/H source consumer with positive normalized conditional mixture. Forty targeted controls including original96 builder and independent rational64-state Fock defect4/27;no physical weight selection or newLean. No general nongaussian claim for fixed u,complex weights,other connections or extra conditional fermion vertices. No local4D gauge observable,scattering or C_Sigma/P_F/mu origin derived. Primitive quasifree source BEFORE H integration remains possible. Reuse R026 cumulants and earlier conformal Wick averaging in their own scopes.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4ce51bb84103edda1d8ffc83",
        "source:7d601d942d874de66665bf25",
        "source:778b80138946befe005e7178",
        "source:0062466fd3d3dd1872e4116e",
        "source:7b9d208a53a0b23d563bbef4",
        "source:0ab6ca67e919cee3cb9b790f",
        "source:2192deb6e7ee96bf4ca5fc42",
        "source:37d8b3d9fa0981776fabedf6",
        "source:b2e5cc82888fa744942ad173",
        "source:a1d32ea509c78e7b29ad8496"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:bounded-fixed-rank-spectral-action-does-not-normalize-noncompact-higgs-volume",
      "titleEN": "Finite bounded spectral trace does not normalize ordinary Higgs volume",
      "statementEN": "Whole fixed finite rank class has |Tr_N f(K/chi)−Tr_M f(Kref/chi)|<=(N+M)||f||infty=C,even with H-dependent bound reference or positive chi(H). Thus flat C2 integral exp(−S_B) and absolute integral |P|exp(−S_B) for any nonzero finite polynomial P diverge. Pure eta phase gives no absolute damping. Positive epsilon|H|2 yields Z between exp(±C)pi²/epsilon² and ball mass<=exp(2C)R4epsilon²/2->0,so no tight probability family on same C2. Compact section base and constant Gram normalization do not bound coefficient amplitude;local positive quartic is not a global bound on exact bounded trace.",
      "scopeEN": "Conditional original-source inference discriminator,elementary known integrability mathematics. Actual TFPT measure is not asserted flat;no global TFPT exclusion or continuum theorem. Preserve existing finite transfer/CAR/full-word sources. Joint rank/IR limits,unbounded f,other original measure/support/action require actual producer. Signed moments may vanish and bounded responses converge despite escape;not exclusion of all algebraic state limits. Native96 is internal constructor control,not whole4D bosonic operator.30 controls,no newLean or ledger promotion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:fixed-rank-bounded-cutoff-with-ordinary-noncompact-higgs-volume",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:dbc675d17c46b87657163f72",
        "source:1b36759710d7122c27fd42ff",
        "source:684445a6b519c00edaacf9d6",
        "source:65c861d14cdba0b8fc7dcbb6",
        "source:ff07c789b5637f3d21805b06",
        "source:92c213b9a580a64fe9a50de1",
        "source:a2365982abe03f02b3eabc70",
        "source:fd684fe779705729d5389c88",
        "source:11e0d54b8cc47b851c5169b9",
        "source:4b5ca7f9a1950adca0a4280e",
        "source:8d3c02b49682d7c22f239881"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-original-quarter-source-bounds-higgs-weight-uniformly-through-joint-mode-ir-limits",
      "titleEN": "Whole original quarter source bounds Higgs weight uniformly through joint mode and IR limits",
      "statementEN": "Exact full square and Tonelli give TrF(h_H^2/chi^2)<=96Balpha for whole infinite original circle and every geometric mode cut,uniform entireC2 H and mode count,no Yukawa invertibility. Whole same-product reference gives−96Bref<=S_N<=96Balpha. Ordinary flatC2 Boltzmann volume remains nonnormalizable uncut;every joint N→infinity,epsilon_N→0 has ball mass<=exp(96(Balpha+Bref))R^4epsilon_N^2/2→0. This closes R055 rank loophole in stated original constant source class. Positive full-trace W needs no commutation;compression beforeF needs actual reduction. Same proof extends to already given R031 graded compact product with finite baseline.",
      "scopeEN": "Conditional infinite original-source class test,no new spacetime/profile/measure or primitive Ksigma/Drel identification. Finite Balpha explicit,not inferred from compactness. Constant H may be measure-zero in full H(x) space;no full functional-integral exclusion. No uniform infinitePfaffian or prohibition of bounded observable limits. Other variable connection/geometry/scale,nonLaplace profiles and actual measures require actual map. Native96 is internal spectral multiplicity.58 targeted controls,no newLean or ledger promotion. Preserve whole transfer/CAR/Yukawa/Flavor/Alpha,E8/clocks and source.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:whole-constant-original-quarter-source-positive-traceclass-profile-and-flat-higgs-volume",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:38ee3dd32e67afa4c47b0a55",
        "source:ea827387209681cf514a3dcd",
        "source:6109df65a0556233de48493e",
        "source:b0f7cc1e92acacbfed9ce0f5",
        "source:4fe7b0ff448a21091bd59663",
        "source:41d16f2d65876de2ec629793",
        "source:62d356f5b644ec8cb8a9d431",
        "source:65c861d14cdba0b8fc7dcbb6",
        "source:0062466fd3d3dd1872e4116e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-o1-covariance-leaves-full-radial-higgs-law-and-exact-fourier-source-readout",
      "titleEN": "Original O1 covariance leaves whole radial Higgs-law class and exact Fourier source readout",
      "statementEN": "All stated invariant marginals are H=sqrt(u)xi with Haarxi onS3 and arbitrary radial probabilitynu,Eu=2c. Same whole mode covariancecTT* fixes neither nu norEu². Fourth tensor Eu²/6(deltaij deltakl+deltail deltakj). Sphere and Gaussian Eu²4c²/6c² are nonidentifiability witnesses only,no physical selection. Original wholePhi expected quadratic2cA+M2 same,quartic B Eu²+8cC+M4 ranges[4c²B+8cC+M4,infinity) forB>0. Exact real Fourier sourcechi=int2J1(sqrt(u)|j|)/(sqrt(u)|j|)dnu uniquely determines whole nu;finite4moment gives logchi=−c|j|²/4+(Eu²−6c²)|j|⁴/192+o(j⁴). Reused actual-source pullbackchi=Zorig[iTj,0,0]/Zorig[0] keeps all complement fields integrated.",
      "scopeEN": "Complete conditional constant invariant marginal class,no general radial H(x)/fixed gauge background or whole coupled source. Modekernel→fieldcovariance,equivariantT and actualZ remain real extra origin maps. c not derived from geometry. Gaussian/sphere not asserted same whole-action solutions. R054 zero witness does not prove quark quasifreeness. Whole Fourier function continuous/bounded,not generically analytic/entire;moments require determinacy. Retain all reference/eta/H0/Z0 and mixed fermion sources.47 controls,no newLean or ledger promotion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-o1-mode-isometry-and-weak-invariant-positive-higgs-covariance-marginal",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d493eb704d2d3008a1117b14",
        "source:f115db237d0e9d3e59430c8c",
        "source:932fcda20d7d530756bfb668",
        "source:a2365982abe03f02b3eabc70",
        "source:55380af15fe611a52cf5c0f5",
        "source:76ea4fc6c765c752b59a0e49",
        "source:8afa68ccad62332d3a623113",
        "source:70b1f01d68a49cd34cd63578",
        "source:92c213b9a580a64fe9a50de1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-process-reconstruction-priority-and-original-locality-geometry-input-audit",
      "titleEN": "Whole process as reconstruction target and first original localization question",
      "statementEN": "68 is restrictedL/J word carrier;existing full mode hull is infiniteV_E8 with actual charges,grades and supported fields. Globalclock/erasurecommutators are not spatial adjacency. P1 boundary realization assumes smooth geometric spectrum/Diracdata;v975d4 remains conditional on named physical inputs;v1000 inputsN³,tensor space andP_TT Hessian;v1013 retains given quasilocal thermodynamic class closure with commonIRcone open. Lean standard-pair/scaling compositions retain realization axioms.27websitecards have4fixedpoint/5identity/16conditional/2open metadata;distinct frozenregistry16predictions+2assigned+2bands+2nonpredictionvariants. Supplied leading inflation formulas give r=3(1−ns)²,alpha_s=−r/6,As*r=c3^7/(2pi²),N-Jacobianrank1 at fixedc3.",
      "scopeEN": "Source and priority audit,no new physical spacetime/gravity,no whole-source exclusion,no newly completed origin subtask. Existing complete local source hull and class dynamics not reopened. Actual intrinsic inclusion/support map remains to construct.9dependencylabels not9independentclaims;functionalrank1 says nothing about independentmeasurements/significance. Preserve higher/mixedsource,absoluteZ0,reference/eta/H0 andR046–R057. No newLeanbuild orledgerstatus.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:literal-whole-source-localization-and-geometric-readout-contracts",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:b16a8bfb0e63f9c08fd835ff",
        "source:aa1a83c562f2dd4fbe5929b2",
        "source:205c404a0498273fd2011515",
        "source:f32b1211c9b3102b9b142a92",
        "source:c2536b3e06839cda2ea661dd",
        "source:4d8e65f4e9c9f33e7b44317e",
        "source:a4b2a95b4fbac4e861179085",
        "source:537e21ff12783b0c23253b33",
        "source:12831fd01905029b29c3eca2",
        "source:b58cecb0b28dad87167ef35d",
        "source:185f20a67444d6ccaca54265",
        "source:e760ecbf18662ac1b67ab6ae",
        "source:0eddb8cebd77b4a6b891e723"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-disjoint-local-weyls-acquire-spurious-commutator-under-bare-native-compression",
      "titleEN": "Actual disjoint local Weyls acquire spurious commutator under bare code compression",
      "statementEN": "For every disjoint properintervalpair actual smooth profiles realize arbitrary prescribed mode1 displacements ae0,b(e0+e1) via positive invertible two-frequency momentGram. Full bounded Weyls A/B commute exactly. PAP=lambdaA M(a),PBP=lambdaB M(b),actualstrictlypositivewhole-modefactors. Whole statedreal two-strength class has only rawcommutatorentries01=c,10=−12c with c=a⁴b⁴(a²−4)(a²−12)(b²−2)(b²−6)/4608. At a=b1,c55/1536,rank2,orthonormal01=55sqrt3/768,HSsquared3025/98304 before strictlypositivewholeprofilefactor. Firstjointorder8. Whole source retainsPABP=PBAP;exact[PAP,PBP]=PBQAP−PAQBP. Existing losslesswordreader retains these intermediatecontributions.",
      "scopeEN": "Exact original-source counterexample to naive localgraphreadout from ordinary5codecommutators. Only statedtwo-strengthclass/givenP,no generalno-go for finiteeffectivedescriptions orTFPT. No physicalsignal/measurementlaw/3+1D proof. NoGibbs/vacuumstate replacement:Bargmannfactor is matrixelementidentity,notZ0/newmeasure.68 onlyL/Jalphabet,not claimed sufficientforWeyls. Preserve existingconstructive neutralMoebiusstandardpair,no reopened infiniteexistencegap;P1state/time/reflection/chargedwordmap remain.60exactcontrols,actualsupport/allmodeproofs analytic. NoLean/paper/ledgerpromotion.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-proper-local-current-weyls-and-bare-native-code-compression",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:44bb3ab32b08d2dd42f20620",
        "source:c3706f83172ac46f0d77c330",
        "source:02f3774aa097218be4c42de5",
        "source:a1aca80bb8cb5965ff59f51a",
        "source:33d361a8ea8d9925aa37f433",
        "source:27d50f4baf6dc66675b8e155",
        "source:85f35396a9dbfeaaf66329c0",
        "source:b52e3ed67ae75eed66eb87cb",
        "source:f32b1211c9b3102b9b142a92",
        "source:09f123d8a14174c6a5960c2c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-quarter-current-state-excludes-nontrivial-geometric-local-point-time",
      "titleEN": "Actual quarter current state excludes nontrivial geometric local point-time",
      "statementEN": "First actual compactly supported Weylprobe f=chiprime(theta−pi/4),chi=b*tildeb,has exactdotV<0 under v=cos(theta) for every finitebeta;chargefactor logmodulus has firstderivative0. Whole statedC5 class decided at BOTH actualquarter sources beta4pi:connected kernel K(d)=−1/d²+a0+a2d²+...,a0=VarQ−1/12+2S1,a2=−1/240−S3. Geometricinvariance forces vthird=12a0vprime and(4/5)(5a2+3a0²)vprime0. Whole originalchargevariance/Lambertseries satisfy exact0<VarQ+2S1<1/12,hence−1/12<a0<0,a2<−1/240,5a2+3a0²<0. Thusvprime0 andfixedintervalendpoints forcev0. Scalar affinephases cannot repairconnectedcovariance.",
      "scopeEN": "Only actual unchangedcurrent/supportdictionary and statedC5 pointtransportclass,both actualquarters. No exclusion ofallgeometries,genericbeta forstronger theorem,fieldmixing,actualmodulartime,physicaltime orTFPT. KnownHardy/Gibbs distinction/globalrhoP not countednew. Supportedprobe/classification areallmode proofs,not Fouriertruncationinference.71localcontrols,no newLean/4D/ledgerpromotion.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-elliptic-quarter-supported-current-and-interval-car-modular-test",
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0e72de1e79fe537fd50ab004",
        "source:8847acbeb528204256879983",
        "source:ab885109249bdd62b1a3ff00",
        "source:e886cf7b7423adaac3b26754",
        "source:f41d1fafdb24cb56d6c28b07",
        "source:e8e683594febda1ab5930596",
        "source:09f123d8a14174c6a5960c2c",
        "source:85f35396a9dbfeaaf66329c0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-elliptic-interval-car-source-produces-local-modular-generator",
      "titleEN": "Actual elliptic interval CAR source produces its local modular generator",
      "statementEN": "Extensionbyzeroiota gives actualC_I=iota*C_alpha iota,endpointkernels0;modulatedsupportedprobes show0/1 spectralendpoints. Entire selfadjointk_I=log((1−C_I)/C_I) on spectraldomain,unboundedbothsides. Resolventreader integral0infinity[(C_I+s)^−1−(1−C_I+s)^−1] yieldsgivenfreeCAR modularflow sigma_t(a(u))=a(exp(−itk_I)u),antilineara. No localdensitymatrix forinfinitealgebra. Actual3mode subalgebra u_j=sqrt2exp(2ijtheta)1_I retainswholeHardysea exactly viatrigamma/digamma pluswhole exponentialthermalcorrection;independent8D Fockcalculation matchesoriginal2/4field/twonumberunitarywords andmodularsign.",
      "scopeEN": "Constructive givenfree localCAR reader,no newGaussianfit/primitive measurederivation. Log AFTERintervalrestriction,no assertedcompressedglobalgenerator. Finite3mode logmatrix onlysubalgebratest,notprovedfullk_I approximation. Given currentsubnet notsilentlyidentifiedwithlocalU1 fixedpoint;no blanketnoninvariance orfullCAR kernelnonlocality assertion. NoGaussianizationofR054 Higgsintegration;retainwholeE8,Y/Flavor/Alpha,clocks,originalRP/ref/eta/Z0.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-elliptic-quarter-supported-current-and-interval-car-modular-test",
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0e72de1e79fe537fd50ab004",
        "source:8847acbeb528204256879983",
        "source:ab885109249bdd62b1a3ff00",
        "source:e886cf7b7423adaac3b26754",
        "source:f41d1fafdb24cb56d6c28b07",
        "source:e8e683594febda1ab5930596",
        "source:09f123d8a14174c6a5960c2c",
        "source:85f35396a9dbfeaaf66329c0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-proper-two-face-regions-do-not-contain-pure-local-source-double",
      "titleEN": "Actual proper two-face regions do not contain the entire pure local source double",
      "statementEN": "For everyproperregionpair I_R,J_L actualR=S*PS isnotprojection. Reusedprojectiondefectidentity giveson(0,f) exactly||Q_JXiota_If||²+||Q_ICiota_If||². Firsttermstrictpositiveforeachfnonzero:actualXhasexponentialmultipliers andmapsL2togloballyrealanalyticfunctions;zeroonopenJcomplementforcesXf0 andinjectivityforcesf0. Hence no state-preservingunitarylinearCAR identificationwithpurecanonicallocaldoublefromonlythatproperoppositearc. WholePremainspure;regionalrestrictionmixed.",
      "scopeEN": "Entirestatedgivenfree-source/properregionclass,noexclusionoflocalreflection/RP/geometries/TFPT. Nouniformgap,no supportproofbyfinitesamples. Projectiondefect/abstractHSdoublingalreadyknown;newstepisactualanalytic supporttest. FinitetwoprobedeterminantalsoincludesomittedmodesINSIDEI,notalloutsideleakage. Nosignallinglaw,4Dorphysicalclosure.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-elliptic-two-face-projection-with-genuine-regional-support",
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d082cfa0568324c545a3069b",
        "source:68923e5b7e6e835511c580fa",
        "source:7a090dd5afa4a5a63112e789",
        "source:eac3dd13f9a62b215b2f5fa4",
        "source:e824212d52da9093d601a78c",
        "source:73ee19623fa909fea78ac7bc",
        "source:0e72de1e79fe537fd50ab004",
        "source:4ce51bb84103edda1d8ffc83",
        "source:d8cdf210465eadc80591e139"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-elliptic-whole-environment-fixes-regional-car-partner",
      "titleEN": "Original whole elliptic environment fixes the regional CAR partner",
      "statementEN": "In sameoriginalP takeU=rightL2(I),E=wholeleftplusrightIcomplement. Bf=(Xiota_If,Q_ICiota_If),B*B=C_I(1−C_I)=A². ZeroendpointkernelsgiveuniquepolarisometryB=TAonallU,noboundedAinverseassumed. DT=T(1−C_I)yieldsactualreducingU⊕TUwithcovariance[[C_I,A],[A,1−C_I]]. WholemixedCARwordsfollowinsameoriginalstate. ContractiveT_eps=B(A²+eps)^−1/2convergestrongly;onu=Agerror≤sqrt(eps)||g||,fixedwordsconvergenorm. Explicit single supportedprobeu=sqrt2 1Ihasdistinctsubsystemcutandpartnert=(Xu/a,(Cu−cu)/a),c=<u,Cu>,a²=c(1−c). Wholeoccupiedsea1/4analytic,actualchargedcrosswords/fourfieldwordevaluatedforbothquarters.",
      "scopeEN": "Constructivesupportbridgewithingivenfreewholesource,nonewphysicalmeasurechoice/postselectedstate. FullintervalTnotidentifiedwithsingleprobeT,finiteepsnotexactCARisometry/nouniformnormconvergence. ActualgeometricquartercomplementsC/transportsfacesandsupport;nonewphysicalfaceswap. No geometricOSTheta=localTomitaJ identification. R054connectionONLYunderitspositivenonconstantradialmixturepremise:integratedquarksourceisnonquasifreedue24Var(m)>0,sopureprojectorCARdoublecannotreplaceitbylinearrestriction. Primitivefree sourcebeforeHintegrationremainspossible.58targetedcontrols,noLean/ledger/4Dpromotion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-elliptic-two-face-projection-with-genuine-regional-support",
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d082cfa0568324c545a3069b",
        "source:68923e5b7e6e835511c580fa",
        "source:7a090dd5afa4a5a63112e789",
        "source:eac3dd13f9a62b215b2f5fa4",
        "source:e824212d52da9093d601a78c",
        "source:73ee19623fa909fea78ac7bc",
        "source:0e72de1e79fe537fd50ab004",
        "source:4ce51bb84103edda1d8ffc83",
        "source:d8cdf210465eadc80591e139"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-original-color-triplet-has-spectator-dependent-modular-field-law",
      "titleEN": "Original color triplet has spectator-dependent modular field action",
      "statementEN": "Actualfixedrightuprestriction C_H=t(u)I3 givesrho=d_N,d_k=int t^k(1−t)^(3−k)dmu,sectorprobabilitiesbinom3k d_k. FullK=−logrho=k0+J1N+J2binomN2+J3binomN3 withJ1=log(d0/d1),J2=log(d1²/(d0d2)),J3=log(d0d2³/(d1³d3)). M_c=otheroccupations0,1,2 gives sigma_s(a_c)=sum exp(isDelta_m)P_cm a_c andsqrt(rho)a_c=sum sqrt(d_m/d_(m+1))P_cm a_c sqrt(rho),Delta_m=log(d_m/d_(m+1)). Entirepositive nonconstantradialclassforces J2<0,Delta0>Delta1>Delta2,Delta_m<0. J3canhavesign±. Actual96builderincludingMajorana,correctrightgrading,sameH-independentfamilyvectorand8Fockmatriceschecked.",
      "scopeEN": "Modularlawofthisactualinternalmarginal,notrestrictionoffull96modularfloworphysicaltime. Quartic/sexticstatelogcoefficientsarenotaddedactionvertices/QCDcouplings. Physicald_k/mustillrequireoriginalsource. ReusesR054nonGaussianityandabstractHSlaw,notcountedasanewdiscovery.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:226bffa52492ec42de0429dd",
        "source:e6a5497a201f4003d56b7131",
        "source:cd46cb448abc2cc1d4d75340",
        "source:2dc4ed5a956f60fad2ea4374",
        "source:973c23b9c7e1c5ecf7837c04",
        "source:4ce51bb84103edda1d8ffc83",
        "source:0062466fd3d3dd1872e4116e",
        "source:7b9d208a53a0b23d563bbef4",
        "source:e824212d52da9093d601a78c",
        "source:4f168b718350ace3f95c32d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-color-marginal-has-complete-finite-source-reader-and-mixture-criterion",
      "titleEN": "Whole original color marginal has finite reader and complete mixture test",
      "statementEN": "PositiveevenSU3invarianttripletstatehasrho=d_Nby1_even,3_odd,3bar_even,1_odd;SU3alonepermitssingletcoherences,parityremoves. FourboundedF(z)=Z_orig[z^N]/Z_orig[1] at1,i,−1,−i recoverwhole dbyDFT;F1trivial,F−i=conjFi,not4independentrealdata. m1=d1+2d2+d3,m2=d2+d3,m3=d3. CompletefiniteHmixturedecision:v=m2−m1²<0reject;v0requirea<m1≤b,m3=m1³;v>0 G=[[1,m1],[m1,m2]],X=[[m1,m2],[m2,m3]], X−aG>0,bG−X≥0necessaryandsufficient. GselfadjointT=G^-1X,Te0=e1gives2positivespectralnodesin(a,b] matchingm0..m3,eachinvertibletoactualfiniteu. Lowerendpointstrict,upperH0boundarysemidefiniteallowed. Exactclassifierandcountercontrols executed.",
      "scopeEN": "CompleteexistencetestONLYforthismarginalpositiveHclass. Two-nodewitnessnotphysicalmeasureselection,nouniquenessoffulllaworotherfieldcompatibility. ReaderdoesnotsupplymissingmasterZ/mu. FourphasesnotprimitiveC4clockproof. Validpositivequantumstatecanfailmixturetest;notgeneralTFPTexclusion. StandardGaussquadraturewithselfcontained2x2halfopensupportproof,notclaimofanewgeneralquadraturetheorem.80controls,noLean/paper/ledgerclosure.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:226bffa52492ec42de0429dd",
        "source:e6a5497a201f4003d56b7131",
        "source:cd46cb448abc2cc1d4d75340",
        "source:2dc4ed5a956f60fad2ea4374",
        "source:973c23b9c7e1c5ecf7837c04",
        "source:4ce51bb84103edda1d8ffc83",
        "source:0062466fd3d3dd1872e4116e",
        "source:7b9d208a53a0b23d563bbef4",
        "source:e824212d52da9093d601a78c",
        "source:4f168b718350ace3f95c32d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:two-and-four-field-words-do-not-complete-original-color-triplet-source",
      "titleEN": "Two and four field words do not complete the original color marginal",
      "statementEN": "Exactadmissiblet_j=11/20+j/100,j0..3,positivew±=1/4±(−1,3,−3,1)/24 haveidenticalm0,m1,m2,thusalltriplet two/fourfieldwords,butm3differsby1/2000000. Sixfieldresponse/modularlogdiffer. Allnodeslieinoriginalrange. HenceentireR054fourfielddefectalonecannotcompletethissource.",
      "scopeEN": "Excludestwo/four-data-onlyreconstructioninthisclass,notanoriginalproducerthatsupplieshigherwords.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:226bffa52492ec42de0429dd",
        "source:e6a5497a201f4003d56b7131",
        "source:cd46cb448abc2cc1d4d75340",
        "source:2dc4ed5a956f60fad2ea4374",
        "source:973c23b9c7e1c5ecf7837c04",
        "source:4ce51bb84103edda1d8ffc83",
        "source:0062466fd3d3dd1872e4116e",
        "source:7b9d208a53a0b23d563bbef4",
        "source:e824212d52da9093d601a78c",
        "source:4f168b718350ace3f95c32d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-original-quarter-occupation-tower-uniquely-reconstructs-common-radial-higgs-law",
      "titleEN": "Whole original quarter occupation tower uniquely reconstructs the common radial Higgs law",
      "statementEN": "F(z)=int z tanh(ell sqrt(z²+y²u))/sqrt(z²+y²u)dmu isholomorphicpositive-realintheRHPwithoutHmoments. Coshproductgives2/ell sum_j z/(z²+y²u+omega_j²),omega_j=pi(j+1/2)/ell. ExplicitSchwarznormal-familybounduniformujustifiestheintegral. BoundedCayleyfunctionatactualp_n=n+alpha uniquelyfixesFbydivergentBlaschkesum. F(sqrtz)/sqrtz is2/ellStieltjesofsigma=sum_j T_omega_j²nu,nu=(y²)_*mu. Fixedbackshiftgivesrho=nu+sum_j≥1 T_delta_jnu,delta_j=pi²j(j+1)/ell². CumulativeV(x)=R(x)−sum_delta≤xV(x−delta)isfinitewell-foundedtriangularrecursiononeachcompact,recoveringnuincludingatoms.",
      "scopeEN": "Exactidentifiabilityandconstructiveradialinverseinthisoriginalcommonconstant-sourceclass. NOTphysicalmeasureselection/computationofmissingmastervalues/H(x)/otherfieldjointlaw/physicaltime/4Dorigin. Onesinglewholetowersuffices;bothimprovefinitebounds. Noarbitraryanalyticinterpolationwithoutpositive-realclass. R062fixedtripletambiguityretained:differentinputinformation.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-common-positive-constant-higgs-law-over-whole-quarter-tower",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:900878bc7bc22c923d00805b",
        "source:402c96581dd621e85e7c3d43",
        "source:d22def604eddd47014d1dc36",
        "source:71f944879378972cc9584937",
        "source:7f9969891b15fb022c5aa3fe",
        "source:f0444048c97035e96bb6f6b5",
        "source:0865b0b6d6287c910ba8ab8f",
        "source:a7814b152f78c3c9f2d590eb",
        "source:226bffa52492ec42de0429dd",
        "source:4ce51bb84103edda1d8ffc83",
        "source:d493eb704d2d3008a1117b14",
        "source:0062466fd3d3dd1872e4116e",
        "source:7b9d208a53a0b23d563bbef4",
        "source:e8e683594febda1ab5930596",
        "source:4f168b718350ace3f95c32d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:finite-original-tower-reader-and-existing-weak-symmetry-fix-shared-matter-responses",
      "titleEN": "Finite original tower reader and existing weak symmetry determine shared matter responses",
      "statementEN": "MultipointSchurforward/backwardrecursionreadstargetouterintervalsfromactualfinitepanswers. ExactagreementonNanswersineachquartergivesoccupationdifferenceatmathematicalq1/2≤2/(16N²−1);individualBlaschkeproducts1/(4N∓1). Occupation=1/(1−s),s∈(−1,0],derivative≤1,sofactor2correct. N1000eachgives2/15999999. PositivePickGramnecessaryonly,notStieltjesorH-classsufficiency. UnderadditionalunchangedR057weak-invariantpositiveHmarginalandgenuinefieldmap,xiHaarS3independentofradius;identifiedmufixeswholeconstantHmarginandeachGIVENconditionalfermionwordintmu intHaarW_A(sqrtu xi),withoriginalY/MR/Pf/phases. Direct96leptonresponsefromsamereconstructeddiagnosticlawagreeswithoutYfit.",
      "scopeEN": "Momentfreeradialtheorem;symmetrycorollaryONLYwithadditionalexistingR057field/covariance/invariancepremises,symmetrynotnewmeasureselection. Allwordsshareoriginalmu,noperwordfit. NoWickreplacementbyaveragedcovariance. FiniteboundassumesEXACTsampleagreement,notnoiseormeasuredistance.120-digitdiagnosticsnotrigorousintervalarithmetic. q1/2notnewphysicalmode/clock.129controls,noLean/paper/ledger.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-common-positive-constant-higgs-law-over-whole-quarter-tower",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source",
        "premise:given-o1-mode-isometry-and-weak-invariant-positive-higgs-covariance-marginal"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:900878bc7bc22c923d00805b",
        "source:402c96581dd621e85e7c3d43",
        "source:d22def604eddd47014d1dc36",
        "source:71f944879378972cc9584937",
        "source:7f9969891b15fb022c5aa3fe",
        "source:f0444048c97035e96bb6f6b5",
        "source:0865b0b6d6287c910ba8ab8f",
        "source:a7814b152f78c3c9f2d590eb",
        "source:226bffa52492ec42de0429dd",
        "source:4ce51bb84103edda1d8ffc83",
        "source:d493eb704d2d3008a1117b14",
        "source:0062466fd3d3dd1872e4116e",
        "source:7b9d208a53a0b23d563bbef4",
        "source:e8e683594febda1ab5930596",
        "source:4f168b718350ace3f95c32d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:unchanged-free-quarter-source-cannot-be-nontrivial-integrated-higgs-mixture",
      "titleEN": "Unchanged free quarter source is not a nontrivial integrated positive Higgs source",
      "statementEN": "t_p(u)isstrictlydecreasingforeachp>0. UnderEXPLICITunchangedmarkedfieldidentity,thegivenfreeellipticrightdatumatell2piist_p(0)=1−(1+exp4pip)^−1. Exactagreementatonesinglepunderpositivemixtureforcesmu=delta0. SamefreeprimitivecovariancecannotalreadybenontriviallyH-integratedsourceinthisidenticaldictionary. Actualfreevaluesreplayedat2/4/8samples;physicalcarrieridentityremainshypothesis.",
      "scopeEN": "ExclusionONLYforthisunchangedidentifiedsourcecall,notglobalTFPTno-go. PrimitivefreeBEFOREHintegrationallowed;actualfield-dependentcarrier/insertionmapmaychangerelevantresponseandmustbederived. R054Gaussianreplacementexclusionnotcountedasanewindependentconfirmation.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-common-positive-constant-higgs-law-over-whole-quarter-tower",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:900878bc7bc22c923d00805b",
        "source:402c96581dd621e85e7c3d43",
        "source:d22def604eddd47014d1dc36",
        "source:71f944879378972cc9584937",
        "source:7f9969891b15fb022c5aa3fe",
        "source:f0444048c97035e96bb6f6b5",
        "source:0865b0b6d6287c910ba8ab8f",
        "source:a7814b152f78c3c9f2d590eb",
        "source:226bffa52492ec42de0429dd",
        "source:4ce51bb84103edda1d8ffc83",
        "source:d493eb704d2d3008a1117b14",
        "source:0062466fd3d3dd1872e4116e",
        "source:7b9d208a53a0b23d563bbef4",
        "source:e8e683594febda1ab5930596",
        "source:4f168b718350ace3f95c32d0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-e8-record-doily-action-is-signed-p-plus-compatible-point-with-typed-sym2-lift",
      "titleEN": "Actual E8 record acts as signed p plus compatible point with typed Sym² lift",
      "statementEN": "FouroriginalraysperDoilylineLshareunsignedinvolutionfL,fixLandswapsixpairs. Outsidep hasuniquecommutingqinLbutactualoutputfL(p)=p+q,notq;720originalcases/180incidences. rW_pr*=epsilonW_f andactualU_zJ_pU_z*=epsilonJ_f,all900pairs. Q_p+->Q_f^epsilon rank3,mixedrest4. UnsignedcountsT=(3I+2A)/15 symmetricwithspec1,(1/3)^9,(−1/5)^5;fundamentalsignedoperatorresponseW_p/5. NeitherTnorC4restrictionisfullEndH10channel.",
      "scopeEN": "Exactgivensixtyeventsource,notphysicalclock/state/recordselection. DoilyandgenericPauliactionknown;newexplicitincidencecomparisonandactualH10observable/sectorlift. Not15orthogonalprojectorsorsites.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables",
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d50d9fc0b636a8077423d13e",
        "source:0acb05edf29cc8174b1ce271",
        "source:0ac85ab5438433b8c50823d2",
        "source:763db75e32f490c8a546f454",
        "source:bd8ba858670d1e8bb41e66bb",
        "source:8b1558522619703c1fdc1105",
        "source:56cdbd4b74d6f89c4db1ccc9",
        "source:b27666637eb3c1898f8b2403",
        "source:9956bcf33e43b31a8176de33",
        "source:4e18307d5cfd2d0abec91f25",
        "source:5c27d1fe57fbd8353f5c3864",
        "source:30e10bb3b8b961b059594e71"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-e8-record-words-distinguish-order-and-retain-phase-beyond-fifteen-labels",
      "titleEN": "Actual E8 record words distinguish order and retain more than fifteen labels",
      "statementEN": "Originalray0r=diag(−1,1,1,1),ray13s=I−J4/2. OnactualH10,rho=Q_IZ+/3,E=Q_XI+ giveorderedprobability1/3versusreverse1,exactrationalandindependentlycheckedbysymmetric-tensorsingular-valueformula. Jointoriginalrecord/finalprobabilities1/10800versus1/3600,difference1/5400. Wordr0thenr54sendsW_IXto−W_IXatsamelabelandQ+toQ−. Symmetricone-stepreaderdoesnotexcludeorderedprocessresponse.",
      "scopeEN": "Explicitmathematicalpreparationandeffect,notphysicalvacuum/site/3+1causalnet. Existingwholeword/Qmemoryretained,genericcompressionlossnotnewlycounted. Not13Octoberloadedpulseordeployedclock.30controls,noLean/physicalvalidation.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables",
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d50d9fc0b636a8077423d13e",
        "source:0acb05edf29cc8174b1ce271",
        "source:0ac85ab5438433b8c50823d2",
        "source:763db75e32f490c8a546f454",
        "source:bd8ba858670d1e8bb41e66bb",
        "source:8b1558522619703c1fdc1105",
        "source:56cdbd4b74d6f89c4db1ccc9",
        "source:b27666637eb3c1898f8b2403",
        "source:9956bcf33e43b31a8176de33",
        "source:4e18307d5cfd2d0abec91f25",
        "source:5c27d1fe57fbd8353f5c3864",
        "source:30e10bb3b8b961b059594e71"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:literal-doily-incidence-output-and-strict-causal-order-on-fifteen-source-labels-excluded",
      "titleEN": "Literal Doily incidence output and strict causal order on fifteen source labels excluded",
      "statementEN": "12to3mapptoitsuniquecompatiblepointqhasfourpreimagesandisnotinvertible;actualconjugationp->p+qisinvolutive. Henceqisnotliteralunitaryrecordoutput. Everyallowedunsignednativemovehasreversebythesameevent;arbitrarypositiveeventweightsstillyieldsymmetriccounts. Nostrictorderonthesame15namescanmakeallmovesirreversibleforwardsteps.",
      "scopeEN": "Onlyspecified15label/eventidentificationexcluded,notglobalTFPTorigin/time/causalityno-go. Orderedwordshaveresponses;time/localitycanrequireothergenuineoriginaldata. InternalHerm2conenotprovedspacetimedictionary.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables",
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d50d9fc0b636a8077423d13e",
        "source:0acb05edf29cc8174b1ce271",
        "source:0ac85ab5438433b8c50823d2",
        "source:763db75e32f490c8a546f454",
        "source:bd8ba858670d1e8bb41e66bb",
        "source:8b1558522619703c1fdc1105",
        "source:56cdbd4b74d6f89c4db1ccc9",
        "source:b27666637eb3c1898f8b2403",
        "source:9956bcf33e43b31a8176de33",
        "source:4e18307d5cfd2d0abec91f25",
        "source:5c27d1fe57fbd8353f5c3864",
        "source:30e10bb3b8b961b059594e71"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-doily-context-record-characters-have-ranks-four-two-two-two",
      "titleEN": "Actual Doily context records have character ranks four two two two",
      "statementEN": "FourgivenUjperLhaveproductI10;Hj=UjU0formKlein4. WalshQchi=1/4sumchiHjorthogonalranks4,2,2,2,sumI. ConditionalcoherentWalsh/2recordrotationgivesBchi=U0Qchi/sqrt15andeffectsQchi/15insteadofI/60withsameunreadCPmap. ContextchannelAdU0aftercharacterpinching,notplainrank1C4dephasing. Onacharacterstatespecificglobalchance1/15versusoriginalfourtimes1/60,samecontextchance. All15groupsexact.",
      "scopeEN": "Coherentrecordaccessisexplicitresource,notfreeoperationonaclassicalrecord. Specifiedoriginalinstrumentnotdeclaredambiguousbydefinition;physicalimplementation/readoutselectionstilltoderive. Genericrecordbasisfreedomalreadyknown;onlyactualH10realizationnew. Notold20event/5Hodgegroupingandnouniversalrecordmeasurementgateforexistingcurrent/sewingbridge.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables",
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:actual-single-source-event-coherent-stinespring-record"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d50d9fc0b636a8077423d13e",
        "source:0acb05edf29cc8174b1ce271",
        "source:0ac85ab5438433b8c50823d2",
        "source:763db75e32f490c8a546f454",
        "source:bd8ba858670d1e8bb41e66bb",
        "source:8b1558522619703c1fdc1105",
        "source:56cdbd4b74d6f89c4db1ccc9",
        "source:b27666637eb3c1898f8b2403",
        "source:9956bcf33e43b31a8176de33",
        "source:4e18307d5cfd2d0abec91f25",
        "source:5c27d1fe57fbd8353f5c3864",
        "source:30e10bb3b8b961b059594e71"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:canonical-standard-split-localizes-original-source-record-words-with-full-descendant-companion",
      "titleEN": "Canonical standard split localizes original record words with full companion",
      "statementEN": "FullE8characteristraceclassforallbeta>0,hencestandardsplitforstrictintervalinclusionsingivennet. Psi(X)=W*(X⊗I)W normalunitalinjective*-homomorphismontoINFINITEtypeIintermediateF,notcompression. FixesA(I),canonicallyvacuum/symmetrycovariant. V(g)=Psi(rho(g)) genuineSU4rep,AdV=AdrhoonA(I),commutesA(J)′. E_L=W*(E0⊗Omega),Bhat=iV(u)/sqrt60giveBhatE_L=E_L(I10⊗B),fullnormsumI. Allfiniteoriginalrecordwords/phases/givencoherentwordsumswithoutintermediateprojection;R0641/3vs1becomesboundedlocalENCODEDresponse. EntireD5companionandotherE8sectorsretained;(iV(u))²=−V(−iI)isonlyidentityonclass2.",
      "scopeEN": "Conditionalglobal-to-localimplementationtheoreminALREADYgiveninfiniteE8net,usingDoplicherLongo/Longo7.1.6,7.1.13,7.3.3andsourcederivation,notprovedbyfinitechecks. Encodedstate/regionsnotphysicaloriginselection. Wnotnumericallyconstructed,noC*norm/finiteenergyimplementer/originalclockidentitytheorem. NeutraltennotP2matter.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-e8-current-vacuum-net-and-original-grade-two-descendant-with-standard-split",
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c1da80fc2b8cffa25537e42e",
        "source:6fcd545cb2c0ea5a17f72a5c",
        "source:3f5ea95e15b2d6b3f4bd0a88",
        "source:3f7d135b1e1836821b04845b",
        "source:3f8ca2b1ccd063793e6eb99e",
        "source:f0f0d2ffa2799e0711a2471d",
        "source:b14d5e5e924685ef2a8aacab",
        "source:56cdbd4b74d6f89c4db1ccc9",
        "source:e834c61dedcba1332be8a94e",
        "source:25ef2fd811c7f1af50c96118",
        "source:8a5f9e65bd623510e78f6ebb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:unchanged-global-sixty-event-source-fails-local-exterior-current-test",
      "titleEN": "Unchanged global sixty event source fails local exterior-current test",
      "statementEN": "L0E0=2E0givesE0*J_X(h)E0=h0(I10⊗J_XBell)forallsmears;othermodesshiftgrade. OriginalR064rhoQ_IZ+/3withanyD5sigmahasexteriorvalue2h0before,0afteroriginalglobalray13,and(2/5)h0afterunreadC60. AnyactuallocalnonselectiveCPmapwithKrausinA(J)andnormsumIfixesALLboundedexteriorobservables;Weylderivativefixesthisfiniteenergysourcecurrentat2h0. Literalsame-code/same-exteriordictionaryidentificationofglobaleventorunreadC60aslocalinterventionexcluded.",
      "scopeEN": "Onlyspecifiedliteralglobalrecordidentification,notclock/time/P1orotherlocalsourcesno-go. BranchwithpIeffectonWHOLEphysicalHhasexteriorpB;merelyscalarCOMPRESSEDeffectisinsufficient. State-dependentpostselection/exteriormemorynotexcludedandmustretainfullsource/record/normalization.31controlsforfiniteoriginalcoefficients;all-observablelocalityargumentanalytic.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-e8-current-vacuum-net-and-original-grade-two-descendant-with-standard-split",
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c1da80fc2b8cffa25537e42e",
        "source:6fcd545cb2c0ea5a17f72a5c",
        "source:3f5ea95e15b2d6b3f4bd0a88",
        "source:3f7d135b1e1836821b04845b",
        "source:3f8ca2b1ccd063793e6eb99e",
        "source:f0f0d2ffa2799e0711a2471d",
        "source:b14d5e5e924685ef2a8aacab",
        "source:56cdbd4b74d6f89c4db1ccc9",
        "source:e834c61dedcba1332be8a94e",
        "source:25ef2fd811c7f1af50c96118",
        "source:8a5f9e65bd623510e78f6ebb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:canonical-source-localization-changes-exterior-state-and-does-not-select-event-origin",
      "titleEN": "Canonical source localization changes exterior state and does not select event origin",
      "statementEN": "E_Lencodinghasvacuumexteriorindependentoflogicalrho;originalE0sourcehasexteriorstress2h0insteadof0. OriginalQ_IZ±inputsdistinguishedoutsideby±2h0,hencenolocalnonselectivepreparationcanreplacewholefamilybyfixedexteriorencodingandpreserveanswers. Canonicalproducteta≠Omega;PsifixesA(I)butrelocatesoriginalexterioroperatorstocollarrelativecommutant,notglobalstate/localizationpreservingcoordinatechange. ActualvacuumonFhasdensityTr2W|Omega><Omega|W*,notchosenfiniteBellinput. SmoothcurrentprofilepulseisalternativeinterioractionconsumerwithoriginalCARnormq3/4andenergy(3pi²/4)sum n²|f_n|²;doublepulse4energyONLYinthatclass,notuniversalcanonicalsplitcost.",
      "scopeEN": "Originalfield/statecomparisoningivennet,notgeneralno-goforselectivepreparationsoractualexteriorstates. Nofiniteenergyclaimforcanonicaleta/implementers. Givenchiralgeometrytransported,notderivedfrom15labels;physical3+1/spin2/seamstateselectionremainoverallgoal.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-e8-current-vacuum-net-and-original-grade-two-descendant-with-standard-split",
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c1da80fc2b8cffa25537e42e",
        "source:6fcd545cb2c0ea5a17f72a5c",
        "source:3f5ea95e15b2d6b3f4bd0a88",
        "source:3f7d135b1e1836821b04845b",
        "source:3f8ca2b1ccd063793e6eb99e",
        "source:f0f0d2ffa2799e0711a2471d",
        "source:b14d5e5e924685ef2a8aacab",
        "source:56cdbd4b74d6f89c4db1ccc9",
        "source:e834c61dedcba1332be8a94e",
        "source:25ef2fd811c7f1af50c96118",
        "source:8a5f9e65bd623510e78f6ebb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-elliptic-fixed-holonomy-insertion-gives-local-operation-on-unchanged-source",
      "titleEN": "Original elliptic fixed-holonomy insertion gives a local operation on the same source",
      "statementEN": "WholeoriginalD_a+epsilonfhasV=e^ik,k′=−epsilon(f−f0),Cepsilon=VC_(a+epsilonf0)V*. CompletingoscillatorsgivesH+epsilonJf=WkH_(a+epsilonf0)Wk*−epsilon²sum|fn|²andfullpartition/words. Forf0=0,kcanbesupportedinsameI:rhoepsilon=WkrhoWk*,alloriginalexteriorwordsfixedandjointwordsretained. Wholetwofacegraphistransported. Actualforwardinsertion,notinverseinputY.",
      "scopeEN": "Entiregivensmoothscalarclassonexistingcircle;notprimitiveP1measure,sixtyrecordruleorinteractingHorigin. Wkisanormalizedlocalunitaryoperation,notanindependentlyselectedinstrument.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion",
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bf3abd209cdea28089fc2076",
        "source:f5f2e9136620b3db023e9ab3",
        "source:172bb7ab59afa582ae1c7b66",
        "source:5b1654ff56ae0cdd52aeaf19",
        "source:e8e683594febda1ab5930596",
        "source:19db256c3dd54fa62ffc0e23"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-quarter-pair-fixes-square-charge-law-half-response-and-real-quillen-norm",
      "titleEN": "Original quarter pair fixes square charge law,half-response and real Quillen norm",
      "statementEN": "Settingp=q+r,d=q−rthetwoquarterchargeenergyis(p²+d²−d)/4andd↦1−dequalizesparity. HenceP(p)∝exp(−pip²)exactly;PoissonselfdualitygivesVarp=1/(4pi),eachquarterVarQ=1/(8pi),bVar=1/2. Onrealv=t/(2pi),N(v,0)=|chi_pair(2piv)|²identifiesexistingQuillennormandHessian−2pi. Originalequilibriumderivativeis−meanfg+f0g0/2,nonzerooutsidewhenf0g0≠0,excludinglocalTPidentificationofthisfamilynear0,notcausalsignalling.",
      "scopeEN": "Bothoriginalquartersatb=4pi,independentblocksofsamemarginal,nottwofaces. Commoncouplingaddsexteriorcoefficientto1. Notglobalfiniteepsilonno-go,arbitrarycomplextwistpositivity,EMq(alpha)/5/4orspin2identification.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion",
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bf3abd209cdea28089fc2076",
        "source:f5f2e9136620b3db023e9ab3",
        "source:172bb7ab59afa582ae1c7b66",
        "source:5b1654ff56ae0cdd52aeaf19",
        "source:e8e683594febda1ab5930596",
        "source:19db256c3dd54fa62ffc0e23"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-elliptic-source-determines-all-path-normalized-causal-current-response",
      "titleEN": "Actual elliptic source determines normalized causal current response for the whole path class",
      "statementEN": "SameoriginalJ_n(t)=e^−intJ_nandcentralcommutatorgiveU[f]=exp(Bpath)W(−F),withF=intv_tandBpath=−1/2int_t>sc. FullZ_SK=exp(B+−B−+c(F−,F+)/2)omega(W(F−−F+))retainsTheta,cothandphases;Z_SK[f,f]=1forallsmoothpaths. Retardedpulse=−epsilonmean(f′g_t),zerobeforeinsertionandfordisjointtransportedsupports. Correlationandcausalresponseuseonesource,notaGibbsreset.",
      "scopeEN": "WholegivensupportedcurrentpathclasswithGIVENchiralcircletime. Nophysicalclockcalibration,3+1origin,spin2oreventselection;nottransferredtoH-integratednonquasifreesource.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion",
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bf3abd209cdea28089fc2076",
        "source:f5f2e9136620b3db023e9ab3",
        "source:172bb7ab59afa582ae1c7b66",
        "source:5b1654ff56ae0cdd52aeaf19",
        "source:e8e683594febda1ab5930596",
        "source:19db256c3dd54fa62ffc0e23"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-higgs-quark-source-has-exact-whole-su3-counting-response",
      "titleEN": "Original Higgs quark source has exact whole SU3 group response",
      "statementEN": "Actualrealcolorinsertiononoriginal36quarksubspacegivesXi_a,u(G)=prod_n,jdet3[I−s(E_j)(2I−G−G*)],E_j=sqrt((n+a)²+y_j²u),s=1/[4cosh²(bE/2)]. FillednegativeEcolortripletdetG1fixesseaphase. Summableuniformbound12exp(−b|p|)givesfulltowerconvergenceforallu>=0,allSU3. ForG!=I,u>0andnonzeroY,Xi_u>Xi_0. CartanvarianceK_a=4sum_ns(E)strictlydecreaseswithu,K_a0=3/pi. Actualoriginalpi/Jlift,36covariance/determinantandindependent64stateFocktraceexecuted.",
      "scopeEN": "GivenwholeconstantquarterconsumerwithoriginalscalarkineticsandfixedH. Noprimitivemeasurechoice,physical4Dobservableorcompletedynamicalgaugesource. Majorana/complementretainedinwholeweight;nophysical96CARdoublecount.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-quark-particle-color-group-counting-on-whole-constant-quarter-source",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d9a5a2e035e761e772ff8fa6",
        "source:8aea7c4760d7eb152299afbe",
        "source:78e93be13348590471385e7b",
        "source:64109cd73101cc56c12fc59e",
        "source:4ce51bb84103edda1d8ffc83",
        "source:bf3abd209cdea28089fc2076",
        "source:0ab6ca67e919cee3cb9b790f",
        "source:aadcb4da1e764a25d13798e6",
        "source:63814e38bca34d3a1262acac",
        "source:19db256c3dd54fa62ffc0e23"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:single-original-color-parity-separates-free-quillen-from-positive-higgs-integrated-source",
      "titleEN": "One original color parity separates free Quillen response from positive Higgs source",
      "statementEN": "WholefreequarterpairresponsealongGthetaexactlyequalsN(theta/(2pi),0)^12. Jacobiandsquareselfdualitygiveexact1/64EXPECTATIONatGstar=diag(−1,−1,1),notprobability. EverycompletepositivenormalizedHweightwithmu(u>0)>0andnonzeroquarkYgivesthesameboundedgroupvalueSTRICTLYabove1/64; equalityforcesu0almostsurely. NoHmomentassumption,radialscanorsmallHtruncation. Thisisasingleexactbefore/afterHsourcescopeprobe. CARcurrentcoefficients12/12remain;changingglobalvarianceisnotchangingprimitivec3.",
      "scopeEN": "OnlyspecifiedpositiveconditionallyquasifreeconstantHclass. Signedweights,extrafermionvertices,spacetime-dependentgauge/H,Gauss/Pfaffianrestrictionsneedactualconsumer. FreeprimitiveBEFOREHallowed. Nouniformfinitegap/noisystabilityclaim. ColorcountingnotprimitiveEMormetricvariationwithoutactualref/domain/measuremap. F1isanorigintaskname,notanumericalcoupling.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-quark-particle-color-group-counting-on-whole-constant-quarter-source",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d9a5a2e035e761e772ff8fa6",
        "source:8aea7c4760d7eb152299afbe",
        "source:78e93be13348590471385e7b",
        "source:64109cd73101cc56c12fc59e",
        "source:4ce51bb84103edda1d8ffc83",
        "source:bf3abd209cdea28089fc2076",
        "source:0ab6ca67e919cee3cb9b790f",
        "source:aadcb4da1e764a25d13798e6",
        "source:63814e38bca34d3a1262acac",
        "source:19db256c3dd54fa62ffc0e23"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-original-quarter-graph-color-response-is-relative-and-diagonal-singlet",
      "titleEN": "Whole original quarter graph reads relative color in a diagonal singlet state",
      "statementEN": "WholeSU3xSU3characterdet[E*diag(UL,UR)E]=XiH(GL^-1GR)withoutmutualcommutation. CanonicaldiagonalsourceliftfixesSlatervectorforeveryH;response1,whileonefacehasR067freepairGstar1/64andlargerpositiveH-integratedvalueinthestatedclass. Fullmodecharactersconvergeuniformly. JointchargecovarianceKH[[1,-1],[-1,1]]retainsH-dependentrelativecorrelationsandzerototalcharge. SamecompletepositiveHmixturepreservesdiagonalidentity,notgeneralquasifreeness.",
      "scopeEN": "ExistingconditionalconstantHwholegraphclass,notHweightchoice,physicalcarrierPadmidentity,Gausslawor3+1/spin2derivation. NobareinfinitedetU,unspecifiedFockvectorlimitorgenericHdisjointnessclaim. DistinguishcountedonefaceoperatorfromcanonicalGNSsymmetryimplementer.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-whole-quarter-graph-and-canonical-diagonal-original-color-lift",
        "premise:typed-source-structures",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:original-quark-particle-color-group-counting-on-whole-constant-quarter-source",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:stipulated-e8-h8-with-original-color-center-selector"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:377825c67ecee1407ae2bafd",
        "source:087f66c1ae30fe4cf5f4f3c8",
        "source:fddfebdad65d5403d1f9a1fd",
        "source:fbd12086f8d5ad261424e92e",
        "source:d22c445aa8725bb11c735c66",
        "source:966943f4fdbb324306a1ee19",
        "source:d9a5a2e035e761e772ff8fa6",
        "source:aadcb4da1e764a25d13798e6",
        "source:dac409f6dd7c97e7a542fcb5",
        "source:a4424871611c71642a9067f2",
        "source:358747d0fcd73fdc64773f7a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-center-selector-requires-typed-state-field-and-face-transport",
      "titleEN": "Original center selector requires typed state field and face transport",
      "statementEN": "TotalcenterfixeswholeGstatebutonefaceconditioningchangesit:exactoriginaltripletcoefficientc1/5givesGstar9/25,selectionweight13/25,conditional1. InvariantobservableRESTRICTIONleaves9/25. Onefaceconditioningisratioofcenter-shiftedXi;integrateHbeforetakingratio. EquivariantfundamentalquarkSLOTembeddingintoSAMEcenterneutralSTATEsectorobeysT=zetaT,hencezero;native96oneparticlecenterwouldretain24leptonsandkill72quarks. NophysicalPadmidentityasserted;chargedfieldsactintersector. OriginalfixedZref0cancelsinnormalizedZrelstateanddoesnotselectH.",
      "scopeEN": "Specifiedrepresentationsanddistinctoperationorders,notabanonquarkfieldsorTFPT. NeitherdiagonalliftnoronefaceconditioningidentifiedwithphysicalPsing. SU3singletiscompatiblewithZ3selector. Notallmixturesarenonquasifree;retainR054conditions. Otherfield-dependentrelativeactionvariationsrequirefullR043.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:given-whole-quarter-graph-and-canonical-diagonal-original-color-lift",
        "premise:typed-source-structures",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:original-quark-particle-color-group-counting-on-whole-constant-quarter-source",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:stipulated-e8-h8-with-original-color-center-selector"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:377825c67ecee1407ae2bafd",
        "source:087f66c1ae30fe4cf5f4f3c8",
        "source:fddfebdad65d5403d1f9a1fd",
        "source:fbd12086f8d5ad261424e92e",
        "source:d22c445aa8725bb11c735c66",
        "source:966943f4fdbb324306a1ee19",
        "source:d9a5a2e035e761e772ff8fa6",
        "source:aadcb4da1e764a25d13798e6",
        "source:dac409f6dd7c97e7a542fcb5",
        "source:a4424871611c71642a9067f2",
        "source:358747d0fcd73fdc64773f7a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-color-center-fixes-whole-e6-a2-source-and-charged-ward-word-action",
      "titleEN": "Original color center fixes whole E6 A2 source and charged Ward word action",
      "statementEN": "ActualmarkedColorL0=ker tmod3equalsE6_perpColor orthogonalsumA2_Colorbyinclusionandequalindex3,forALLlatticevectors. WholefixedpointVOAretainsalloscillatorsandchargedV1,V2;weight1split86/81/81,actualcolorweights3x27withnorms2/3,4/3. E6commutesColor,notoldD5(4not40intersectionroots). OriginalWardtriality1andwholeweak24blocktriality0;allfieldcoefficientsPrYqPsonlyforr=s+tq. Balancedwordsretainneutralendpointsandchargedpaths;adjointWardnorm1iskilledonlybyfactorwiseP0. Existingproperlysupportedlocalcurrentgivesneutralbounded(I+A*A)^-1inthesamelocalfixedpointnet.",
      "scopeEN": "GivenstipulatedE8branchandoriginalmarks;genericE6glueandoldJtheoremreused. NophysicalPadm/OS/96CARidentity,HweightornewYderivation. Dimensionsarenotparticlecounts. CenterandglobalSU3fixedpointsretainc8;affinecommutanthasc6. FixedcolorbranchnotnativeJclosed;retainwholeclocks/fields.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-marked-color-center-on-whole-e8-lattice-current-source",
        "premise:typed-source-structures",
        "premise:stipulated-e8-h8-with-original-color-center-selector",
        "premise:local-e8-current-response-realization",
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:67ceba565b20d3598358e934",
        "source:fd306c5ee3e18b011bea1394",
        "source:2d018b5188aa6ca9fa98c546",
        "source:39f26f9aba8a96a06f160b38",
        "source:1f403314639c66c6c915985c",
        "source:f8b2883aa44f276772596e58",
        "source:c9d7e7c8aa15bc8f911b1fc2",
        "source:358747d0fcd73fdc64773f7a",
        "source:f8a30f8d81abbe00ef94c815",
        "source:85f35396a9dbfeaaf66329c0",
        "source:15b8f8d3b3fcaeb0e549a677"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-color-neutral-lattice-class-cannot-supply-odd-fields-by-inherited-superlattice-extension",
      "titleEN": "Original neutral lattice class admits no odd inherited superlattice extension",
      "statementEN": "CompleteZ3²discriminantq=(2k²+l²)/3mod1hasdistribution5/2/2at0,1/3,2/3andno1/2. OriginalE8isotropicZ3gluehaschargedh1. ALLintegraloverlatticeswithSAMEconformalvectorareeven:det9forcesindex1or3,whereasoddnormkernelwouldforceevenindex. RenamingchargedbosonicE8currentsasquarkCARundertheunchangedinheritedchiralgradingisnotanoriginmap.",
      "scopeEN": "Onlyspecifiedintegrallattice/superlatticeclasswithinheritedstress. Noprohibitionofphysical3+1fermions,primitiveCAR,nonlocalintertwiners,actualsourcecovers/gradedmapsorTFPT. Nofreeexternalfermionsectorrequired. Distinguishconformalweight,internalSpin10indexandphysicalLorentzspin.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-marked-color-center-on-whole-e8-lattice-current-source",
        "premise:typed-source-structures",
        "premise:stipulated-e8-h8-with-original-color-center-selector",
        "premise:local-e8-current-response-realization",
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:67ceba565b20d3598358e934",
        "source:fd306c5ee3e18b011bea1394",
        "source:2d018b5188aa6ca9fa98c546",
        "source:39f26f9aba8a96a06f160b38",
        "source:1f403314639c66c6c915985c",
        "source:f8b2883aa44f276772596e58",
        "source:c9d7e7c8aa15bc8f911b1fc2",
        "source:358747d0fcd73fdc64773f7a",
        "source:f8a30f8d81abbe00ef94c815",
        "source:85f35396a9dbfeaaf66329c0",
        "source:15b8f8d3b3fcaeb0e549a677"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-color-center-extends-to-folded-ns-but-full-current-action-needs-spin-sector-transport",
      "titleEN": "Color center acts on original NS source while full color currents require spin-sector transport",
      "statementEN": "At unchanged original M,M^T w=(1,-1,0,-1,-1,-1,0,-1),so given Z3 color center extends to all integer NS charges. Exactly±(e1-e2) among six actual color A2 roots lie in M D8;other four have half-integral source charge in every coordinate and full monodromy−1 with each original odd vector generator. This stipulated root-current action is not an internal full SU3 action on the unchanged NS charge space. Common center-neutral even lattice D0=(M D8)∩ker(t mod3) has index6 in E8 and determinant36. E8_center and (M Z8)_center are distinct even/odd index2 neighbors over D0,both determinant9;the latter does not contain the former. R069 no odd overlattice of the ENTIRE E8_center remains unchanged.",
      "scopeEN": "Exact fixed source/color Cartan and charge-lattice interface with inherited chiral vertex monodromy. Algebraic center transport is not physical gauge/support/state identification;center neutrality is not SU3 singlet. Retain existing AIA parent,actual spin/defect/covers or nonlocal charged maps;no universal point-local1D dictionary required. No new chosen fermion sector,physical96 map,measure,time,3+1 or spin2. 58 own exact controls plus all-lattice proof,one actual analytic The reviewed review;no new Lean or ledger promotion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-fixed-color-and-folded-ns-cartan-interface",
        "premise:typed-source-structures",
        "premise:original-marked-color-center-on-whole-e8-lattice-current-source"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029",
        "contract:canonical-seam-fermionization-20261025"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:287ca461dd15e94d8591b190",
        "source:e6d8b501f6f9a11803ff206b",
        "source:6ebe094a387a7a965e3e3a53",
        "source:ad7c5b52ce0da9511f3d4d20",
        "source:9aca508a4dcd3b920f5d5470",
        "source:67ceba565b20d3598358e934"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-color-spin-car-mixed-word-has-complete-thermal-source-and-cyclic-sewing",
      "titleEN": "Actual mixed color-spinor CAR word has full thermal response and spin-sector sewing",
      "statementEN": "For original q=M^T(e2-e3),three other missing color roots and every v=e_j,the full(q,v,-v,-q) word is explicit: entire Theta_NS zero modes,all oscillator prime factors and original-time exp(delta.X),with cross-ratio power q.v=±1/2. Old actual cocycle fixes paired adjoint factor1. Independently recover original whole-sea CAR two-point and absolute scalar source partition. Full thermal sewing G_NS(word)=G_R(cyclic) at x1→x1-T,T=8beta follows exact theta/prime/time cancellation. Under actual center,retain Z_NS0 F_NS0=Z_R0 F_R0(cyclic),not equality of normalized answers. Retain all spin/charged paths and individual q/v monodromy−1. Explicit positive NS state extension and bounded midpoint form require no forced extra sector weighting.",
      "scopeEN": "Given free original quarter source and retained AIA parent,ordered analytic fields,entire modes/charge class. Positive given-state extension is not primitive state selection. Midpoint positivity is not full physical OS/RP,no unregulated sharp bounded bilocal or ordinary common point-locality. No Gaussianization of H mixture,no96-matter/physical-time/3+1/spin2 origin closure. 598 controls with analytic all-mode/cyclic proof,two actual analytic The reviewed CLI rounds;no new Lean or ledger promotion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-thermal-quarter-source-and-retained-spin-parent-mixed-word",
        "premise:typed-source-structures",
        "premise:original-fixed-color-and-folded-ns-cartan-interface"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:f815383971a70929f21ae42f",
        "source:33d3e3199b22e08136572731",
        "source:127685fdcd2fc41ac2413f07",
        "source:e99f977d97d97cdfa1fd6a22",
        "source:e70218bdf191ad9494d4c978",
        "source:0e72de1e79fe537fd50ab004",
        "source:fc019ac4856e124bedb6de4d",
        "source:e6bade8f6c28872bfe4fe62c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:exact-original-ns-ramond-heat-equality-does-not-identify-fixed-color-restricted-source",
      "titleEN": "Exact NS Ramond heat equality does not identify the fixed-color source",
      "statementEN": "P swaps first/last four source coordinates,r=(1/2)^4(-1/2)^4. Both original quarters obey P^T(r+delta)=delta and r²/2+delta.r=0. k→Pk+r bijects whole NS/R with same given energy and oscillator multiplicities,so Z_R=Z_NS exactly and Theta_R(X)=exp(r.X)Theta_NS(P^T X). It does not preserve actual fixed color center:Mr=e1+e4 has triality1. Retain prior removal of R zero state while NS vacuum remains. Hence Z_NS0≥1 and Z_R0≤Z_R-1=Z_NS-1<0.06 at beta4pi,with analytic rational bound. Optional NORMAL full-B(H_parent) KMS extension has unprojected NS/R weight1/2 but not after actual center restriction. Do not select it as a physical rule.",
      "scopeEN": "Actual fixed free source time and marks. Prior zero-state removal is reused,not recounted;no physical probability/measure choice. Transporting all data jointly remains a different valid coordinate comparison. Heat equality is not same-source identification with unchanged fields/marks/trace. Do not replace original spin seam,Ref/Eta/H0/Z0 and insertions by new Gibbs rule.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-thermal-quarter-source-and-retained-spin-parent-mixed-word",
        "premise:typed-source-structures",
        "premise:original-fixed-color-and-folded-ns-cartan-interface"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f815383971a70929f21ae42f",
        "source:33d3e3199b22e08136572731",
        "source:127685fdcd2fc41ac2413f07",
        "source:e99f977d97d97cdfa1fd6a22",
        "source:e70218bdf191ad9494d4c978",
        "source:0e72de1e79fe537fd50ab004",
        "source:fc019ac4856e124bedb6de4d",
        "source:e6bade8f6c28872bfe4fe62c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-scalar-cover-profile-cannot-implement-fixed-spin-cartan-loop",
      "titleEN": "Original scalar cover profile cannot implement actual color Cartan loop",
      "statementEN": "Original Gphi is eta-diagonal,required Vq=Ualpha diag(exp(-iq_k b)) Ualpha*. The two diagonal algebras intersect exactly in CI. All four actual q have2/6 signs,q²2,sumq=±2,so Vq is arc-diagonal iff b in2piZ. Smooth compact proper-interval support forces b0. Exact offdiagonal squared norms are3/2 for Aq and6sin²(b/2) for Vq,both quarters. Entire scalar profile class decided without frame/profile fit.",
      "scopeEN": "Only identification of this actual smooth Cartan operation with scalar original-cover Weyl profile. No exclusion of neutral sources,composite CAR fields,physical3+1 orTFPT. Aq is Cartan,not charged vertexYq.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-eightfold-arc-residue-source-and-fixed-spin-cartan-insertion",
        "premise:original-fixed-color-and-folded-ns-cartan-interface",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:26a24d24275a225963ce94f7",
        "source:45c0606161e627fb4b821bcd",
        "source:681f138e563942418ee5a51a",
        "source:fa9bc910b6619512584e0e80",
        "source:ad7c5b52ce0da9511f3d4d20"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-spin-cartan-composite-source-retains-multi-arc-support-and-fails-additive-even-locality",
      "titleEN": "Actual composite current retains multi-arc support and fails additive even localization",
      "statementEN": "Existing Jq=:chi*diag(q)chi:=:eta*Aq eta: fixes smooth operation and levelq²2,no free matrix. Aq contains actual cross-arc bilinears. Full even CAR support stays in U=F^-1(K). Original scalar Weyl with pi on one arc,0 on others commutes with additive join of separate even arc observables. Its Rr=I−2|r><r| fails to commute with Vq where Aq is offdiagonal,so q operation generically is not in that additive even algebra. Distinguish interval hull,full union algebra and additive arc algebra. Smooth neutral transport remains possible;endpoint monodromy does not imply blanket local or3+1 noGo.",
      "scopeEN": "Given actual folded CAR representation and original operator action before physical source identification. No primitive choice of composite current,no sharpYq/NSR completion,newHiggsmeasure or96/3+1/spin2 origin.66 own controls plus analytic class/commutant proofs;no newLean/ledgerpromotion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-eightfold-arc-residue-source-and-fixed-spin-cartan-insertion",
        "premise:original-fixed-color-and-folded-ns-cartan-interface",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:26a24d24275a225963ce94f7",
        "source:45c0606161e627fb4b821bcd",
        "source:681f138e563942418ee5a51a",
        "source:fa9bc910b6619512584e0e80",
        "source:ad7c5b52ce0da9511f3d4d20"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-color-selector-admits-exactly-eighth-periodic-original-density-variations",
      "titleEN": "Actual color selector admits exactly eighth-periodic scalar density variations",
      "statementEN": "Exact||(I-P0)J(phi)Omega||²=sum_m>0 ell_m|phi_m|² with ell_(8k+s)=kD_s+L_s,D=(0,6,4,6,2,6,4,6),L=(0,1,1,3,1,3,3,5). Unique w0=1 supplies original witnessa0*a_-mOmega for every m outside8Z;ell_m=0 iff8|m. ENTIREexp(itJphi)group reducesP0 forALLt iff phi(theta+2pi/8)=phi(theta). cos(theta) exact vacuum leakage norm²1/4. Actual qCartan source preserves color but is not a uniform scalar current. E_Z(Jm) retains matching-residue bilinears;whole neutral words retain charged paths.",
      "scopeEN": "Given original NS source/color contract,no fullP_adm=P0. Class of entire continuous individual scalar operations,not exclusion of other neutral fields/whole words or isolated unitaries. Analytic all-mode proof plus36 own controls,no physical measure,3+1,spin2 ornewLean.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-ns-color-center-continuous-density-and-coordinate-net",
        "premise:original-fixed-color-and-folded-ns-cartan-interface",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a77665b4ece921aac72845db",
        "source:115e082a9a1e21fe0a2fd3c2",
        "source:937b0941aedf8f9bf05acfda",
        "source:30cf23e8bdb7752a6c3eb187",
        "source:ad7c5b52ce0da9511f3d4d20",
        "source:47d7d1a5e11ad8c530190f68",
        "source:562d274a53921abff4c65a45",
        "source:1d25b2cdf1039980bb68472e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-color-is-internal-exactly-on-eightfold-coordinate-source-regions",
      "titleEN": "Actual color center is internal on eightfold coordinate source regions",
      "statementEN": "Zarc=Ualpha diag(exp(2pi iw/3))Ualpha*. Exact diagonal-commutant equations have rank7,kernelCI. Original coordinate support obeys[P_O,Zarc]=0 iffO=F^-1(K) modulo nullsets. Finer original cover localization is not preserved by this internal color center:|Z10|²3/64 and||[Zarc P_arc0 Zarc*,P_arc1]||HS²183/2048. Same matrix preserves all existing8channel quotient regions and commutes with actual source time/covariance. This fixes finest compatible ordinary coordinate regions of THIS cover,no unique physical spacetime.",
      "scopeEN": "Full GIVEN CAR coordinate net and neutral current bridge,not all intermediate/dual nets,noncoordinate localization or physical3+1 sources. Do not identify order3Z with order8clock. Reuse existing whole neutral bilocal reconstruction and its connected-interval/relative-commutant scope;no new elementary coupling percomposite required. Primitive seam/determinant/gap and P1 source image remainopen.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-ns-color-center-continuous-density-and-coordinate-net",
        "premise:original-fixed-color-and-folded-ns-cartan-interface",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a77665b4ece921aac72845db",
        "source:115e082a9a1e21fe0a2fd3c2",
        "source:937b0941aedf8f9bf05acfda",
        "source:30cf23e8bdb7752a6c3eb187",
        "source:ad7c5b52ce0da9511f3d4d20",
        "source:47d7d1a5e11ad8c530190f68",
        "source:562d274a53921abff4c65a45",
        "source:1d25b2cdf1039980bb68472e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-whole-two-face-multiplier-reduction-is-only-constant-residue-diagonal",
      "titleEN": "Whole original two-face multiplication reduction is constant residue diagonal",
      "statementEN": "On the full original graph,bounded2x2 cover multiplication reducesG iffA=cI2. In actual periodic8fold,entire16x16 multiplication reducesG iffA_m[k,l]=delta_m0 delta_kl c_k I2. Analytic tail,strictC and nonzeroX proof covers all modes and matrix symbols;no nonzero properly supported multiplier.",
      "scopeEN": "Given whole source,matrix multiplication class and original frames/labels;not full bounded-operator commutant or physicalOS/Padm/localitynoGo. Do not identify Cauchyselection and physicalH_adm. Reuse already existing Psing center definition.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-full-two-face-graph-and-local-matrix-operations",
        "premise:actual-product-collar-two-face-data",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f431205642543b650f4569a8",
        "source:502ec45f007a04d03012cd55",
        "source:58f3b199a5c998064def59ee",
        "source:a9f4800c2969f84839fa84ca",
        "source:75ddc9998eb934f37c1e1d29",
        "source:f6d6378d70ac5fa3822addaf",
        "source:314138550b441b8f49e5986a",
        "source:1d25b2cdf1039980bb68472e",
        "source:beaf175662922ce618a76838"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-two-face-local-fock-implementation-and-exact-source-variation-differ-from-reduction",
      "titleEN": "Implementable original two-face operations change Cauchy graph with exact norm",
      "statementEN": "Entire smoothU16 multiplication is implementable in givenG Fock iff faceblockdiagonalU8×U8;reducers only constant sharedU1^8. CoverpointwiseU2 has separateU1×U1 class,not same localization as fold. Exact||[Mv,G]||HS²=sum_m2m tanh(beta m/4)|v_m|² by whole-sea telescoping,alphaindependent. Actualq.q2 commonfold lift gives4sum_m m tanh(2beta m)|b_m|²;variance1/2HS²,not commonSchwingerterm. AlwaysC_V=E_R* V G V* E_R;retain common/relative lifts and fullsource.",
      "scopeEN": "ChargedCAR and givenwholeG source;implementation is not local-algebra membership,stateinvariance,neutrality,parity orP1origin. BarefaceswapnotHS;old combinedreflection withBsign reversal remains. No freegeometry/temperature/coupling;retainZ0/Ref/Eta/H0/higherwords,originalOSsource/Padm still required.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-full-two-face-graph-and-local-matrix-operations",
        "premise:actual-product-collar-two-face-data",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f431205642543b650f4569a8",
        "source:502ec45f007a04d03012cd55",
        "source:58f3b199a5c998064def59ee",
        "source:a9f4800c2969f84839fa84ca",
        "source:75ddc9998eb934f37c1e1d29",
        "source:f6d6378d70ac5fa3822addaf",
        "source:314138550b441b8f49e5986a",
        "source:1d25b2cdf1039980bb68472e",
        "source:beaf175662922ce618a76838"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-undecorated-transfer-does-not-determine-original-marked-field-source",
      "titleEN": "Even the whole undecorated transfer does not determine the marked field call",
      "statementEN": "Exact primitivePauli CP transfer E(I)=I,E(sigma)=sigma/3 with same PerrondensityI/2 remains identical underA0/Ax Kraus rotation,while same fixed marked O=|0><0| gives1/2 versus1/3. Joint transport ofO is basis equivalence;fixed marks require actual source decorationE_O. Finite positiveP/separating diagonal-family matrix-algebra conclusion remains valid but is not displayed source decoration.",
      "scopeEN": "Typed source audit and exact counterexample to E_I determining E_O. Not wholeTFPT twins,chosen physicalKraus family,or neutral-source impossibility. Reuse older weight-producer gap and OS moment repair,not new discoveries. MPS is named route,not universal axiom;another complete original field rule also suffices.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-blocked-transfer-algebra-and-marked-source-uniformity-audit",
        "premise:given-original-two-stage-admissibility-complex-and-blocked-weight-caller",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f584bd5f40f25cc86cff1130",
        "source:9113c7cb4e6f07e2f3957130",
        "source:ae9ddcb0a38eb64b6ef127ad",
        "source:29a6b485f10379ecc3c34ec6",
        "source:92b690e99950ef3123614626",
        "source:e3a4c851c9b7381edbe7b598",
        "source:b5a0a83bd5cbf3f42575e2ac",
        "source:c7bf0d12e45b76b2f52a704b",
        "source:d1b9adf9909f8865f224e5b0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:volume-wise-injective-positive-transfer-does-not-prove-uniform-parent-gap",
      "titleEN": "Injectivity at each volume does not prove uniform parent gap",
      "statementEN": "Exact MPS familyA0=|0>(a<0|+b<1|),A1=|1>(b<0|+a<1|),a²=1-e,b²=e,0<e<1/2 is length2injective with fixedD=d2 and canonical range3 norm1 parent projectors. Ringnorm1+lambda^L and exact whole variance give direct Rayleigh gapH_L(e)<=9(1-lambda)/(1+lambda)(1+lambda^L)/(1-lambda^L). e_L=1/(4L) givesO(1/L) to0,without equating PF and parent gaps.",
      "scopeEN": "Excludes automatic uniformity from per-volume positivity/separation/injectivity for changing tensors. Does not contradict fixed-tensorFNW or prove actualTFPTgap collapse. ActualC6/weights/carrier must produce common tensor or controlled family. No physical3+1/spin2 orLean validation.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-blocked-transfer-algebra-and-marked-source-uniformity-audit",
        "premise:given-original-two-stage-admissibility-complex-and-blocked-weight-caller",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f584bd5f40f25cc86cff1130",
        "source:9113c7cb4e6f07e2f3957130",
        "source:ae9ddcb0a38eb64b6ef127ad",
        "source:29a6b485f10379ecc3c34ec6",
        "source:92b690e99950ef3123614626",
        "source:e3a4c851c9b7381edbe7b598",
        "source:b5a0a83bd5cbf3f42575e2ac",
        "source:c7bf0d12e45b76b2f52a704b",
        "source:d1b9adf9909f8865f224e5b0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-c6-half-power-has-exact-entire-positive-ordered-word-expansion",
      "titleEN": "Original C6 half-power has exact entire positive ordered-word expansion",
      "statementEN": "ForQ=a(I-qC),kappa=a(1-q)>0,Rnu=kappa^nuQ^-nu is stochastic in bareC6 and every literal directed lengthn word has(1-q)^nu(nu)_n/n!(q/2)^n. OriginalK usesnu1/2,Green1;all lengths,intermediates,backtracks/windings retained before endpoint reduction. Concatenating independent full words sums all split positions,Vandermonde gives pnu+mu on EACHliteralwholeword.",
      "scopeEN": "Canonical analytic expansion at fixed original operator/alphabet,not uniqueness of all path measures for an endpoint kernel or primitive physical state. nu/n/6labels not physical time/spacetime. OriginalcompressedKstr not automatically bareQ;no stepwiseP. Preserve solvedHol/Y/flavor.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-bare-c6-fixed-analytic-half-power-and-literal-word-alphabet",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c6a6dd34f3fb5b5504486b89",
        "source:5d5265d09d317ad92fb8f62a",
        "source:c2236d31ef6e57cb3d2d4f2f",
        "source:e23b836f2ae4c73b75cb01a3",
        "source:0a72fd34ea834dedf7fa2e8f",
        "source:1fbbff8434dc693a8f47154e",
        "source:c2052d33fddf157d2d5e6083",
        "source:11775899d9d3f17201e2cdea",
        "source:5b49103a6a4caad1f41401c5",
        "source:543e66d4de5ff3b3e64af6f0",
        "source:92b690e99950ef3123614626"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-c6-whole-word-sewing-retains-source-amplitude-and-controlled-infinite-tail",
      "titleEN": "Whole word sewing retains original amplitude and controlled infinite tail",
      "statementEN": "K=kappa^-1/2Rhalf,Y=kappa^-1R1,retain absoluteHol amplitudes. Eachword original homogeneousdelta score -2nu delta/a+n(1/delta-2delta/a),normalized qprime[n/q-nu/(1-q)]mean0. Wholeepsilon>=0 hasq<=q0<1;half remainder<=q^(N+1)/sqrt(1-q),finite-degreecount derivatives controlled on compactgapped sets. Same originaldeterminant closedword q^nTrC^n/n,not open1/n.",
      "scopeEN": "57 own checks using unchanged nativeU6,spectrum and oldpolynomial;infinite statement analytic. Ftroriginalstationarity functional,not identifiedlogZ/statisticalmeasure. Formalmarkers not physicalJ;actual extraweight/carrier/selector/fieldcall remains. NoLean/physicalvalidation.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-bare-c6-fixed-analytic-half-power-and-literal-word-alphabet",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c6a6dd34f3fb5b5504486b89",
        "source:5d5265d09d317ad92fb8f62a",
        "source:c2236d31ef6e57cb3d2d4f2f",
        "source:e23b836f2ae4c73b75cb01a3",
        "source:0a72fd34ea834dedf7fa2e8f",
        "source:1fbbff8434dc693a8f47154e",
        "source:c2052d33fddf157d2d5e6083",
        "source:11775899d9d3f17201e2cdea",
        "source:5b49103a6a4caad1f41401c5",
        "source:543e66d4de5ff3b3e64af6f0",
        "source:92b690e99950ef3123614626"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:historical-parent-and-actual-field-time-bridges-must-be-reused-before-new-source-models",
      "titleEN": "Reuse historicalparent and actualfield/time bridges before new source models",
      "statementEN": "Originalv42§035definesformalexpWk/Gamma/propagatorandallhigherSadmvertices. Originalcircle,microscopicCAR/F8fieldtimechain,wholecoupled96Hresponsealreadyexist. v990providesactualfiniteWJwith2species/2sites/6link,v486inversespectralrates. Reusethese,notmissingformulasornewphysicaloriginselection.",
      "scopeEN": "Targetedsourceaudit/reuse,notfullcorpusrevieworglobalabsencetheorem. Formaldefinitionnotmeasureexistence. OldStageDnotedoesnotreopensolvedYukawas.38scopedF1subtasksretained,nophysicalclosure.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-finite-v990-source-and-historical-parent-recovery",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f90f6ba7f988ac8cd1bed668",
        "source:a665df83e74c28b8257e6025",
        "source:74f861a03fbd4850688bdf60",
        "source:f5e4cbe750db8336d80ee3e4",
        "source:1ba25b17f38834c6f3762b65",
        "source:2e035b6b59e9bd4a72225f22",
        "source:a3836f627ccae389d1d394a2",
        "source:ef589f22780ef166a95a08ac",
        "source:d5916ed3499f118d9c4094c5",
        "source:f274e99cedff9e0f71fe9540",
        "source:426282baf86cc97970fc7567",
        "source:5108b907082fe61904b9d4ca",
        "source:484d365e7e5fe4b0ceb9949c",
        "source:a98b976eed56f3891f2474a0",
        "source:1b695d3b144e27f540e10410",
        "source:bd1b6a8e4fc9bb24b74a0a39",
        "source:67f1bfaedaabe297db9385ec"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-native-v990-full-timed-words-recover-kubo-response-distinct-from-instantaneous-variance",
      "titleEN": "Actual timedv990 words recover originalKubo response distinct from instantaneousvariance",
      "statementEN": "SameactualH_W0/OPSfixesallorderedwordsTr[e^(-(beta-tn)H)On...O1e^-t1H]/Z0. OriginalJwithoutbetagivesHessW=beta^-1intC(tau)dtau. OriginalOZ:C0=.49988408263643,Kubo=.49033650199002,Cmid=.48558570858218;integralcomparison1.7e-16. PureCARalgebraI6tensorM16,commutantM6tensorI16,emptyCARsectorrank6;Hcoupleslink/matter.",
      "scopeEN": "Analyticfinitetimedwordandactualnativeconsumer.18uniqueoldmodulechecks(v99013,v4865),6focusedcontrols;returnframereplaynot13newindependentchecks. Imaginarythermaloriginalmodeltime,notprimitiveTFPTtime/measure/3+1/spin2.96manybodyspacenotautomatically96SMon eparticlespace.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-finite-v990-source-and-historical-parent-recovery",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f90f6ba7f988ac8cd1bed668",
        "source:a665df83e74c28b8257e6025",
        "source:74f861a03fbd4850688bdf60",
        "source:f5e4cbe750db8336d80ee3e4",
        "source:1ba25b17f38834c6f3762b65",
        "source:2e035b6b59e9bd4a72225f22",
        "source:a3836f627ccae389d1d394a2",
        "source:ef589f22780ef166a95a08ac",
        "source:d5916ed3499f118d9c4094c5",
        "source:f274e99cedff9e0f71fe9540",
        "source:426282baf86cc97970fc7567",
        "source:5108b907082fe61904b9d4ca",
        "source:484d365e7e5fe4b0ceb9949c",
        "source:a98b976eed56f3891f2474a0",
        "source:1b695d3b144e27f540e10410",
        "source:bd1b6a8e4fc9bb24b74a0a39",
        "source:67f1bfaedaabe297db9385ec"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-original-higgs-force-has-complete-ordered-fermionic-determinant-source",
      "titleEN": "Original Higgs force has complete ordered fermionic determinant source",
      "statementEN": "Actualfourv252oneformderivativesgiveTa=-igammaVa,Ka=dGammaTa,wholeorderedexponentialdeterminantandCov=TrCTa(1-C)Tb. Neutraldirectionpaircommutatornorm²=24[Tr((Yu*Yu)^2)+Tr((Yd*Yd)^2)]>0. ActualSU2/hypercharge/colormapchecked;36nonredundantquarkmodesread2^36occupationstatesexactly.",
      "scopeEN": "ActualgivenquarkCARconsumer,notwholeprimitivesource;other96sectorsandMajoranaretained. Seed252,p1/4,ell1arithmeticcontrols,notphysicalscalechoice.27ownchecks;noLeanorphysicalF1closure.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-finite-car-higgs-force-and-faithful-collective-source"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ed66fe4529e8f8df6a876c7f",
        "source:4488f6475fc838331cbc6c07",
        "source:100131655234bb9aa75ceb6c",
        "source:c3d6d542896b29a49c51a7ed",
        "source:bf991c6861aa93bfdfb73676",
        "source:75c3c214feda154e9f135b8b",
        "source:88d7ae510503c94877ce869b",
        "source:7b9d208a53a0b23d563bbef4",
        "source:a881bc45c8d7535e078badd4",
        "source:475e7c90cb51d463ffa5a8b9",
        "source:37d8b3d9fa0981776fabedf6",
        "source:0ba5acb99c0f2aeb12cbb2cf",
        "source:41bb6ee655146b0ce8297b71",
        "source:131751903c6895be3e43ab55",
        "source:9a64da1ea24bbcddb00b9043"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:finite-covariant-higgs-composites-have-no-nontrivial-positive-instantaneous-classical-law",
      "titleEN": "Finite covariant Higgs composites have no nontrivial positive instantaneous classical law",
      "statementEN": "Any commuting selfadjoint four-vector in a finite algebra with exact continuous SU2 Higgs-doublet action is zero. ApositiveclassicalR4representationofomega(expijK)fornoncommutingcovariantKforcesmu=delta0viaequalfinitedirectionalspectraandcountabledensedirections. Nonzerosecondmomentexcludesit;stateinvariancenotrequired.",
      "scopeEN": "Exactfixedfinitealgebra,exactSU2doubletcovariance,instantaneousWeylcharacteristic,positivejointclassicallaw. Noexclusionofinfinitelimits,collectivequantumfields,otherorderingorgeneralEuclideanHsources. GibbsWcol(ij)isnotthischaracteristic.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-finite-car-higgs-force-and-faithful-collective-source"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ed66fe4529e8f8df6a876c7f",
        "source:4488f6475fc838331cbc6c07",
        "source:100131655234bb9aa75ceb6c",
        "source:c3d6d542896b29a49c51a7ed",
        "source:bf991c6861aa93bfdfb73676",
        "source:75c3c214feda154e9f135b8b",
        "source:88d7ae510503c94877ce869b",
        "source:7b9d208a53a0b23d563bbef4",
        "source:a881bc45c8d7535e078badd4",
        "source:475e7c90cb51d463ffa5a8b9",
        "source:37d8b3d9fa0981776fabedf6",
        "source:0ba5acb99c0f2aeb12cbb2cf",
        "source:41bb6ee655146b0ce8297b71",
        "source:131751903c6895be3e43ab55",
        "source:9a64da1ea24bbcddb00b9043"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-original-collective-mean-has-exact-ball-domain-and-relative-entropy-action",
      "titleEN": "Original collective mean has exact ball domain and relative entropy action",
      "statementEN": "Faithful original CAR source gives exact Gibbs Wcol and relative-entropy Legendre dual. All force means form exactly the closed4 ball of radius3(sum svYu+sum svYd); gradW maps bijectively to its interior. Together with j=2ell deltaH this completes the nonlinear conditional H-to-mean coordinate and d4H=d4m/[(2ell)^4 det HessW]. An actual original weight transports completely. Flat H-volume pushforward retains infinite total mass; compact closure is not normalization.",
      "scopeEN": "Given finite constant-H family/source,not entire primitive H(x) field theory. YuorYdnonzero,0<C<I,pairing0. No new Yukawa derivation,no m=H,no exp(-Gamma)dm,no claim actual TFPT measure is flat. Preserve full Ref/Eta/H0/Z0,other sectors,vertices.29 own focused controls,no physical/Lean validation.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-finite-car-higgs-force-and-faithful-collective-source"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ed66fe4529e8f8df6a876c7f",
        "source:4488f6475fc838331cbc6c07",
        "source:100131655234bb9aa75ceb6c",
        "source:c3d6d542896b29a49c51a7ed",
        "source:bf991c6861aa93bfdfb73676",
        "source:75c3c214feda154e9f135b8b",
        "source:88d7ae510503c94877ce869b",
        "source:7b9d208a53a0b23d563bbef4",
        "source:a881bc45c8d7535e078badd4",
        "source:475e7c90cb51d463ffa5a8b9",
        "source:37d8b3d9fa0981776fabedf6",
        "source:0ba5acb99c0f2aeb12cbb2cf",
        "source:41bb6ee655146b0ce8297b71",
        "source:131751903c6895be3e43ab55",
        "source:9a64da1ea24bbcddb00b9043"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-uniform-allmode-force-clt-is-nonzero-only-before-fixed-time-smearing",
      "titleEN": "Uniform original all-mode force CLT loses signal under fixed time testing",
      "statementEN": "For the whole original symmetricM=2N mode class all finite same-time ordered exponential words of centered force/sqrtM converge to classical isotropic Gaussian Cov3AqI. Same actual time givesCov->0 for0<|t-s|<pi and fixedSchwartzVarFN(f)<=Bf/M->0. Hence this normalization has no nonzero temporal distributional Higgs limit,no white noise.",
      "scopeEN": "Only given constant original circle source,fixed internal dimension/Y,symmetric uniform fluctuation. R078 finite theorem retained;no norm convergence,no exclusion of other all-mode sources/general physics. Retain mixed chiral trace terms,resonanceskpi separate.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-whole-circle-product-car-force-and-original-time-smearing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2096f4155750a93e78123719",
        "source:2f7e9b4fa93bd37b1dc30df4",
        "source:5efece337fcc943d46589877",
        "source:8fe3c4e09ded82685461268d",
        "source:88d7ae510503c94877ce869b",
        "source:0decd9f461c2818284c62f1a",
        "source:d9df14dce43de122925db351",
        "source:bd9dcd442c0d79e0178e32df",
        "source:07b0dc1d9b48696511ecb92a",
        "source:a00ef03eb014f57051594211",
        "source:ed66fe4529e8f8df6a876c7f",
        "source:4488f6475fc838331cbc6c07"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-unscaled-time-smeared-force-has-selfadjoint-whole-ordered-source",
      "titleEN": "Original unscaled time-tested force has selfadjoint whole ordered source",
      "statementEN": "Original UNSCALED time-smeared centered force has summable vp(f)=TrCp Ap(f)(1-Cp)Ap(f);full sum exists on dense local CAR domain. Centered exponential groups and adjoints converge strongly,uniformly in source parameter on compacts;Stone gives selfadjoint generator agreeing there. Every finite ordered word has absolutely convergent product of CENTERED Klich factors. Native source cumulants2/3/4=26.0852990825,-61.3898994583,168.7909914713,so Gaussian replacement loses information.",
      "scopeEN": "Given constant circle quarksource and own time,spatially integrated insertion. RealSchwartz sufficient not necessary;rectangular windows also summable. No essential-core claim/no operator-norm convergence. Centering is connected reader,not absoluteZ0 fix. No primitiveHmeasure,Ka=H,physical3+1/spin2 or newLean validation. Native numbers original seed252 arithmetic controls,not predictions.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-whole-circle-product-car-force-and-original-time-smearing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2096f4155750a93e78123719",
        "source:2f7e9b4fa93bd37b1dc30df4",
        "source:5efece337fcc943d46589877",
        "source:8fe3c4e09ded82685461268d",
        "source:88d7ae510503c94877ce869b",
        "source:0decd9f461c2818284c62f1a",
        "source:d9df14dce43de122925db351",
        "source:bd9dcd442c0d79e0178e32df",
        "source:07b0dc1d9b48696511ecb92a",
        "source:a00ef03eb014f57051594211",
        "source:ed66fe4529e8f8df6a876c7f",
        "source:4488f6475fc838331cbc6c07"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-local-higgs-force-has-whole-centered-hilbert-schmidt-determinant-source",
      "titleEN": "Original local Higgs force has whole centered Hilbert Schmidt determinant source",
      "statementEN": "PointwiseoriginaloneformgivesM_FTaandwhole space/timeAFinS2. Fullsourceisdet2[1+C(U-1)]expTrC(U-1-iL),U=orderedproductexpilambdaAk,L=sumlambdaAk. Bothfactorsforced;S2/S1continuitygivesallorderedwords,strongunitary/adjointlimits,selfadjointStonegenerator. Temporalfilteralsoallowsboundedspatialrectangles.",
      "scopeEN": "Originalgivenconstantcirclequarkconsumer,fixedY/state/time. NoprimitiveHorigin,Ka=H,Hmeasure,physical3+1/spin2ornewLeanvalidation. CenteringconnectedreaderdoesnotfixabsoluteZ0. Native28controlsnotphysicalpredictions.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-constant-circle-local-higgs-force-and-hilbert-schmidt-time-source"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8f6a57abe438221d13e6e0d7",
        "source:0dc01cd9929443f2a106b159",
        "source:70302a9023f9fe01afd3d085",
        "source:5a9b680353ada09f982a57b0",
        "source:a06cc895309dd60f6f2c72e0",
        "source:88d7ae510503c94877ce869b",
        "source:2096f4155750a93e78123719",
        "source:039eb8d38b194a51c6147af4",
        "source:564e7acecdb7446c33d223d0",
        "source:7d06947a1dd9a01c847cd586",
        "source:2b321176c647dfb916f0350f",
        "source:431a73dbab9520e4607eddd4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:given-original-circle-force-source-generates-an-exact-causal-local-net",
      "titleEN": "Given original circle force source generates exact causal local net",
      "statementEN": "Givenprincipalgammahasfinitepropagationspeed1. CompacttestsallpointpairsdistS1>|t-s|giveAFAG=AGAF0. FourgroupwordimplementsidentityonCARandhassourceexpectation1;cyclicitygivesidentityonwhole mixedGNS. ForceunitariescommutestronglyandA_force(O)isisotonic/localonthegiven1+1cylinder.",
      "scopeEN": "CausalityWITHINgivenoriginalcylinder/operator/domain,notnewphysicalspacetimechoice. NofullPoincare/OS/RPorprimitive3+1derivation. Gaussian timeprobesnotcompact;causalconnectivitydoesnotforce noncommutation. Fouriercutofferrornotphysicalsignal.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-constant-circle-local-higgs-force-and-hilbert-schmidt-time-source"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8f6a57abe438221d13e6e0d7",
        "source:0dc01cd9929443f2a106b159",
        "source:70302a9023f9fe01afd3d085",
        "source:5a9b680353ada09f982a57b0",
        "source:a06cc895309dd60f6f2c72e0",
        "source:88d7ae510503c94877ce869b",
        "source:2096f4155750a93e78123719",
        "source:039eb8d38b194a51c6147af4",
        "source:564e7acecdb7446c33d223d0",
        "source:7d06947a1dd9a01c847cd586",
        "source:2b321176c647dfb916f0350f",
        "source:431a73dbab9520e4607eddd4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:literal-archived-global-rg-kernel-does-not-preserve-finite-measures",
      "titleEN": "Literal archived global RG kernel does not preserve finite measures",
      "statementEN": "LiteralarchivedpositiveRGmapwithglobalK>=m>0,Lebesguetargetdt[0,infty),finitenonzeronuandfinitepositiveZpsigivesTnu([0,L])>=mnu(total)L/Zpsi. Outputmassinfinite,nofiniteselfmap/claimedfinitefixedpoint. CompatibleDiracoperators/positiveweightalonedonotreplacewholeconditionalmarginalidentityE[e^-Sm|pi=x]=(Zm/Zn)e^-Sn(x)oractualRP.",
      "scopeEN": "Exactlyarchivedglobalpositivelowerkernelboundwith infiniteLebesguetargetandfinitenormalization. NoglobalTFPTrefutation,noexclusionofotheroriginalsupports/references/kernels. Nofreerepairmeasure;retainY/flavor/alpha/E8/clocks.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:literal-archived-global-positive-kernel-finite-measure-map"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8f6a57abe438221d13e6e0d7",
        "source:0dc01cd9929443f2a106b159",
        "source:70302a9023f9fe01afd3d085",
        "source:5a9b680353ada09f982a57b0",
        "source:a06cc895309dd60f6f2c72e0",
        "source:88d7ae510503c94877ce869b",
        "source:2096f4155750a93e78123719",
        "source:039eb8d38b194a51c6147af4",
        "source:564e7acecdb7446c33d223d0",
        "source:7d06947a1dd9a01c847cd586",
        "source:2b321176c647dfb916f0350f",
        "source:431a73dbab9520e4607eddd4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-higgs-marginal-retains-induced-vertex-and-noether-response",
      "titleEN": "Actual native Higgs marginal retains induced vertex and Noether response",
      "statementEN": "For the same given finite CAR Higgs source, the BKM log-partition Hessian obeys original weak-orbit r²W11-rW3=0; ordinary equal-time covariance fails the native test. Diagnostic gamma+ restriction gives CP=PCP,Keff=logit CP and its Frechet derivative. Bare P dKH P=0 while induced H response is nonzero for p,H,Y nonzero. Original Yu singular-pair formula proves mechanism. Whole static retained words and unnormalized partial trace preserve Zfull/Zkeep with det(I+exp K). Physical time words still need partner/PQ memory; modular reader is not autonomous physical time.",
      "scopeEN": "Exact scoped connection of existing R060/R077/R078 readers at supplied background and diagnostic grading. No physical P selection, H measure,3+1 or spin2 derivation. Retain nonquasifree whole words after H integration.42 native controls; no new Lean, experiment or original-ledger promotion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-constant-circle-local-higgs-force-and-hilbert-schmidt-time-source",
        "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2534de4bf5c121338fede9d2",
        "source:7d425f403bbc83fc1784a494",
        "source:6ea15860f408e7f5cf009f17",
        "source:24935f1565d04fc744ec761f",
        "source:8ac161c4006dd4b460a59e46",
        "source:88d7ae510503c94877ce869b",
        "source:2bdc6a5a5c44ffcdef5e84bc",
        "source:03bff0df81a25b0cfdeddcd8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:isospectral-noether-orbit-does-not-supply-original-metric-higgs-variation",
      "titleEN": "Isospectral Noether orbit does not supply original metric and Higgs variation",
      "statementEN": "Tr fprime(D)[X,D]=0 is an isospectral orbit identity, valid even at radially nonstationary backgrounds. Proposed local X=gTa generates a first-order symbol term because Ta is odd, hence is not the actual zeroth-order Higgs insertion. Entanglement first law alone selects no state/Einstein equation. Same constant96 circle source has Theta(t)~96sqrt(pi/t), unchanged in exponent by finite internal fibre or exact fold. Only named shortcuts excluded. Original common action plus exact marginalization remains constructive continuation; actual origin inputs are not supplied by this test.",
      "scopeEN": "Only specified inner-generator identification and literal same circle-operator relabeling. No global TFPT, relational, entropic or emergent no-go. Full relative reference/domain/eta required under unitary transport. R081 is hypothesis assessment, not another physical F1 closure.13October UV finding corrected as reuse.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-constant-circle-local-higgs-force-and-hilbert-schmidt-time-source",
        "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2534de4bf5c121338fede9d2",
        "source:7d425f403bbc83fc1784a494",
        "source:6ea15860f408e7f5cf009f17",
        "source:24935f1565d04fc744ec761f",
        "source:8ac161c4006dd4b460a59e46",
        "source:88d7ae510503c94877ce869b",
        "source:2bdc6a5a5c44ffcdef5e84bc",
        "source:03bff0df81a25b0cfdeddcd8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:metric-dtn-form-bound-needs-transfer-comparison-for-gap",
      "titleEN": "Metric DtN form bound needs comparison to transfer generator",
      "statementEN": "The printed Delta−2v gap conclusion does not follow from the stated DtN graph norm bound: on the existing v311 transfer representative N=H and V=vP0−v(1+Delta)P1 have weighted norm v but gap Delta−v(Delta+2)=0.6923902, below 1.6475515. Without N/H comparison a second diagnostic makes the gap arbitrarily small. These N/V are mathematical witnesses, not identified original operators. If on a shared form domain N+I<=aH+bI, va<1 and the result is positive, minmax gives gap>=(1−va)Delta−2vb; sharp for N=H. v76/v29 numerical arithmetic remains valid; the printed strict >1.648 is false. No full RP, measure or physical gap follows alone.",
      "scopeEN": "Specified abstract norm inference and finite native v311 representative only; no refutation of actual TFPT geometric coupling and no physical F1 closure. Original common source and actual operator bridge remain to be derived.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8bb310821555d42d8e22c314",
        "source:8cab7332de91c8650add1c94",
        "source:cde0753cf2f17da4327b6aa8",
        "source:dc639aaececb58dee0d406b5",
        "source:726efcef79bcda434ee0e806",
        "source:982722255d08136aa551289a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:conditional-higgs-pair-winding-protection-in-common-circle-carrier",
      "titleEN": "Dynamic Higgs response and protected winding on conditionally shared circle",
      "statementEN": "The actual R081 Higgs singular pair has c_m(n)−1_{n+alpha>0}=O(n^-2) with nonzero Higgs response for fixed m,ell>0. Under the ADDITIONAL shared Hardy-circle carrier and original shift hypothesis, the existing pair-index theorem gives relative determinant (1−z)^−1 for positive polarization independent of m. This is a new scoped application of the old theorem to the existing R081 reader, not a new general index theorem nor a claim about the full alpha prediction. Numeric control uses the same v252 seed; full state, field and clock intertwiner not derived.",
      "scopeEN": "Fixed Higgs singular pair, existing diagnostic gamma+ restriction and additional shared circle shift assumption; not physical P_F/P_adm, not the whole E8 source or physical 3+1 prediction.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:edd68e39ef9370297a308fe3",
        "source:83ef4d0250534b76c27dd063",
        "source:83d073715bb280f4fc83612f",
        "source:78ab68c44fe047e066926688",
        "source:1811e7cd753a105a17ef6cab",
        "source:8cab7332de91c8650add1c94"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:natural-five-clock-carrier-excludes-invariant-three-transfer-compression",
      "titleEN": "Natural five-clock carrier excludes invariant three-dimensional transfer compression",
      "statementEN": "Under the specifically hypothesized natural five-letter permutation action C e_j=e_(j+1), G e_j=e_(2j), GCG^-1=C², the carrier decomposes irreducibly as 1+4, its commutant is span{I,J}, and invariant dimensions are 0,1,4,5. Existing v311 3x3 transfer with three distinct eigenvalues cannot be an equivariant invariant compression of this single natural five-carrier. Exact matrices and commutant checked; no premise says v311 must be this carrier.",
      "scopeEN": "Only the specified natural single five-dimensional representation and invariant equivariant compression; larger carriers, covariance, extra degrees or different original unifications not excluded.",
      "status": "excluded_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:edd68e39ef9370297a308fe3",
        "source:83ef4d0250534b76c27dd063",
        "source:83d073715bb280f4fc83612f",
        "source:78ab68c44fe047e066926688",
        "source:1811e7cd753a105a17ef6cab",
        "source:8cab7332de91c8650add1c94"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:shared-scalar-shift-whole-retained-higgs-sector-has-index-minus-eighteen",
      "titleEN": "Hypothetical common scalar shift gives index minus eighteen on whole retained Higgs sector",
      "statementEN": "The original diagnostic R081 quark gamma+ restriction has18 retained components. At fixed Higgs the whole 18-channel covariance differs from positive Hardy projection by trace class. IF the same original scalar shift acts on each channel, the already established pair index gives −18 and relative Fredholm determinant (1−z)^−18; the prior (1−z)^−1 factor is one component only. Native v252 builder and finite convergence test with5 checks executed. Physical primitive unit winding requires the actual full-source selector, opposite orientations, bound reference or another derived mechanism, none freely selected.",
      "scopeEN": "Whole diagnostic 18-channel gamma+ quark sector at fixed background with hypothesized common scalar shift; ordinary relative Fredholm determinant, no physical Majorana Pfaffian, full source identification or alpha prediction.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d882e7abd99259fd881bd8aa",
        "source:0fde8037aae0e88607ea662e",
        "source:ea0791d638a753c72a4d66ec",
        "source:78ab68c44fe047e066926688"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:whole-coupled-quark-circle-common-shift-cancels-relative-winding",
      "titleEN": "Whole coupled quark source has cancelled winding under common shift",
      "statementEN": "For the existing constant 36-quark R081 circle with h_p=p gamma+V odd and additionally hypothesized common scalar shift U=S⊗I36, UCU*−C is S1 though C−Pfree is generally only S2 when V!=0. The actual whole relative Fredholm determinant is1 for twists1/4 and3/4, by full 2x2 paired blocks and telescoping. Coupled whole H response remains nonzero; do not multiply P/Q marginal block determinants. 23 native checks.",
      "scopeEN": "Constant given 36-quark consumer with hypothesized common shift; ordinary relative determinant. No original physical shift identification, full E8, Pfaffian, H integration or 3+1.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3b99ce1fa7d2d11347ecd6c9",
        "source:6f69c19d3aa3e342655fc5cc",
        "source:526fb40f82ab13683a9bb60c",
        "source:3ab936d2e188bd99a4df6ca0",
        "source:b5e99700843a1b7a1a1af043",
        "source:ccc2cfb22c46ed01a62a8030",
        "source:31a4c9dfcf9b18c9afca8b8d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:one-sided-shift-full-higgs-pair-is-hilbert-schmidt-not-trace-class",
      "titleEN": "One-sided shift on full Higgs pair is S2 but not S1",
      "statementEN": "For the coupled actual R081 singular pair m!=0 and diagnostic Usel=S Pgamma+ + Pgamma−, Usel C Usel*−C has cross block (S−I)diag(b_n), b_n~m/(2|n|). Its diagonal −b_n is not summable; the whole difference is not trace class but is S2. Hence no ordinary relative Fredholm determinant exists for this coupled full-space action, even though the separate gamma+ marginal has one. The counterexample vanishes at m=0. Eight native checks; Gemini corrected its prior opposite claim.",
      "scopeEN": "Only a specifically hypothesized selective shift on the coupled fixed-Higgs singular pair, not an assertion that it is the original physical selector or a general TFPT no-go.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3b99ce1fa7d2d11347ecd6c9",
        "source:6f69c19d3aa3e342655fc5cc",
        "source:526fb40f82ab13683a9bb60c",
        "source:3ab936d2e188bd99a4df6ca0",
        "source:b5e99700843a1b7a1a1af043",
        "source:ccc2cfb22c46ed01a62a8030",
        "source:31a4c9dfcf9b18c9afca8b8d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:selective-coupled-higgs-reader-has-well-defined-det2",
      "titleEN": "Selective coupled Higgs reader has mathematically defined det2 response",
      "statementEN": "For diagnostic selective shift X=−z(Usel C Usel*−C)(I−zC)^−1 lies in S2 and det2(I+X) is mathematically defined by Hilbert-Schmidt continuity. Open finite original-pair computations at z=.3, ell=.2, alpha=.25 give m=.682388 N64/128 .97682565/.97637155 versus m0 .99574841/.99574841. These are finite controls without certified limiting error. The S2 limit exists; its physical normalization and identity with R080 Z0/ref/eta are not established. The det2 product rule includes a trace correction.",
      "scopeEN": "Specific fixed original singular pair and hypothetical selective shift, mathematical det2 reader; not original full source, Pfaffian, H mixture or physical prediction.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3b99ce1fa7d2d11347ecd6c9",
        "source:6f69c19d3aa3e342655fc5cc",
        "source:526fb40f82ab13683a9bb60c",
        "source:3ab936d2e188bd99a4df6ca0",
        "source:b5e99700843a1b7a1a1af043",
        "source:ccc2cfb22c46ed01a62a8030",
        "source:31a4c9dfcf9b18c9afca8b8d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:v311-population-reader-does-not-identify-quantum-channel",
      "titleEN": "Complete v311 population history does not identify the quantum channel",
      "statementEN": "For the original three-dimensional v311 transfer matrix Phi_e(X)=eX+sum_ij(T_ij-e delta_ij)E_ij X E_ij* gives a completely positive trace-preserving family for 0<=e<=731/2187. Every channel has the same population history T^n for all inputs and n, but rho_01=e/2 in the stated coherence test. The matrix is compared with the original numerical v311 call; positivity and trace preservation follow exactly from rational Kraus and Choi decompositions. Independent original source responses may constrain this family.",
      "scopeEN": "Diagnostic extensions of the v311 population reader on an auxiliary three-dimensional carrier. No identification with the TFPT channel or complete process tensor; interventions, E8, Higgs, RP and time data may exclude extensions.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:af23faa331a8d7362aacea99",
        "source:f01fbde94e46c7dcab86ed5a",
        "source:3b97d224a16d0cbbe2c8a1ab"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:declared-charged-pair-relation-leaves-five-word-ambiguity",
      "titleEN": "Declared charged pair relation leaves a five-letter word undetermined",
      "statementEN": "For the declared single chiral alpha=1/4, ell=4log4 source omega(gamma0 T gamma0)−16 omega(gamma2 T gamma2)=0. An m=2 run with this relation and vacuum moments is numerically optimal but automatic exact completion remains inconclusive. A separate exact four-dimensional completion using ten supplied original moments of degree at most four and normalization obeys the relation, but gives zero for gamma0 gamma2 T gamma2 gamma0 versus 1/256 independently computed from the given original source operator. Only the ten supplied moments are asserted equal, not all short words.",
      "scopeEN": "Declared single-chiral charged particle-hole control, m=2; alpha/ell and full original source are not selected by P1/P2. The internal search quarter rotation is not the oppositely charged quarter action. No physical source selection or global TFPT conclusion.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-positive-kernel-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:fc5070a22880a284740922a4",
        "source:8aa957ae438ba5045211552e",
        "source:3965aa8808aea49bb3b6a5e6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-creator-relations-close-fixed-free-two-mode-ambiguity",
      "titleEN": "Full creator relations resolve the fixed free two-mode control",
      "statementEN": "In the given four-dimensional Fock representation, vacuum normalization and both full creator relations T a_i†=r_i a_i† T for r=(1/4,1/64) uniquely imply T=diag(1,1/4,1/64,1/256). The previous exact x=0 countercandidate violates two of the 32 basis-word relations. The existing m=2 moment search returns numerical extrema 0.0039062495971 and 0.0039062519290, not exact numerical certificates. The free multiparticle law was already known; its use as a source relation against the R085 countercandidate is new.",
      "scopeEN": "Fixed free particle-hole control before Higgs integration with supplied full one-particle action and vacuum normalization; no derivation of the interacting original whole source or uniqueness across the general search space.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-positive-kernel-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:145e9ec83959cfe2eb87e9ea",
        "source:7392a1b33f15bd2ec0c0644d",
        "source:916197bce97e7e0a72a93604"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:comoving-diagnostic-clock-exact-response-but-nonlocal-mode-transport",
      "titleEN": "Comoving diagnostic clock has exact response and non-pointwise-local transport",
      "statementEN": "For a supplied constant Higgs singular pair and U_m=W U_0 W*, U_m C U_m*−C is trace class with trace norm 1 and relative determinant (1−z)^−1 for 0<z<1; r coupled pair sectors conditionally give (1−z)^−r. For m≠0 U_m−U_0 is Hilbert Schmidt but not trace class, and its n-dependent Fourier diagonal excludes pointwise multiplication. Both quarter phases are treated.",
      "scopeEN": "Given constant pair and diagnostic selective shift, not identified with the original clock; nonlocality excludes pointwise multipliers only, not the full OS algebra. Dynamic H fields, mixed words, original reflection and normalization remain open.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-full-two-face-graph-and-local-matrix-operations",
        "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f3b8204e9f9ff8b847792e1f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:free-quarter-two-face-response-strip-with-relative-zero-mode-defect",
      "titleEN": "Entire free two-face response is strip response with relative zero-mode defect",
      "statementEN": "For the given free scalar two-face projection, all nonzero Fourier modes of the commutator quadratic response equal exactly the Dirichlet-to-Neumann matrix of a strip of width beta/2 by pointwise identities and telescoping. At beta=4pi and alpha=1/4 or 3/4 the constant relative eigenvalue is half as large: N_source=N_strip−Pi_relative/(2pi), and N_strip/2≤N_source≤N_strip as forms. The normal-ordered variance is Q/2. In the given coupled 2×2 background, the same scalar face operations change nonzero modes as well: at m=0.3, k=1 gives N11≈1.54580712 versus 2.00001395 at m=0 (two internal components), with explicit sum-tail bound 1.26e−7 and floating-point arithmetic.",
      "scopeEN": "Given massless geometric Cauchy graph and R066 quarter identity. No identification of the graph with the physical whole-state covariance, no general Higgs-coupled matrix identity and no derivation of a physical spacetime dimension. The coupled example is a fixed comparison field, not the dynamical physical source and not a test of the comoving clock.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:actual-original-full-two-face-graph-and-local-matrix-operations"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9e26918f42fe15847d29221b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e8-hodge-event-perfectly-distinguishable-from-every-unitary",
      "titleEN": "E8 Hodge event is perfectly distinguishable from every unitary evolution",
      "statementEN": "On given ten-dimensional H=Lambda²C5, every nonzero C(z)=sum z_m C_m has six singular values ||z|| and four zero singular values. Convex separation yields, for every U:H→H*, a density matrix rho with Tr(rho U*C_m)=0 for every m; a normalized purification perfectly distinguishes Phi from Ad_U. Hence ||Phi−Ad_U||_diamond=2 for every unitary identification. An original basis input distinguishes one explicit unitary completion of C0 even without reference. With R086, a globally TP operation using only epsilon-span Kraus amplitudes therefore cannot have a continuous unitary start for all sufficiently small times. E_t=exp[tλ(Psi−id)] with Psi=Ad_U* o Phi gives a mathematical CPTP Poisson embedding. Every finite t requires a Kraus amplitude outside the strict span; λ and U are additional choices.",
      "scopeEN": "Finite given carrier and dual output, original C_m and R086 global trace preservation; no physical source theorem or exclusion of other branches, registers, memory or a finite event. The universal conclusion uses an analytic convex separation argument, not finite sampling.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:29094375beee5273c5c74e48"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:common-five-slot-transfer-preserves-e8-bracket-not-automatic-tp",
      "titleEN": "Common five-slot transfer preserves E8 bracket but not automatically trace preservation",
      "statementEN": "For A on C5, D=Lambda²A and original bilinear C_m:H→H*, D^T C_m D=sum_n adj(A)_(n,m)C_n, including singular A. Invertible A preserves the whole span and the concrete five-cycle the given equally weighted channel. A common scalar normalizes the simple equally weighted channel to trace preservation iff adj(A)adj(A)*=rI, equivalently AA*=sI for invertible A. A=diag(1,1,1,1,1/2) gives effects 1/2 and 1/4. An exact Duhamel integral of [V,a†] gives the free creator-relation defect for supplied H=dGamma(h)+V; the existing two-mode counterexample gives 1/256.",
      "scopeEN": "The same A is assumed on both correctly typed legs; no source origin of A, no identification of the two-mode carrier with C5, and no universal TP exclusion. Other family weights or channels remain possible; interaction formula assumes the specified finite generator decomposition.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5342f9756d80307c0576c4f2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:comoving-clock-dynamic-higgs-connection-and-charged-flow",
      "titleEN": "Comoving clock carries charged winding flow and dynamic Higgs connection",
      "statementEN": "In the given 2×2 singular block the comoving selective shift has a rank-one defect of trace +1 relative to the negative sea projection; the cotransported charged quarter acts on its implementer with phase i. The shift itself is not order four. For time-dependent real m(t), the comoving generator is sign(p)E_p sigma_z − p m_dot/[2(p²+m²)] sigma_y. Under the additional proposal to replace the original free quarter loop exp(2pi i Hfree) unchanged by positive coupled energies E_n at m≠0, the phases disagree for sufficiently large positive modes.",
      "scopeEN": "Only the stated time-dependent pair block and cotransported charge/reference frame; no identification of original physical P1 clock or OS reflection, 96-dimensional dynamics, H measure or full source transport. A separate geometric quarter generator remains possible.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2bf800d5d65ead6320bc3994"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r064-sixty-record-channel-exact-distance-and-continuous-record-parent",
      "titleEN": "Sixty-record event channel: exact distance and continuous record parent",
      "statementEN": "The given equally weighted R064 channel on Sym²(C4) has normalized Choi spectrum 0×45,(1/75)×45,(2/75)×9,(4/25)×1. An integer Gram polynomial and traces certify rank55; an F101 test certifies product rank100. The minimum half-diamond distance to unitary channels is exactly 21/25, from the maximal Choi overlap bound and Φ=(4/25)Id+(21/25)Ψ. A Hermitian involution parent with 60 records reproduces the given endpoint channel and allows continuous intermediate times; reused and fresh records produce different multitime answers. This concerns a different channel from the R088 Hodge P5 channel on Λ²(C5).",
      "scopeEN": "Exact finite channel and specified comparison construction; original source, physical timescale and record preparation not identified. Do not confuse rank change and semigroup theorem with a general exclusion of continuity.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:cf361ee9bef2f7b9d70f20bb",
        "source:9b9edfae77f380170ab161e9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:two-syntheses-shared-source-priorities-and-typed-limits",
      "titleEN": "Two source syntheses connect clock words, E8, Higgs measure and absolute source",
      "statementEN": "For given implementable Q and centered J_C(A), the required correction is Tr[(Q*C Q−C)A]; this separates the ordered CAR word source from the R084 relative covariance determinant. Transported Ω supplies the X→XΩ representation for a given form but does not automatically identify native pointers or states. Compact BKM expectation-value closure does not ensure a finite measure; force cumulants are not the R054 Higgs mixture witness. A complete normalized matter source does not fix geometric absolute normalization Z0.",
      "scopeEN": "Typed free or conditional contracts; the general original source, Hilbert space, force operator, dynamic Higgs measure and geometric normalization map are not derived. External notebook visible, not fully rerun locally.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:0ad639043ce46c5a08619a56"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:weighted-index-trace-and-selfdual-theta-require-original-selection",
      "titleEN": "Weighted clock index reduces to the full chiral trace under commutation assumptions",
      "statementEN": "For finite-dimensional γ=γ*=γ⁻¹ and V=V* with {γ,V}=0, and λ=λ* with [λ,γ]=[λ,V]=0, tr_ker(V)(λγ)=tr(λγ), since V pairs opposite chiralities with the same λ charge off its kernel. Periodicity, actual integral charge normalization, and Fermi/sea covariance remain additional clock and relative-determinant conditions. C=I/2 shows the missing general covariance assumption in the supplied index claim. Full-fiber λ=I index zero and quarter variance 1/(8π) at the self-dual theta function are already in the record; original selection of the quarter and β=4π is a new hypothesis to test.",
      "scopeEN": "Finite matrix class and named independent original sources; no general P1 index theorem, automatic P1/neutrino relation, prior physical selection of λ or self-duality derived from P1.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0ad639043ce46c5a08619a56"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:ordered-quarter-fourfield-e8-record-and-charge-filters",
      "titleEN": "Ordered quarter word, E8 channel separation and original charge filters",
      "statementEN": "The conditional constant R062 colour triplet gives an exact ordered matter/quarter/four-field word in m1,m2,m3 for Q=i^N and O=4N(N−1). Two positive comparison laws in the actual t range share m1,m2 but differ in m3; global quarter, complement and dynamic time transport are not identified. The 60-record E8 channel and the Hodge channel have half-diamond distance at least 24/25 on six original charts and at least 11/15 for arbitrary unitary identifications. No positive classical selection of unitary records produces the Hodge channel; coherent or nonunitary refinement remains possible. In the six-generator space the full Higgs family and nonzero Majorana permit only 3B and two colour Cartan generators, with vanishing weighted chiral trace.",
      "scopeEN": "The stated finite carriers and assumptions only; no original common master source, dynamical multitime response, physical Choi measurement or F1 solution. Other clocks and Higgs co-transport remain possible.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9bb8265c8779da934936d2a7",
        "source:46a57b4bcdfafea610935a31",
        "source:762238292eaa435f37be6319"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r091-recovered-native-hodge-sewing-and-full96-quarter-complement",
      "titleEN": "Native Hodge current sewing, typed record targets and full 96-mode complement",
      "statementEN": "Original Ω=I⊗iY and the five gamma matrices XI,YX,YY,YZ,ZI satisfy the pointer relation and generate the native Hodge channel as A3 current zero modes. In the specified current net compact OPE sewing supplies the internal contraction without a record measurement; the P1 field/state/reflection/sewing map remains open. With coherent record access the native Spin5 target has optimal probability 1/15 in one step and 4/75 in two; the earlier duad target has probability zero in one step and 1/25 in two. Target typing and P1 selection remain distinct. The fixed original 96-mode Higgs source word for diagnostic z^N factors into its reducing six-mode block and H-dependent 90-mode determinant; three original-constructor controls confirm the factorization numerically.",
      "scopeEN": "Recovered existing exact finite source contracts and conditional fixed quasifree 96-mode block; no global original clock, multitime dynamics, P1 selection, H measure or physical F1 completion. Native family Pauli gamma is not automatically physical 96-mode Dirac gamma.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:df14c56c3b0cce796bacea2d",
        "source:29e4a066acbf1c350afec4d1",
        "source:46a7858c30c7f5e339323165"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r092-fold-ward-target-neutral-source-and-smaller-creation-branch",
      "titleEN": "Folded Ward target and smaller neutral source route",
      "statementEN": "The given rational fold matrix M maps s=(1/2)^8 exactly to e3+e6 and q=(1,...,1) to 2(e3+e6). For the normalized lattice-vacuum Ward formula at z=0,w=1,u=3 the old eight components −1/12 become −1/6 on H3 and H6; the transported total current is −2/3 on both sides. This is a target calculation and does not identify a P1 response. The existing grade-2/U5-residue-3 creation30 branch and smooth neutral half-kink on the folded even-CAR quotient form a smaller approach than assuming a full 50-event process; they do not derive a P1 local embedding, source, reflection, state or OS time. The marked colour-charged intermediate must be retained in the neutral pair.",
      "scopeEN": "Exact fold matrix and normalized lattice-vacuum target test; existing conditional quotient sources and finite creation30 contracts. No primitive P1 Ward response, automatic physical time or F1 completion. The historical one-channel checker is currently blocked by a stale source pin and not counted as a fresh PASS.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8251ede4d516e986e27415a8",
        "source:dd99ba128603c769e12d31da"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r093-original-kink-time-response-distinguishes-quarter-states",
      "titleEN": "Original neutral kink time response distinguishes the two quarter states",
      "statementEN": "In the given folded CAR source contract the full ordered T(t)T* response on the five actual states is determined by the original Schur kernel and an explicit Weyl Gaussian including all modes. The state polynomial has modes 8,16,24,32 due to cover degree 32; the Gaussian retains all modes. Normalized original P0 states in quarters 1/4 and 3/4 differ already in R8=||J8P0||²/||P0||²: 766710528/328635469 versus 770249472/331641421. A smooth admissible comparison profile with b3=0 distinguishes their responses at t=pi in the quadratic term. An additional smeared CAR total current is a derivative of the same Weyl source. The historical mixed-current-origin checker was replayed in a targeted temporary overlay with original pins and returns 29 PASS, PARTIAL and no local origin; the full ledger-checked overlay was not passed.",
      "scopeEN": "Actual original folded CAR source contract, fixed input states, source time K_alpha and smooth comparison profiles; no primitive P1 OS time identification, original profile selection, full Ward or dynamical Higgs source, or F1 completion. Historical replay does not validate active source pins or ledger projection.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ca74bd8be536afb9e98ba0eb",
        "source:ac7eafc86733ff999c13c763",
        "source:726964243a044dbc174e973d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r093-ordered-current-kink-and-eight-arc-locality",
      "titleEN": "Original ordered current word and direct eight-arc locality test",
      "statementEN": "In the given folded CAR source contract the derivative of the same ordered Weyl source computes the left-inserted smeared total current response J(h)T(t)T*, including its noncommutative phase and alpha-dependent state kernels. An independent one-mode Fock test confirms the operator order and sign. For a nonconstant smooth phase profile the direct pullback T=W(-b∘F), F(theta)=8theta, acts nontrivially on a bounded even CAR bilinear in each of the eight disjoint cover arcs; hence T is not in the even local von Neumann algebra of any single such arc.",
      "scopeEN": "Given CAR source time, smooth profiles and direct cover pullback; the one-mode Fock case tests an identity and is not a TFPT source state. Other local P1 embeddings or compressions are not excluded. No identification with OS time, all E8 Cartan currents, Higgs measure or F1.",
      "status": "conditional",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1ee8583d66cf6566968d9dc1",
        "source:49601b18dc1e234d09c2ec26",
        "source:ad108dfddb9abe33c265f9d3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r094-original-five-excitations-distinct-from-clustering-vacuum",
      "titleEN": "Original five source inputs are excitations, not the clustering vacuum for this time",
      "statementEN": "All five original charge-zero inputs have K_alpha energy 4. The original J8 Gram is positive definite for both quarters with the stated exact determinant. A smooth quotient profile with nonzero first coefficient gives a bounded eight-arc Weyl word that reaches energy 3 from every nonzero vector in the input span. The connected Euclidean response based on K_alpha-4 grows on the infinite half-line; the same applies to positive states supported entirely in this span. The P0 vacuum channel J32 has the two exact R32 weights in the source. The R093 response remains an original vacuum word with the finite raising-current polynomials B_i.",
      "scopeEN": "Fixed original CAR time and admissible eight-arc word; the P1 seed does not specify the clustering direction. No exclusion of other P1 times or states, finite KMS interval, CAR vacuum, or excited insertions; no derivation of P1 localization, reflection or physics. The input basis is not orthonormal.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8e33a96257b920e119025a6c",
        "source:1ad024bd53787d1245211704"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r096-joint-higgs-twoface-source-constraint",
      "titleEN": "Joint Higgs and two-face response gives quantitative source constraint",
      "statementEN": "For one positive Higgs mixture and full two-face covariance, Tr L(Pbar-Pbar²)L >= Var(m)/6 = DeltaO/144 under R054 conditional quasifree premises, strengthening the earlier qualitative nonprojection result. The unnormalized linear identity Z[O]=8 Z[mN] requires matching conditional fibers and weights, not positivity. On the original 36-dimensional quark carrier the two-face trace g(u)=6 sum_j[2 cosh(ell sqrt(p²+y_j²u))]^-1 is strictly decreasing, implying Cov(u/(1+u),B_Q)<0 for a positive nonpoint radial law. Original 96 constructor and exact abstract rank-six control checked.",
      "scopeEN": "Constant Higgs and same actual two-face carrier, color symmetry and R054 conditional quasifreeness for the four-word part. No derived physical Higgs measure, general H(x), P1 seam, or independent gauge transport. The mixed source insertion is not assumed present in search alphabets without an actual source map.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:r096-same-constant-higgs-twoface-carrier"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9881bac8323cf340a482d229",
        "source:21af7c2f6466c12c2fdebacc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r096-positive-twoface-fourword-defect-bound",
      "titleEN": "Quantitative joint positive two-face bound",
      "statementEN": "For Pbar=integral P_H dmu and m=Tr(L P_H L), Tr L(Pbar-Pbar²)L>=Var_mu(m)/6. Under the additional named R054 fiber premises Delta_O=24Var_mu(m), giving the same lower bound Delta_O/144. Var(m)>0 excludes projection of Pbar; a pure primitive state before H integration remains possible.",
      "scopeEN": "Only the specified R096 branch under its jointly required premises. No derived physical Higgs measure, general H(x) field theory or P1 source completion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:r096-same-constant-higgs-twoface-carrier",
        "premise:r096-positive-normalized-contraction-mixture",
        "premise:r096-conditional-r054-color-wick-fibers"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2aa2268c0098413f66382814"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r096-unnormalized-mixed-source-linear-identity",
      "titleEN": "Linear mixed-source identity without positivity",
      "statementEN": "The conditional identities <O>_H=24m(H)^2 and <N>_H=3m(H) give Z[O]=8Z[mN] with the same integrable unnormalized weights. Positivity is unnecessary for this branch. Actual origin of the mixed insertion in the original solver remains open.",
      "scopeEN": "Only the specified R096 branch under its jointly required premises. No derived physical Higgs measure, general H(x) field theory or P1 source completion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:r096-same-constant-higgs-twoface-carrier",
        "premise:r096-conditional-r054-color-wick-fibers",
        "premise:r096-same-integrable-unnormalized-weights"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:70c497f139d6061ef1d44e85"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r096-original-quark-crossing-negative-covariance",
      "titleEN": "Strictly negative original quark crossing covariance",
      "statementEN": "For actual X_H=(2cosh(ell h_H))^-1, g(u)=Tr_Q X_H=6sum_j[2cosh(ell sqrt(p²+y_j²u))]^-1. Under the specified real face frame and positive nonconstant radial law g strictly decreases, f(u)=u/(1+u) strictly increases, and Cov_mu(f,B_Q)<0. The face identifications cannot be independently rotated without the actual transport.",
      "scopeEN": "Only the specified R096 branch under its jointly required premises. No derived physical Higgs measure, general H(x) field theory or P1 source completion.",
      "status": "established_scoped",
      "problemId": "problem:automated-operator-source-synthesis",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:r096-same-constant-higgs-twoface-carrier",
        "premise:r096-real-face-quark-crossing-positive-radial-law"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c2b6bcb3fc11dfb0c025ce50"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:known-fourmark-system-has-three-and-five-canonical-views",
      "titleEN": "Already proved: three and five are two canonical views of the same four-mark system",
      "statementEN": "Existing v189 and the Origin paper obtain rank H1(P1\\D)=3 and h0(P1,O(D))=5 from ONE four-point divisor D=mu4 on P1. This is an established common geometrical/topological origin of both numbers, not a new hypothesis or reopened task. Retain known anchor identities and reverse selection. Every genesis continuation starts from this theorem; open further source maps do not downgrade it.",
      "scopeEN": "Two canonical invariants of the given four-mark object. Not a new proof task; evaluate original field/state maps separately. This records an existing result to repair retrieval and continuity, without claiming a new scientific finding.",
      "status": "established_scoped",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "topicIds": [
        "topic:origin",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f97430629d77c95d9249faeb",
        "source:a744e4da5c557fb4f126e5fd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:reverse-bootstrap-retained-operator-scope",
      "titleEN": "Reverse selection is retained; the checked maps supply numbers and closure data",
      "statementEN": "Origin954–981 and v6/v15/v350–v352 recover g_car=5 and eight within the chosen closure framework; v154 supplies the conditional local extension. The checked v350–v352 functions do not construct Phi-dependent D_rel/D_ref or physical insertion operators. This scopes those calculations, rather than asserting general impossibility.",
      "scopeEN": "Source audit of the specified reverse chain. No retraction of numerical self-consistency and no independent derivation of the framework.",
      "status": "established_scoped",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "topicIds": [
        "topic:origin",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:reverse-bootstrap-e8-closure-framework",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f25dd599bf8251f8132347f0",
        "source:677467faf078bb6f888aebab"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e8-current-dictionary-all-separated-responses",
      "titleEN": "All248 boundary currents have explicit multi-field responses",
      "statementEN": "The executable E8 dictionary contains240 root vertices and8 Cartan currents with cocycle, adjoint signs and quarter grades60/64/60/64. The vertex formula and Cartan Ward recursion determine all separated current coefficients of the normalized source series. Mixed spinor currents have5/8+3/8=1; the checked connected four-point response is nonzero. Standard lattice theory implemented and independently checked here, not a new physical interaction.",
      "scopeEN": "Stipulated E8_1 lattice vacuum representation. Bosonic currents are not identified with elementary4D fermions or native CCR mediators. Internal quarter grading is not physical quarter time. Contact terms, Z[0], absolute phase and original P1 Phi-dependence do not follow from these normalized coefficients.",
      "status": "established_scoped",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "topicIds": [
        "topic:origin",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:reverse-bootstrap-e8-closure-framework",
        "premise:local-e8-current-response-realization",
        "premise:quarter-phase-retained",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-collar-multifield-20261016",
        "contract:seam-joint-ward-state-20261014"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2049549fdb5c17e5e16dab15",
        "source:40a2d2895f4da06c0040cf75",
        "source:1c57381e86a92ee27ef9bf44",
        "source:65e1d38891021f0cc9aade6e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:charged-scaling-microscopic-map-still-unspecified",
      "titleEN": "First microscopic field and refinement map is unspecified in the original",
      "statementEN": "The original charged scaling contract starts with H_N as the actual QWZ/CAR GNS space and declares Psi_lambda,N by a normal boson exponential. Its concrete refinements I_charge tensor Gamma_s(j) act instead on a separately chosen bosonic lattice Fock space. No microscopic B_N between these systems with B_2N J_N,2N=V_N,2N B_N and state, energy, parity, sector and localization compatibility is constructed there. The exact charge-lattice isometry F(2q)=lambda does not replace this field morphism.",
      "scopeEN": "Source audit of this particular original path. No nonexistence claim for B_N and no rejection of the established P1/P2 compiler or mathematical E8 field extension.",
      "status": "established_scoped",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "topicIds": [
        "topic:origin",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:literal-microscopic-charged-scaling-and-v988-slater-data",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:516f9a3fddb841f3e2bfcf02",
        "source:0e9701cad0ba023655726683",
        "source:552542d7c2106340c7f396bc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-slater-proxy-fitted-bound-fails-actual-norm",
      "titleEN": "Original proxy constant fails on the actual first Slater norm",
      "statementEN": "On unchanged v988 data Nx16,Ny6,M1 the twist1 Slater state against h0 has exact variance formula Tr(P h0(1-P)h0P)=||(1-P)h0P||HS^2. Numerically it gives7.0875042817 and first excitation norm2.6622367065. The original first central sum proxy is identically0; its fit C=1.2040009128 gives C^2=1.4496181980 and already fails to bound the actual norm here.",
      "scopeEN": "Only this proxy-fitted constant in this actual finite original case is excluded. The formula is exact; numerical values are checked to1e-9 tolerance. Larger constants, separate historical value2.86 and general continuum estimates are not excluded.",
      "status": "excluded_scoped",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "topicIds": [
        "topic:origin",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:literal-microscopic-charged-scaling-and-v988-slater-data"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3d92bb34945c6c455b1d841c",
        "source:6d7fdb3fcc8b67038099f3db"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:periodic-microscopic-zero-modes-distinguish-source-state",
      "titleEN": "Periodic zero modes distinguish original covariance and Slater choice",
      "statementEN": "On unchanged v988 Nx16 Ny6 M1, explicit integral boundary zero vectors, modular ranks over F65537 and exact sign pairing prove ranks190/192/192/192. Periodic counts are95 negative,95 positive,2 zero; other twists96/96/0. Original covariance C=Pminus+Pi0/2 differs from pure occ_frame projector P=Pminus+Q with rankQ1 in the nullspace: norm(C-P)HS²=1/2 and norm(C-C²)HS²=1/8. Both original functions are valid and deliberately distinct. A state-preserving microscopic dictionary cannot silently exchange these periodic states.",
      "scopeEN": "Exact finite original case. No nonexistence of B_N, selected continuum state or E8 refutation. Previous energy test uses twist1 without zero modes and is unchanged. Numerical norm diagnostics normal and -OO byte-identical; independent proof review and rerun accepted.",
      "status": "established_scoped",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "topicIds": [
        "topic:origin",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:original-v988-periodic-zero-mode-state-comparison",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:011a47851fa66548fe2d160c",
        "source:7f72ab5eae77e919dc08c70f",
        "source:3c5064eb00ba83f764e093cb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r097-original-q-twins-are-integrally-conjugate-before-fixed-source-form",
      "titleEN": "Original Q twins are integrally conjugate before fixing the source form",
      "statementEN": "Actual v568 pairs (U0,V0) and (U2,V2) have simultaneous GL3(Z) intertwiner G=[[1,0,0],[0,1,0],[0,2,-1]], G²=I,detG=-1, commuting with Sigma and fixing the specified winding data while sending leading vector (1,2,0) to (1,2,4). All simultaneous intertwiners are tG. The fixed theta(A)=Sigma A^T Sigma is not preserved and its reflected word gives4/8; transporting the entire form gives4/4. Explicit linear intertwiners connect the original three-rate clock to both Qplus/3, so rates alone do not select a twin.",
      "scopeEN": "Exact algebraic equivalence of original unmarked pairs and covariance of full passive form transport. No claimed physical P1 symmetry, spatial mirror interpretation of detG, or independently produced source normalization. Original fixed source form and reader still distinguish marked realizations.",
      "status": "established_scoped",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "topicIds": [
        "topic:origin",
        "topic:e8",
        "topic:quantum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:682d7bacb5cf9d4d166c7886",
        "source:392eb60d759092440cf038ac"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:replicated-deterministic-consistency-iff-influence-dag",
      "titleEN": "Replica consistency exactly for acyclic influence structure",
      "statementEN": "For arbitrary finite alphabets/interfaces, existence under every finite joint local replica control, uniqueness under every such control, acyclic static influence and compatibility with at least one fixed total order are equivalent. A directed cycle of length m allows at most m copies with separately sensitized edges and odd XOR feedback without a solution. Acyclicity gives unique triangular recursion. No unique total order or physical time is selected.",
      "scopeEN": "General elementary finite deterministic theorem, mathematically reviewed twice. Arbitrary encoders, decoders and erasure are used; no general reversible two-copy theorem. Interfaces are not derived events. No novelty priority claim.",
      "status": "established_scoped",
      "problemId": "problem:fundamental-process-classification",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T8",
        "goal:universalraum"
      ],
      "premiseIds": [
        "premise:finite-deterministic-joint-replication-control"
      ],
      "attemptIds": [
        "contract:foundational-process-classification-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:25d57dd80a61f0d953b6cd97"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:three-binary-processes-two-copy-reversible-classification",
      "titleEN": "Complete binary three-interface classification",
      "statementEN": "Of 4096 no-self-influence candidates,744 are uniquely consistent under all64 local one-shot contexts.488 are acyclic; each of the remaining256 has an explicit reversible local two-copy control with zero or two fixed points (128 each). All744 process/order entries and256 witnesses were independently reproduced. The488 positive cases analytically work for all replica counts and arbitrary joint deterministic controls.",
      "scopeEN": "Complete bounded classification of three binary interfaces; no particle/generation/dimension interpretation. One-shot consistency does not force a fixed order.",
      "status": "established_scoped",
      "problemId": "problem:fundamental-process-classification",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T8",
        "goal:universalraum"
      ],
      "premiseIds": [
        "premise:finite-deterministic-joint-replication-control"
      ],
      "attemptIds": [
        "contract:foundational-process-classification-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:698cf4709c9855600965c27c",
        "source:eb4852870bbea610dc3da520"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:independent-poset-information-composition-consequences",
      "titleEN": "Independent order, information and composition classes",
      "statementEN": "Event posets provide ideal states and possible histories but do not generally select growth weights. Supplied finite updates give cycles/transients and closed record cells relative to errors/observation; sink SCCs count maximal separated record cells, not necessarily exhaustive invariant record functions. Transformation monoids allow stable sectors, periodic steps and visible classical noncommutativity together; action and effects remain inputs. Counterworlds show these properties do not follow from composition or information alone.",
      "scopeEN": "Separate classes with separate premises, no shared physical derivation. Exact poset/endofunction censuses through size4 and elementary structural claims checked. Cycles do not select a canonical phase origin.",
      "status": "established_scoped",
      "problemId": "problem:fundamental-process-classification",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T8",
        "goal:universalraum"
      ],
      "premiseIds": [
        "premise:finite-event-poset",
        "premise:finite-update-observation-errors",
        "premise:finite-operational-composition-action"
      ],
      "attemptIds": [
        "contract:foundational-process-classification-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:394588cf49d710a2904dd8ff",
        "source:7a6b772a239d10291503b100"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:reset-diagnosis-not-global-tfpt-underdetermination",
      "titleEN": "Workflow reset without global TFPT impossibility claim",
      "statementEN": "The checked origin attempts leave operation alphabet, state/correlation family and intervention rule unspecified. This motivates a methodology change but does not prove global underdetermination of all complete P1/P2 models: scalar/matrix comparisons change A, while A, state and time belong to the full source tuple. The four independent classes force neither a five-direction carrier,3+2,E8,quartic nor TFPT clocks. Compare TFPT only after their characterization.",
      "scopeEN": "Refinement of already reviewed diagnosis and explicit counterworld comparison of new classes; no refutation of all TFPT and no closure of a physical goal.",
      "status": "established_scoped",
      "problemId": "problem:fundamental-process-classification",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T8",
        "goal:universalraum"
      ],
      "premiseIds": [
        "premise:foundational-reset-no-target-input"
      ],
      "attemptIds": [
        "contract:foundational-process-classification-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b28f6d4deb5b6f81e678850e",
        "source:3af34c35f41058bef30971bb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:three-inequivalent-repeatable-observation-countermodels",
      "titleEN": "Repeatable distinctions select no unique response geometry",
      "statementEN": "Three explicit single-system theories satisfy the same sharp repeatability benchmark and are operationally inequivalent: R has two classes without mixing, I a classical simplex, D a square with nonunique decompositions. XZX preserves the first X report with probability1 in I and1/2 in D; D identifies both diagonal mixtures under all generated protocols while I distinguishes them by parity. All30 X/Z words through length4 were checked exactly. D has a classical hidden two-bit implementation of its generators; not all classical models are excluded.",
      "scopeEN": "Three countermodels, not an exhaustive classification of operational worlds. I/D assume probabilities/convexity; their numbers are predictions, not new measurements or physical dimensions. All-context equality follows analytically from linearity, not the finite word check.",
      "status": "established_scoped",
      "problemId": "problem:fundamental-process-classification",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T8",
        "goal:universalraum"
      ],
      "premiseIds": [
        "premise:repeatable-distinction-benchmark",
        "premise:three-explicit-observability-countermodels"
      ],
      "attemptIds": [
        "contract:foundational-process-classification-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8389c0de29d22b75f9d8a9f4",
        "source:2b10b09d9301b0f6af77f825"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:repeatable-reports-do-not-imply-full-state-stability",
      "titleEN": "Report repeatability is not complete state stability",
      "statementEN": "The separate benchmark assumptions give at least two continuation-distinguishable classes and preserve the selected report label under uninterrupted repetition. This largely restates the substantive repeatability premise rather than explaining physical origin. A test can preserve its report while incrementing a separately readable modulo3 counter; result repetition therefore forces no complete idempotence, preservation of all correlations, metric time or eternal material memory. Possible reports alone select no numerical weights.",
      "scopeEN": "Standard residual representation consequence and explicit counterexamples, not a new ontology. Distinguishability, repeatability, context reproduction and serial availability are separate assumptions. Separate L1/L2 from L3.",
      "status": "established_scoped",
      "problemId": "problem:fundamental-process-classification",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T8",
        "goal:universalraum"
      ],
      "premiseIds": [
        "premise:repeatable-distinction-benchmark"
      ],
      "attemptIds": [
        "contract:foundational-process-classification-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f20c548ebf8e52a02aaf210f",
        "source:9a4c8051ac35642b41eb3a88"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:finite-sequential-data-admit-classical-history-realization",
      "titleEN": "Finite sequential data admit a classical history realization",
      "statementEN": "Every finite normalized prefix-consistent response family with past marginals independent of future choices has a finite classical stochastic realization: preparation/full history as memory, conditional ratios as transitions, append the next choice/report pair. The construction also reproduces adaptive protocols. It was checked exactly on all requested D tables through horizon4. Finite sequential disturbance and order dependence alone do not exclude unrestricted classical history models.",
      "scopeEN": "Conditional representation theorem without novelty claim, not efficient or local physical simulation. History/preparation dependence and growing memory are allowed; Bell, noncontextuality or resource witnesses under independently justified extra conditions are not invalidated. Protocol direction is assumed, not physical causality derived.",
      "status": "established_scoped",
      "problemId": "problem:fundamental-process-classification",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:universalraum"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T8",
        "goal:universalraum"
      ],
      "premiseIds": [
        "premise:finite-prefix-consistent-sequential-data"
      ],
      "attemptIds": [
        "contract:foundational-process-classification-20261016"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5c46d5d6cfc83f319c9bb915",
        "source:b52207be171dbf379d3d8427"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:pascal-carrier-rank-unique-unbounded-source-proof",
      "titleEN": "Pascal condition has exactly the solution five for all natural g",
      "statementEN": "CarrierRankUniqueness.carrier_rank_pascal_unique states and proves for every natural g that 2^g=g^2+g+2 iff g=5. Its proof combines the small cases with pascal_growth for all g>=6. This is unbounded; PascalLadder has a separate bounded K=2 statement. For g=5, N_fam=3 and g+N_fam=8 are computed.",
      "scopeEN": "Algebraic uniqueness under the stipulated Pascal/half-spinor exhaustion condition. Original source and proof text reviewed; no fresh Lean kernel run. AX.P2.01 remains a declared physical interface; the equation does not select itself from an original source.",
      "status": "established_scoped",
      "problemId": "problem:carrier-pascal-glue-formal-scope",
      "topicIds": [
        "topic:e8",
        "topic:origin",
        "topic:validation"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "premiseIds": [
        "premise:pascal-carrier-exhaustion-equation"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3bda9d111ec25627408a7600",
        "source:18a8d14c95fd7ee844183b04"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:finite-carrier-glue-elements-orbits-and-halfway",
      "titleEN": "Glue elements, two orbits, spinor swap and halfway stage are explicitly formalized",
      "statementEN": "In Fin4 x Fin4 with qZ=(5x^2+3y^2) mod8, named Lean declarations classify all six isotropic elements and four odd-coordinate isotropic generators. Explicit orbit identities give H1 and H2; klein_not_isotropic gives the nonisotropic Klein witness, spinor_swap_exchanges swaps the two orbits, and unique_halfway_stage classifies the only nonzero isotropic order-two element (2,2). Index and sector arithmetic are additional separate declarations.",
      "scopeEN": "The concrete element/orbit and arithmetic statements are available. No fresh kernel run, nor a newly checked single Lean theorem about all abstract subgroups or lattice isomorphisms. The general subgroup conclusion also uses finite group theory; concrete E8 basis embedding and physical carrier selection are separate.",
      "status": "established_scoped",
      "problemId": "problem:carrier-pascal-glue-formal-scope",
      "topicIds": [
        "topic:e8",
        "topic:origin",
        "topic:validation"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2"
      ],
      "premiseIds": [
        "premise:specified-finite-carrier-discriminant-form"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:cbb06f4fd3e64040410deba8",
        "source:0459e7af53a44432dbd08e39"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:marked-seam-category-and-character-valued-full-lift-factor",
      "titleEN": "Marked-seam category and full character-valued lift factor formula",
      "statementEN": "Marked lattice transport functors with explicit reflection/clock markings define a category, products and boundary gluing under inverse-conjugate holonomies. Ordered generator phase eta gives the full factor c(g,h)(y)=eta_h(x)eta_g(hx)/eta_gh(x), x=(gh)^-1y. It is Hom(L,F2)-valued with coefficient action, not generally scalar or central.",
      "scopeEN": "Declared definitions and derived standard extension/gluing algebra, not a classification of all object groups.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:marked-seam-monodromy-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1bfc9034f5a4df960187e85f",
        "source:3854d5aac809adf947a7b5f0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:quarter-clock-sign-lift-complete-four-puncture-classification",
      "titleEN": "Complete quarter-clock sign-lift classification with526336classes",
      "statementEN": "Gamma=F2^8 semidirect C4 has order1024. Peripheral classes C_u over J are indexed by F2^4. Four ordered classes admit product1 iff sum ui=0. Normal forms(x,y) modulo translation(u1+u0,u2+u0) give256classes for diagonal profiles,128otherwise. Total526336;4096orbits size16 with stabilizer C4×C2^4 and522240size32 with stabilizer C2^5. Image-order census4:16,8:720,16:14880,32:80640,64:430080; no surjection.",
      "scopeEN": "Complete only for declared ordered quarter-clock/sign-lift stratum under Gamma conjugation; not full G31/W(E8) reflection moduli or additional equivariant structures.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection"
      ],
      "attemptIds": [
        "contract:marked-seam-monodromy-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a2c2c9fdb36a450726d42bb4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:quarter-lift-central-quotient-class-and-all-subgroup-restrictions",
      "titleEN": "Nontrivial central quotient class and all subgroup restrictions",
      "statementEN": "Z(Gamma)=F2^5 and Gamma/Z=F2^5, with full central cocycle kappa((u,e),(a,f))=(ea,ef). Restriction vanishes exactly on subgroups in e=0; otherwise a nontrivial square obstructs an order2 lift.32central characters yield16marked U1 classes,15nonzero: pure clock carry is a U1 coboundary, other classes are distinguished by commutators.",
      "scopeEN": "Central quotient extension with trivial coefficient action, distinct from split noncentral extension over<J> and the G0 factor.16classes describe the Z-induced family, not all H2(F2^5,U1).",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:marked-seam-monodromy-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e7d56864a843a85f74338e51"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-clock-reflection-full-factor-cocycle-trivialization",
      "titleEN": "Full G0 lift cocycle trivialized by explicit cochain",
      "statementEN": "For actual G0=<J,R>=C4×C2 the full8×8factor table of the original ordered lattice lift is computed. Its Hom(L,F2) class vanishes: b=(0,86,6,80,136,223,142,217), ordered1,R,J,JR,J²,J²R,J³,J³R, satisfies b(g)+g.b(h)+c(g,h)=b(gh) on64pairs. All512cocycle triples checked.",
      "scopeEN": "Full cocycle and global trivialization on G0 only; no splitting decision for full G31 or W(E8).",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "attemptIds": [
        "contract:marked-seam-monodromy-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4010a7af20112a64f04d056d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-quartic-exterior-local-cohomology-distinguishes-clock-monodromies",
      "titleEN": "Native quartic/exterior cohomology distinguishes equal-order monodromies",
      "statementEN": "Existing inclusions P5->Sym4(V4) and exterior²V4->V4⊗V4 are G0-equivariant. J versus JR gives complex H1 dimensions8/8 onV4,12/15 on exterior²V4,15/14 onP5. Integral E8 system with fourJ has H0=0,H1=Z16⊕(Z/2)^4,Hk=0 fork>=2; Smith form1^4,2^4. Local coefficients distinguish marked systems of equal clock order.",
      "scopeEN": "Cohomology of specified local systems on four-punctured sphere; no identification of differently dimensional representations or invariants of every bundle/bordism.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "attemptIds": [
        "contract:marked-seam-monodromy-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8acc33457a992359dc66e509"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:orbifold-lift-criterion-and-determinant-eight-divisibility",
      "titleEN": "Equivariant lifting and divisibility by eight",
      "statementEN": "Central orbifold H2 decides lifting; based lifts form an H1torsor and unbased lifts require centralizer quotient. Cone power defects are complete on oriented punctured quotient surfaces. The existing determinant class on C_m*C_mwith opposite parity lifts exactly for8|m, then16lifts; an original order8matrix example is given.",
      "scopeEN": "Original60reflection class, ordered punctures, marked central generator and simultaneous inner conjugation. General theorems use their explicitly stated hypotheses.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "attemptIds": [
        "contract:equivariant-monodromy-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9de4c60a4e0237131b839cad"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-g31-reflection-census-and-all-integral-cohomology",
      "titleEN": "All17G31classes and integral cohomology",
      "statementEN": "Complete local rerun confirms14760ordered quadruples,17conjugacy classes and5Hurwitz orbits. All17integral Smith forms give one Z22H1, three Z20+Z/2(typeA), thirteen Z20; H0ranks6or4and higher cohomology zero. Central lifts through the same lattice projection cannot change this cohomology.",
      "scopeEN": "Original60reflection class, ordered punctures, marked central generator and simultaneous inner conjugation. General theorems use their explicitly stated hypotheses.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "attemptIds": [
        "contract:equivariant-monodromy-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2a42e484aa0049185ec372c7",
        "source:d00a6edd1536477a5899a3ec"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:all62-original-clock-obstructions-and-central-variants",
      "titleEN": "All62clock obstructions and central transport variants",
      "statementEN": "All62original order4clock classes obstruct:30have(0,2),32have(2,0). Central clock power alone still gives zero. Defined central covariance with product1requires d=1,3and gives960classes with strict clock or1984with central clock power.992projective orbifold pairs instead have meridian productz2. Same existing extension, explicitly separate contracts.",
      "scopeEN": "Original60reflection class, ordered punctures, marked central generator and simultaneous inner conjugation. General theorems use their explicitly stated hypotheses.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "attemptIds": [
        "contract:equivariant-monodromy-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:017ad00134377035c6b429ce",
        "source:74676ca7b7382c5e8cf0d63f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-sign-lift-g31-group-comparison",
      "titleEN": "Actual group comparison and central pushout exclusion",
      "statementEN": "An explicit lattice isometry identifies Gaussian and standard E8roots and preservesJ. Gamma_sign projects to<J>inG31. Neither group embeds in the other; common quotients are precisely1,C2and cannot retain order4clock. Zero invariant lattice mod2space forbids a nonzero equivariant sign-kernel map to trivialZ4and that central pushout identification.",
      "scopeEN": "Original60reflection class, ordered punctures, marked central generator and simultaneous inner conjugation. General theorems use their explicitly stated hypotheses.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "attemptIds": [
        "contract:equivariant-monodromy-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:33a9ac93fb8b29dde231bfcc",
        "source:cd2a1506d4d559f10f76b71a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:complete-g31-lift-invariants-and-explicit-collisions",
      "titleEN": "Complete invariants and explicit collisions",
      "statementEN": "Complete invariants are canonical ordered tuple orbit, centralizer clock orbit and ordered central phases. Clocks0/3and0/5share monodromy,spectrum,lattice cohomology and obstruction but have centralizers64and128. Without clocks there are1088central lift classes. Phase tuples(2,0,0,0)and(0,2,0,0)over the same tuple are not conjugate.",
      "scopeEN": "Original60reflection class, ordered punctures, marked central generator and simultaneous inner conjugation. General theorems use their explicitly stated hypotheses.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "attemptIds": [
        "contract:equivariant-monodromy-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8db5206a99823766262c7c25",
        "source:ef383811336ba7c4b2f84ee6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e7-quarter-pairs-literal-native-g31-reflections",
      "titleEN": "E7 pairs are the original Gaussian reflections",
      "statementEN": "In the given E8 root system J with J²=-I exchanges the120 root-normal E7 slices in60 pairs. Their intersections are D6 with60 roots and their normal planes A1+A1. The operator s_alpha s_Jalpha is literally the original complex Gaussian root reflection of v634; the60 distinct operators generate the existing G31 realization of order46080. Operator equality, not group order alone, supplies the dictionary. The two actual E7 subalgebras contain192 roots; their mixed brackets generate all48 missing roots in one round. Their integral lattice sum is E8 at index1. The60 pairs form a transitive G31 orbit.",
      "scopeEN": "Fixed native Gaussian J and actual root subsystems; no arbitrary Lie-subalgebra embedding classification, new lattice-lift class or physical identification.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:e-series-quarter-clock-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1edf2559765041bd9e2616fc",
        "source:c7cfdc7b10abcfa988bd47cc",
        "source:0724e53c35faab165806e9a6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e6-root-subsystem-quarter-clock-discriminant-obstruction",
      "titleEN": "E6 root subsystems admit no invariant native quarter clock",
      "statementEN": "No E6 root subsystem is preserved by J: its induced action on K*/K=Z3 would square both to identity and, from J²=-I, to nontrivial inversion. The same argument applies to A2. All1120 regular A2 complements form560 J pairs; their E6 intersections have12 roots in640 and24 roots in480 subsystem cases. An explicitly marked D5<E6<E7<E8 chain with40/72/126/240 roots exists but is not J invariant.",
      "scopeEN": "The discriminant proof covers all E6 root subsystems. The finite census covers the specified regular A2 complements. No claim about arbitrary non-root Lie subalgebras or physical scales. This does not forbid transported real E6/E7 reductions on the parity double cover with remaining ±I holonomy.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:e-series-quarter-clock-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f8a30f8d81abbe00ef94c815",
        "source:c7cfdc7b10abcfa988bd47cc",
        "source:2b55ad62ad7d9ea868c57316"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e-series-square-cover-family-and-quarter-descent",
      "titleEN": "Intrinsic square curves and transported E7 reductions",
      "statementEN": "Each of60 Gaussian root lines gives a representative-independent square marking and w²=(v/alpha)^4-1 with elliptic compactification j1728. For the separately supplied all-J representation on CP1 minus mu4, the parity double cover has ±I holonomy and permits chosen parallel real E6/E7 root reductions. E7 descends as an unordered pair. The parity character has8 C4 lifts; cyclic marking symmetry leaves2 uniform orientations. Deck, base rotation and fibre J are different maps. The loop around all4 finite marks is trivial here but not in the existing uniform mu3 cover.",
      "scopeEN": "Fibre holonomy at4 removed branch points remains-I; no ordinary flat extension to the compact elliptic curve. The intrinsic family does not yet identify the original seam/peripheral data. No necessary selection of an individual chart.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:e-series-quarter-clock-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9c66de51aeff8053c3d0b853",
        "source:c7cfdc7b10abcfa988bd47cc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e-series-integral-glue-and-normalization-nonidentifiability",
      "titleEN": "E7 distinguishes glue types and conditional normalization rules",
      "statementEN": "The native E8 quotients for D6+A1+A1, E7+A1, E6+A2 and D5+A3 are C2²,C2,C3,C4. The E7-pair index4 is not cyclic C4 glue. Conditional continuations1/(pi*r) and1/(2pi*m), with selected exceptional rank r and lattice extension index m, agree at E6/E8 but differ at E7:1/(7pi) versus1/(4pi). The anchors do not determine the continuation. Complete conformal windows retain total rank and central charge8.",
      "scopeEN": "Exact lattice quotients and non-identifiability of an extra normalization map. No identification of original modular index I with m in each projection, no selection of a law or E7 coupling/scale prediction. The historical7pi window is no independent measurement. The established P1/P2→D5+A3→E8 construction and phi_base=(4/3)c3 remain intact. This comparison concerns only an additionally proposed E7 continuation and is not a missing step in the existing compiler.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:e-series-quarter-clock-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:db1b9ccfff9d7440a86a5a9a",
        "source:7ab3b9bc22d967d7ddc94334",
        "source:c7cfdc7b10abcfa988bd47cc",
        "source:c5d887dee53787437b600fe2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:global-original-g31-character-lift-nonsplitting",
      "titleEN": "Global original G31 lattice lift class is nonzero",
      "statementEN": "The original A=Hom(E8,Z2) extension is nonsplit over all G31, with order-two H2 class. Seven original relation equations give0=1 on an order16 subgroup H, while all22proper subgroups split. The exact order512 lattice quotient encodes the same lift problem.",
      "scopeEN": "Original cocycle and actual G31module. H is inclusion-minimal; no claim of minimum order among all witnesses.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension"
      ],
      "attemptIds": [
        "contract:global-g31-lattice-lift-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:31ab7f3b070882373cb123a0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:all62-original-character-clock-lifts-complete",
      "titleEN": "All62original clock objects admit character-valued lifts",
      "statementEN": "All62original clock objects admit strict C4*C4 lifts into the inherited lattice extension. Full conjugation gives11356classes=6856+4272+228. Every normal form and automorphism order is stored; independent Burnside verifies all62counts. Clocks0/3and0/5 give212and176classes.",
      "scopeEN": "Ordered punctures, clock order4, full lift conjugation. No extra meridian square relation; distinct from central Z4extension.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "attemptIds": [
        "contract:global-g31-lattice-lift-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4c8bf38c5d4e2df829b3b171",
        "source:ac90922527f53987d0399544"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:all17-original-character-monodromy-lifts-complete",
      "titleEN": "Complete census of original17character-valued monodromy lifts",
      "statementEN": "Full conjugation over the17original reflection quadruple classes gives835456character-valued monodromy lift classes, with a complete affine normal-form criterion. V4embeddings with and without integral Z2torsion give26128and42240classes per ordered orbit.",
      "scopeEN": "F3representations, ordered punctures, full lift conjugation. Census and normal-form criterion; no stored835456-representative list.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "attemptIds": [
        "contract:global-g31-lattice-lift-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:50583fc1638fdcb3ca61fdd1",
        "source:d1f134d65455207d5beaaaf3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e7-pair-full-lattice-field-character-torsor",
      "titleEN": "E7 pairs on all lattice fields and complete correction torsor",
      "statementEN": "For all60 native Gaussian root lines, r=s_alpha s_Jalpha is the original complex reflection. Its actual Tits lift T=n_alpha n_Jalpha has T²=D_k, k(lambda)=<alpha+Jalpha,lambda>mod2, negative on128 roots. T=S_r D_chi holds on every lattice field with explicit input character. Exactly eight corrections per line are involutive and commute with the fixed J lift, a torsor under three-dimensional A^{<r,J>}. They agree on the actual neutral4/5/20 diagram and differ on charged sectors. The full G31 extension remains nonsplit.",
      "scopeEN": "Unchanged eps_e8, ordered integral basis and original lattice VOA. All-lattice equality follows from the character lemma and eight generators; all240 roots and13680 nonzero brackets per line checked separately. Individual lifts do not provide a global group section.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "attemptIds": [
        "contract:e-series-compiler-closure-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7143365590a7eb44d1467620",
        "source:4c6461063647a19b8828400f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e-series-complete-native-compiler-cut-dictionary",
      "titleEN": "Complete E6/E7 dictionary for the original D5+A3 split",
      "statementEN": "The120 E7 cuts form four W(D5)xW(A3) orbits of sizes20,6,30,64, with exactly six containing the original D5. The1120 regular E6 cuts form seven orbits of sizes40,120,320,60,480,4,96. Their560 J pairs intersect320 times in A2+A2 and240 times in D4. Exactly four E6 cuts contain D5, a canonical unordered S4 tetrahedral family with actual weightwise E8/D5/A3/E6/A2 branchings. J sends all four outside this family with common first-four-coordinate D4. The3+2 marking fixes the family but selects no cut.",
      "scopeEN": "Complete finite classification of regular root cuts under the fixed compiler Weyl group, with stabilizers and actual actions. No classification of arbitrary Lie algebra embeddings; retain the original clock.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:e-series-compiler-closure-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:da44cac644a7fb6ce034d4d2",
        "source:7b54351a2d7e5dc24ce8d7c3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:common-cover-clock-and-maximal-integral-phi12-intertwiner",
      "titleEN": "Common covers and maximal actual integral clock intertwiner",
      "statementEN": "C6 and C12 are the minimal marked common covers of C2/C3 and C4/C3, of genera7 and15. J<->Q, sigma<->deck and c=J sigma<->R=Q deck preserve c⁹=J and c⁴=sigma. The unique lift with this full marking is Qn Delta_n^4. Actual real8 has character Phi4² Phi12; the retained rational Burau rank6 model has Phi6 Phi12. Their canonical Phi12 kernels admit an explicit integral Z[C12] intertwiner also transporting J and sigma. Different complementary spectra obstruct full equality; retained alternating forms of types(1,3) and(1,2) obstruct any form-preserving unimodular intertwiner. Peripheral J is deck on C4 while compiler J=c⁹ rotates the base; no phase choice merges these roles.",
      "scopeEN": "Fixed deck orientation, actual matrices and saturated integral Phi12 sublattices. The displayed intertwiner is an explicit certificate, not a uniquely selected identification. Trace form and basis belong to the retained Burau lattice model, without an independent geometric cycle identification. Quartic5, exterior6, erasure20 and permutation characters remain distinct and are completely compared.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-marked-cyclic-cover-and-burau-model",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "attemptIds": [
        "contract:e-series-compiler-closure-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:748ab45b205bcbea5b2e42fd",
        "source:07e8e291de739b0fe1a4e6a9",
        "source:d6d5be194317655ee8cb33cb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-four-cut-projectors-unify48-fourthirds-fivequarters",
      "titleEN": "Four E6 projectors connect48,4/3 and5/4 in the same representation",
      "statementEN": "In the original half-root block B=(16,4), the four D5-containing E6 cuts yield literal rank16 projectors P_t, with P_t P_u=delta_tu P_t and sum P_t=I64. Q_t=I-P_t has rank48 and carries exactly(16,3), with checked D5 and A2 root action. Every cut gives Tr(I64)/Tr(Q_t)=64/48=4/3=phi_base/c3. Every weight of the same block has squared D5 projection5/4 and A3 projection3/4. The same48 lies in(27,3)=(16,3)_1+(10,3)_-2+(1,3)_4, hence81=48+30+3. The E7 missing48 instead carries(12,2,2), whose actual Y character rejects identification with three D5 spinors.",
      "scopeEN": "Canonical unordered S4 projector family on the original root-current block. Exact representation interpretation of the existing seed ratio, without an additional readout law or selection of a tetrahedral vertex.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:e-series-compiler-closure-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c4d285313cb5aed516180c9d",
        "source:a68f94fbe4a523190b2971d5"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:complete-covariant-compiler-voa-source-and-weyl-closure",
      "titleEN": "Complete covariant compiler closure on the same lattice-field source",
      "statementEN": "H=W(D5)xW(D3) with actual J generates exactly W(D8):224 E6 cuts in56 tetrahedral frames. Each frame resolves the entire128 half-root block into four rank32 projectors; complements have rank96 and128/96=4/3, retaining squared norms5/4 and3/4. Original E7-pair operations enlarge closure to W(E8):1120 E6 cuts,7560 A3 frames,27 through each cut. The full original sign extension over W(E8) acts on the existing VOA source. F_ghat[p,v]=[p,ghat v] transports all marks and fibre holonomy and composes exactly, retaining the nonsplit character carry.",
      "scopeEN": "Minimal generated transition closure, not a fixed-J/fixed-D5+A3 symmetry claim.128 is fixed only under D8 and transported under the full action. Organizes the given lattice VOA and covers; no physical-origin derivation or freely chosen helper model.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:joint-native-compiler-cover-covariance-category"
      ],
      "attemptIds": [
        "contract:e-series-joint-source-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d595e5af26c21e1fabbcb2c0",
        "source:7f92b273d0dfba55cb1e471d",
        "source:ef333d95feba6921b1e3625e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:complete-fixed-jhat-cyclic-field-lift-and-associated-clock",
      "titleEN": "One complete cyclic field-lift class and joint associated clock",
      "statementEN": "With original fixed Jhat=S_J, the ninth-power equation has F2 rank6. Exactly four compiler lifts S_c D_a with a=31,62,151,182 have ninth power Jhat; their sigmahat masks are63,30,183,150. The16 Jhat-preserving character gauges give one orbit with stabilizer4. No solution retains both separately generator-normalized J and sigma sections. On Vper=(C12 x V_L)/((Delta12 p,v)~(p,Jhat v)), Chat[p,v]=[R12 p,chat v] satisfies Chat4=sigmahat, Chat12=I and Jcomp=Chat9=Q12 Jper. The two J roles share the same fibre lift while retaining different base components.",
      "scopeEN": "All256 character candidates over the fixed cyclic compiler group; all-field equality from eight generators and unchanged cocycle, with all240 roots checked directly. No full G31/Weyl splitting or identification of different cover automorphisms.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:existing-marked-cyclic-cover-and-burau-model",
        "premise:joint-native-compiler-cover-covariance-category"
      ],
      "attemptIds": [
        "contract:e-series-joint-source-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b2eebefbeb86c972298aa5e3",
        "source:116b0242f93dedd5ef6bdb05"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:relative-native-burau-clock-hom-faithful12-transport",
      "titleEN": "Relative clock-Hom transport forces exactly the existing C12",
      "statementEN": "On the actual common Phi12 lattices, Hom_clock=Q[A12] has dimension4 and integral Hom=Z[zeta12], with integral isomorphisms a unit torsor. Native periphery is A12^9; the Burau periphery induced from the existing mu3 cover deck module is A12^4. Relative Hom transport is therefore H->A12^7 H, with exactly0 parallel clock intertwiners. Every nonzero relative orbit has order12. Exponent vector(7,7,7,7,8) has exactly the original winding kernel modulo12, so the existing C12 is the minimal trivialization.",
      "scopeEN": "Comparison of native and explicitly cover-induced Burau local systems. No independently geometric Gauss-Manin H1 family, forced carrier equality or extra line twist erasing carry. The earlier clock dictionary remains valid but is not a parallel peripheral dictionary.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-marked-cyclic-cover-and-burau-model",
        "premise:joint-native-compiler-cover-covariance-category"
      ],
      "attemptIds": [
        "contract:e-series-joint-source-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c62b845483e5cc9907844f1a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e6-vertex-nonselection-survives-full-field-clock-phases",
      "titleEN": "No E6 vertex selection even with full clock-field phases",
      "statementEN": "C_H(J) has order64 and cyclic4 image on the four E6 vertices. Its Y stabilizer is{I,d}, d=diag(1,1,1,1,1,1,-1,-1), acting by two transpositions without a fixed vertex. d preserves sigma,c and the actual quartic/erasure diagram. With fixed full Jhat and chat=S_c D31, exactly four d field lifts126,127,128,129 commute with both;126 and127 are involutions. Thus genuine automorphisms of the same full associated object fix no E6 vertex. Character-gauge conjugation transfers this to all four cyclic lifts. The supplied field phases therefore select no vertex.",
      "scopeEN": "Complete stabilizer test inside H preserving root factors setwise, with fixed J/compiler field lifts, Y and covariant quartic/erasure maps. No pointwise freezing of every individual quartic vector or separately chosen charged state. The full transported family is the exact object.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:joint-native-compiler-cover-covariance-category",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension"
      ],
      "attemptIds": [
        "contract:e-series-joint-source-20261023"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5de0f3deede7300a5c7286c6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:marked-c4-glue-unique-local-e8-vacuum-source",
      "titleEN": "Marked C4 glue determines one complete local E8 vacuum source",
      "statementEN": "In exactly Ext_H(U) there is one VOA and normalized local Q system class over U, represented by V_E8. q_D5(s)=5/8 and q_A3(f)=3/8 make H Lagrangian; the full abelian associator/braiding class trivializes only on H. H2(C4,C*)=H2(C4,U1)=0 gives uniqueness, with residual automorphisms Hom(C4,U1)=C4. The actual weight1 branching is60+64+60+64=248. Lattice vacuum, Sugawara vector, L0=N+Norm(alpha)/2, all vacuum correlators, unitary structure over U and associated local conformal net are determined in this class.",
      "scopeEN": "Complete conditional mathematical reconstruction for the specified U module and local unitary conformal extension. No derivation of primitive P1 membership or physical time/state/spacetime identification. H3(C4,U1) is not asserted zero; the original nonsplit G31 character extension is not replaced by scalar coefficients.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:marked-c4-unitary-local-extension-reconstruction-class"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b8003524a1f8fa82ab2b1151",
        "source:185b59879a27f7d137da5ae5",
        "source:fe860e1a047e7181877ceda5"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:canonical-vacuum-clock-preserves-e6-nonselection",
      "titleEN": "Canonical vacuum and L0 select no E6 corner and differ from internal clock",
      "statementEN": "Every original lattice-field lift fixes the canonical vacuum and Sugawara vector and commutes with every L_n. Thus the existing d field lifts126/127 remain automorphisms after including these canonical data and still fix no E6 corner. Internal Jhat has eigenvalues+i and-i four times each on the eight weight1 Cartan currents; exp(i theta L0) is scalar there. Hence Jhat is not a conformal time rotation for any theta. The joint cover construction and nonsplit transition carries remain functorial.",
      "scopeEN": "Exactly the existing marked associated E8 object and its standard conformal vacuum realization. No general physical time no-go, base/deck/fibre identification or additional state marking.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-c4-unitary-local-extension-reconstruction-class",
        "premise:joint-native-compiler-cover-covariance-category",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1f8fe97eff1328b7e2fc90b1",
        "source:5de0f3deede7300a5c7286c6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:marked-generator-forces-e8-without-support-multiplicity-or-minimality-input",
      "titleEN": "One marked generator forces E8 without extra sector or minimality choices",
      "statementEN": "Regularity of U and common L0 make W automatically a finite U module. Its connected separable algebra object B has simple regular B module. Every invertible M_a tensor B is simple, so free-module adjunction forces n_a=dim Hom_B(M_a tensor B,B) in{0,1}. Support S is the stabilizer subgroup of B and is isotropic by trivial twist. M_h in W yields H subset S subset Hperp=H, hence exactly four sectors once and the unique marked E8 extension with vacuum and conformal data. Before specifying the generator there are exactly four local conformal extension classes over fixed U: U, V_D8 and the two oriented V_E8 embeddings.",
      "scopeEN": "Complete classification within connected local unitary SAME-CONFORMAL extensions. Corrects the overstrong remark in THEOREMS.txt Section5: merely containing the four sectors already suffices under these remaining hypotheses. A tensor spectator changes the conformal vector. The two E8 classes distinguish fixed U embeddings and become isomorphic after allowing A3 diagram reversal. No derivation of this local realization from primitive P1 or physical completion.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:connected-local-same-conformal-compiler-extension-with-generator"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:386242d1a86ff3a0e1d87e7b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-reflection-rotation-lift-classes-and-forgetful-images",
      "titleEN": "Native equivariant classes and complete forgetful images",
      "statementEN": "Exact original field relations give binary ranks20,20,24,30 on40,40,40,48 variables for reflections s=0,1, rotation and joint s=0 marking. Character gauge rank4 gives65536,65536,4096,16384 marked classes. Complete forgetful images in original Gamma moduli have2176,2560,256,64 classes. All168 columns independently checked in original cocycle field action and ranks with SymPy GF2; all forgetful image orbits separately enumerated.",
      "scopeEN": "Complete only in the explicitly fixed native projection and morphism classes. Not all normalizer reflections or primitive physical source/state selection.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection",
        "premise:fixed-native-reflection-rotation-character-markings"
      ],
      "attemptIds": [
        "contract:seam-equivariant-active-search-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0ed2bf78d20b620aee61834a",
        "source:974b23386979529a3323bb89"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:quarter-clock-pure-mapping-class-complete-quotient",
      "titleEN": "Complete pure mapping class quotient with157696 normal forms",
      "statementEN": "For N=I+A, N²=0, b_i² adds N(ci+c_(i+1)) to both adjacent characters. The pure mapping class action on original Gamma classes factors faithfully through C2×C2. Burnside and independent enumeration of all2^20 character gauge classes give157696 orbits with original Gamma class size census1:4096,2:46080,4:107520, weighted total526336. Every normal form is saved.",
      "scopeEN": "Ordered four J sign lift stratum and pure mapping classes. No puncture permutations, silently frozen reflection marking quotient, or physical origin theorem.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection",
        "premise:ordered-quarter-clock-pure-hurwitz-equivalence"
      ],
      "attemptIds": [
        "contract:seam-equivariant-active-search-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7ff02d3c49c6381fd996db94",
        "source:80e84c947e479d0ffeac7e4f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e8-cut-five-orbital-incidence-algebra-complete",
      "titleEN": "Complete E6 orbital algebra with five irreducible components",
      "statementEN": "The actual Weyl action is transitive on1120 E6 cuts. An explicit stabilizing E6/A2 reflection subgroup is transitive on each intersection class: D5 with81,D4 with270,A4 with648,A2+A2 with120 neighbours. Including equality these are the full five orbitals. All125 structure constants yield the commutative full commutant. Normalized primitive idempotents have ranks1,35,84,300,700, proving the complete irreducible Weyl decomposition.",
      "scopeEN": "Complete for regular A2-normal E6 root cuts in standard E8 under its actual Weyl action; not arbitrary Lie-subalgebra embeddings.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:standard-e8-root-cut-full-flag-incidence-category"
      ],
      "attemptIds": [
        "contract:e-series-incidence-algebra-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e532108a0a1c1c2a921647fd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:compiler-d8-frame-requires-full-d5-a3-flag",
      "titleEN": "Unique D8 frame belongs to the full D5+A3 flag",
      "statementEN": "All135 D8 frames,7560 A3 tetrahedra and their actual incidences were generated. Each full pair of A3 normal system and common D5 core lies in exactly one D8; each D8 contains56 such flags. Bare A3 containment instead gives616 A3 systems per D8, consisting of56 coordinate D3 and560 four-axis A3 chains, and11 D8 per bare A3. Unique tetrahedron-to-frame incidence is therefore a full compiler-flag statement.",
      "scopeEN": "Actual full D5+A3 root flags, not uniqueness from the A3 root subsystem alone.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:standard-e8-root-cut-full-flag-incidence-category"
      ],
      "attemptIds": [
        "contract:e-series-incidence-algebra-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8f6b4b690e788d98a1a34748"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:tetrahedron-incidence-lossless-e6-reconstruction",
      "titleEN": "Tetrahedron sums reconstruct all E6 data without loss",
      "statementEN": "For E6/E7 incidence N and E6/tetrahedron incidence M, every entry satisfies NNt=A_D5+3I and MMt=A_D5+27I. Hence MMt=NNt+24I and for every signal f, norm(Mt f)^2=norm(Nt f)^2+24norm(f)^2. N has rank120 and loses1000 directions300+700; M has rank1120. All tetrahedron sums recover f exactly as (NNt+24I)^(-1)M(Mt f), also through an explicit rational degree3 polynomial. The information theorem does not require irreducible decomposition.",
      "scopeEN": "Linear data reconstruction on the same finite E6 set with counting inner product. Preserves supplied data; does not generate a distinguished corner, source or physical state law.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:standard-e8-root-cut-full-flag-incidence-category"
      ],
      "attemptIds": [
        "contract:e-series-incidence-algebra-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:40aca91e1d2afbc0d04e9bcd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:restricted-clock-lift-and-global-cover-audit-reconciled",
      "titleEN": "General lift and cover audit reconciles with the marked originals",
      "statementEN": "In the original lattice chart SNF(I-J) has invariants1,1,1,1,2,2,2,2:256 J sign lifts yield16 sign-gauge classes and one class if only gauge equivalence is enlarged to quarter phases. Enlarging candidates too gives16 classes. The original additional equation chat^9=fixed S_J has exactly four solutions and one orbit under16 S_J-preserving character gauges. On all five fundamental peripheral loops the original induced Burau comparison has rho_rel=A^(7nu), nu=(1,1,1,1,-4). Faithful order12 proves globally ker(rho_rel)=ker(nu mod12), hence minimal C12. The general C12xC12 degree144 counterexample does not satisfy this factorization.",
      "scopeEN": "Original ordered lattice cocycle, fixed Jhat marking and explicitly induced Burau deck local system; no independent Gauss-Manin identification or splitting of the full G31 character extension.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:joint-native-compiler-cover-covariance-category",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension"
      ],
      "attemptIds": [
        "contract:e-series-incidence-algebra-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0677ff328f5fe3c2d46a325c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:double-scalar-quarter-is-marked-glue-with-two-step-index",
      "titleEN": "Doubled scalar quarter twist is exactly the marked glue generator",
      "statementEN": "F(2q)=lambda is an actual lattice identity, not only equal norm. s=2q has order4 modulo D5+D3 and order2 modulo D8. The tower U to V_D8 to V_E8 has indices2,2 and mu-indices16,4,1. The older SO16 base with index4 mixes two different inclusions.",
      "scopeEN": "Given eight-channel chart and marked lattice generator. Squaring a finite disorder operator is not identified with the local vertex field.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:scalar-eight-channel-twist-and-explicit-compiler-charge-chart"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c1eef33b8c0b286db9baab3f",
        "source:26a6dc6219552f30be2109f6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:scalar-quarter-two-involutive-e8-extensions",
      "titleEN": "Exactly two scalar extensions over D8, both of order two",
      "statementEN": "The canonical scalar torus character g_q on V_E8 has order2 and fixed VOA V_E7 tensor V_A1. Over fixed V_D8 exactly one further extension gamma g_q exists, with fixed VOA V_D8prime and order2. Their weight-one spectra136/0/112/0 and120/0/128/0 exclude identification with actual native Jhat with60/64/60/64, even under full field conjugacy.",
      "scopeEN": "Precisely the given scalar character restricted to fixed D8 subnet. Other source-derived field dictionaries are not excluded.",
      "status": "excluded_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:scalar-eight-channel-twist-and-explicit-compiler-charge-chart",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:befb93d3a40782b0b5820353",
        "source:69cf3554f85326a93944eb9a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-quarter-glue-inner-conjugacy-and-oriented-tetrahedron-flags",
      "titleEN": "Native quarter clock is the inner glue-clock class over tetrahedron flags",
      "statementEN": "Five-carrier parity kappa=exp(2pi i v(0)), v=(1/2^5,0^3), acts on the four U glue sectors as1,i,-1,-i and fixes precisely U. Among all65536 torus points modulo4 exactly15120 match actual Jhat; they form one actual W(E8) orbit. Thus C kappa C^-1=Jhat for a full VOA automorphism C. Each two inverse primitive characters share a fixed root lattice D5+A3; the7560 kernels are equivariantly the actual7560 compiler/tetrahedron flags.",
      "scopeEN": "Complete torus and Weyl classification plus compact E8 conjugacy, not mere matching spectra. C is not preferred and retains other marks only through their joint transport.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e23fb8064f4d6061d70ed158",
        "source:0889e3dbb71be064dd1683d1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-cyclic-compiler-inner-conjugacy",
      "titleEN": "One common inner conjugator for the complete C12 compiler family",
      "statementEN": "After toralizing actual chat and aligning its ninth power to kappa, all candidates c_t=kappa sigma_t are covered by3^8=6561 cubic torus points. Exactly480 have the full original weight-one character and form one orbit under reflections in52 U roots. Thus chat,Jhat=chat^9,sigmahat=chat^4 are simultaneously conjugate to c_t,kappa,sigma_t. Combining kappa with the old frozen sigma already fails on an explicit root.",
      "scopeEN": "One selected actual admissible chat and its whole power family. All four admissible sign lifts have the same cycle character. No frozen full marked-tuple equivalence or microscopic origin is proved.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "attemptIds": [
        "contract:e-series-source-reconstruction-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:21028c876c66a1df902b6e57",
        "source:32d931d52fb6e03c886272cf"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:recovered-e6-closed-81-current-module-and-unique-source-cubic",
      "titleEN": "Recovered complete E6 carrier and unique cubic source correlator",
      "statementEN": "The original18 September proofs identify E6 and A2 as mutual centralizers in the actual Chevalley E8 algebra. The48=(16,3) carrier is not E6 closed; its full closure is81=(27,3) with27=16_1+10_-2+1_4. In the given affine vacuum the actual three-current correlator kappa(a,[b,c]) equals d_ABC epsilon_ijk. Its45 cubic candidates have Ward rank44 and hence a unique relative coefficient line. The positive grade-one Gram gives64/48=4/3 its exact equal-norm current-response meaning. Normalized I4/4 is not a vacuum partial trace. These completed original results are recovered into reviewed findings; missing reviewed coverage was not an open derivation.",
      "scopeEN": "Actual embedded current algebra and the given local unitary affine source. U1 subscripts denote internal charges. No derivation of a four-dimensional fermionic Yukawa action, particle population, mass or primitive physical P1 source identification. Recovery of completed original results, not a new mathematical first proof.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:marked-c4-unitary-local-extension-reconstruction-class"
      ],
      "attemptIds": [
        "contract:compiler-e6-seam-readout-20260918",
        "contract:compiler-vacuum-current-cubic-20260918",
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4441aea72b2a7b5693ea3dd2",
        "source:de2e18ecbd0e063696d8048e",
        "source:5b6ecca783352c9c5eb38b55"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:e-series-operational-role-review-and-source-time-centralizer",
      "titleEN": "E6 E7 E8 operator roles, tetrahedral envelopes and actual horizontal time centralizer",
      "statementEN": "In the fixed original D5+A3 cut, each of the six pairs among the four E6 systems generates precisely its unique E7:104 union roots close to126, with a common40-root D5. Orthogonal root/Cartan projectors onto E6 and E7 are not Lie homomorphisms, as removed opposite-root pairs with nonzero projected coroot show. For the existing H8=8L0-rho_A7.a0+(2a-1)Q/2, Q-neutral E7 membership is not full horizontal energy symmetry: [H8,J_(e0-e1,0)]=-J_(e0-e1,0). At a=1/4 and3/4 exactly8 ordinary n=0 root modes commute, of type4A1; with8 Cartan modes this horizontal centralizer has dimension16. Complete conformal E7+A1 and E6+A2 windows retain their complements and glued modules. A cut sequence is not a derived physical breaking or time history.",
      "scopeEN": "Exactly the fixed native root chart and the given eight-channel time operator. The tetrahedron covers four of1120 E6 and six of120 E7. The Q-neutral E7 has a half-root normal and is not one of those six; Q is not automatically Y. Only ordinary horizontal n=0 modes are classified, not all affine conserved modes. Existing shifted p* sl2 modes and the solved color-center-neutral vacuum selection remain valid. The projector counterexample does not exclude genuine subalgebra inclusions, state restrictions or separately justified physical reductions.",
      "status": "established_scoped",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "topicIds": [
        "topic:e8",
        "topic:clocks"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:marked-c4-unitary-local-extension-reconstruction-class",
        "premise:four-d8-sectors-with-fixed-affine-source-time"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029",
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9fb2e6bb80efe00b267497a2",
        "source:6e34758287fea6c6bbb92ab7",
        "source:959d4a4805288113da15daa1",
        "source:46906ff1d70442c6ee30ce36",
        "source:6ace4826ef1d7a8401eec5a3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-clock-doily-ovoid-kernel-is-native-quartic-five",
      "titleEN": "The actual clock doily reconstructs the original quartic five",
      "statementEN": "The actual ovoid module ker(B^T) of E8/(1−J)E8 is marked-isomorphic to original quartic H5: detT=−96 and N_rT=16TD_r for all60 reflections. Spread and both twists have Hom0. Form diag(1,3,3,3,6), P5 and six rank1 effects follow.",
      "scopeEN": "Given Construction A and J; no P2/D5 or physical measurement identification from dimensions.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "attemptIds": [
        "contract:atlas-defect-synthesis-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ad7e906a333b23b24db322e8",
        "source:020c5c358f731a7b590fea1f",
        "source:b4c7d10ac7bb9222e7f64b7e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:glue-clock-twisted-sectors-share-marked-quadratic-module",
      "titleEN": "Glue and clock sectors share one marked quadratic module",
      "statementEN": "A_Q=C4², q=(5a²+3b²)/8, describes E8 extensions, D8 and four clock sectors; flux=a−b=−r. (i,j)↦(3i+j,2i+j) gives type4{2}; ground spaces1,4,16,4 have the specified actual representations. Level8, T order24; no transverse isotropic complement to H+.",
      "scopeEN": "Given same-conformal E8 class/marks. A_Q≠A_J; modular phase is neither base cover nor physical time; H± remain allowed.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-c4-unitary-local-extension-reconstruction-class",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "attemptIds": [
        "contract:atlas-defect-synthesis-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ce4b183b190486a26cf20628",
        "source:4817bc12940a274df6f3619f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:complete-native-six-effect-covariant-instrument-classification",
      "titleEN": "Complete covariant instruments for the actual six effects",
      "statementEN": "All covariant instruments with the given rank1 effects are I_a(rho)=Tr(E_a rho)[pP_a+(1−p)(I−P_a)/4], p∈[0,1]. Stabilizer commutantdim2, unique stationary stateI5/5, spectrum1,(p−1/5)^5,0^19. Markov histories and effectspan6<25 do not give full tomography; one-Kraus rule additionally selects p1.",
      "scopeEN": "Complete only in this finite instrument class; no physical effect/p/time or GNS coherence selection.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-six-ovoid-covariant-instrument-category"
      ],
      "attemptIds": [
        "contract:atlas-defect-synthesis-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:feb3123b8875895483b122b6",
        "source:3017e2398b8a07a4f7030a07",
        "source:9a12b85ca3512b7e3656aaf9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-six-effect-readout-on-existing-erasure-output",
      "titleEN": "The new observable reaches the original erasure output",
      "statementEN": "Original W:C4⊗H5→C64 is reconstructed exactly. E20_a=I4⊗E5_a has rank4, sumI20; W E20_a W* sums to rank20 projector. All25 rho entries,60 intertwiners and360 covariances agree. Stabilizer average gives P_a=(6/5)E_a.",
      "scopeEN": "Additional logical readout; original loss has effectsI5/4. No identification, Hilbert extension or preparation.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors"
      ],
      "attemptIds": [
        "contract:atlas-defect-synthesis-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:175f7a31800d244ef084a116",
        "source:e81d9e764bb0f42753d9c3f7",
        "source:8802e44c9d4e25aa31ed0c27"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:relational-quartic-singlet-and-invariant-density-separation",
      "titleEN": "Unique relational singlet ray and multiple invariant densities",
      "statementEN": "In given barH5⊗H5 the invariant vector rayOmega is unique. Jointlaw diagonal5/36, otherwise1/180; I25/25 has same marginals, jointlaw1/36. R=ΣbarE_a⊗E_a has spectrum(5/6)^1,(2/3)^5,0^19; maximizing selectsOmega only as an additional rule.",
      "scopeEN": "Tensor sector and pure population are additional premises. Equal Lueders statistics do not prove entanglement.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:relational-native-quartic-tensor-sector-without-state-selection"
      ],
      "attemptIds": [
        "contract:atlas-defect-synthesis-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:aecbd32f19be8d1d773cd66b",
        "source:d32f4b6d1b878fadf62d5a4f",
        "source:4b959b35e333ae4937d63102"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:new-clock-feedback-origin-input-audit",
      "titleEN": "New feedback closes compatibility without a circular origin claim",
      "statementEN": "The loop E8/J→ovoidH5→Pascal/glue→E8 already assumes E8,J and rank4. On C:y³=x⁴−1 the actual Prym clock gives SNF(I−J)=(1,1,2,2), four instead of16 classes; polarization(1,2) is degenerate mod2. V784/V796 exclusions and external bridges remain scoped.",
      "scopeEN": "Input audit of this route and curve; no universal P1 impossibility theorem or stale wrappers as evidence.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-p1-p2"
      ],
      "attemptIds": [
        "contract:atlas-defect-synthesis-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b8c90a526de38c9352a1d969"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-event-channel-cone-intersection-is-tenth-to-half",
      "titleEN": "Exact intersection with original native event channels",
      "statementEN": "Phi_p is a positive mixture of actual AdC5(g) exactly for1/10≤p≤1/2. On End(H5)=1+5+9+10 the zero9/10 blocks force Echi²=1+Echi; integral character bounds are sharp and both endpoints attained. p1 Lueders is excluded in this event class.",
      "scopeEN": "Forgotten-outcome channel only. Recorded native branches have scalar effects; no instrument equality or physical p selection.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-six-ovoid-covariant-instrument-category",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "attemptIds": [
        "contract:atlas-defect-synthesis-20261024"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a65ccb95e8415de59b8a6780",
        "source:2a85c7a3f3bc9c864e53a812",
        "source:2571b6fa3bcda9928f5c3850"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-six-ovoid-observation-first-occurs-at-tensor-degree-three",
      "titleEN": "Informative ovoid observation first occurs at tensor degree3 with complete classification",
      "statementEN": "For actual G31/ovoid action, Hom(H5,End(V4^⊗n))=0,0,1 for n1,2,3. n1/2, including V⊗barV: onlyI/6. All POVMs onC64: F_a(t)=I/6+tW[I4⊗(E_a−I5/6)]W*, −1/4≤t≤1. ImW=Sym³V with uniform44 complement is forced. Bell six carry spread, not ovoid.",
      "scopeEN": "Complete finite tensor category; no physical copying, t/instrument, family count, P2 or spacetime from tensor degree.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:native-tensor-povm-and-coherent-source-category"
      ],
      "attemptIds": [
        "contract:native-observation-arity-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d67b8788dc933e2c74e9cff1",
        "source:178b565cdb77e5a39d9f9263"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-quartic-erasure-and-hamming-octic-share-marked-ovoid-response",
      "titleEN": "Original quartic, erasure and Hamming octic share the same marked ovoid response",
      "statementEN": "Original decoder is (W*x³)_(a,i)=∂a phi_i/2. Actual marked R_A satisfy Igusa and p_A=||gradR_A||²/48, sum||x||⁶. All256 Hamming code pairs give I8=Σx⁸+14Σx_a⁴x_b⁴+168∏x²=96Σf_i²=(1/3)ΣR_A². Restoring allμ4 phases gives all14 marked code/root tetrads.",
      "scopeEN": "Given coherent inputs and constructors. Classical invariants; new comparison concerns marks/operator norm. Holomorphic ≠ Born squares.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:native-tensor-povm-and-coherent-source-category"
      ],
      "attemptIds": [
        "contract:native-observation-arity-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:33abdd7e461456381d59fc83",
        "source:8a22e92eb0d94a254f5a987d",
        "source:065c8ce1e14ed9db56d663a1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-octic-field-ray-is-explicit-but-retained-clock-stress-preparation-fails",
      "titleEN": "Canonical octic ray and exclusion of unshifted vacuum preparation only",
      "statementEN": "F8hat=Σ:f_i²:/sqrt140=I8/(96sqrt140) is normalized and uniquely invariant in ImM; six ovoids are the complete Pi9(v⊗v)=0 locus. Primarity and stress null theorem apply only to Omega,L_n. L_-8Omega of norm²336 is another singlet. a8(dotD) tests direct linear insertion, not higher geometric response; actual quarter fold hits at order8.",
      "scopeEN": "Uniqueness only in15 product sector. Unshifted null theorem remains valid; neither universal seam exclusion nor pure preparation.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock"
      ],
      "attemptIds": [
        "contract:native-observation-arity-20261025",
        "contract:native-octic-seam-origin-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ac3f5eb838f3a9527f038cdb",
        "source:10a45a32895d6cf28e0beee1",
        "source:646bab937ecf222ed9849088",
        "source:28b284db28692d750f69a1b6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-quarter-fold-stress-has-nonzero-octic-eighth-jet",
      "titleEN": "Actual quarter fold reaches the octic ray at eighth order",
      "statementEN": "Original M/O/U+ gives ||d||²=85/128 and F8hat(b)≠0 for BOTH quarters. Exactly <F8;d|(L_-1^d)^8Ω_d>=8!barF8hat(b), L_-1^d=Lcal_-8/8. All22 partitions give norm8!(85/128)_8. For smooth real A_d(g), jets k<8 vanish, k8=8!barF8hat(b)c_-1^8; genuine local bumps with c_-1≠0 hit without truncation. Full Mobius orbit agrees.",
      "scopeEN": "Given source/reference. Nonzero component, no pure preparation/ImM projection or P1 identity; minimum8 for c_-1≠0.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:original-displayed-j-equivariant-cartan-root-isometry"
      ],
      "attemptIds": [
        "contract:native-octic-seam-origin-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7b1662ec7efa0d20a0dc482a",
        "source:28b284db28692d750f69a1b6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-octic-is-an-original-even-car-current-composite",
      "titleEN": "Octic field already lies in the original even CAR current algebra",
      "statementEN": "A=U+^T O^T M obeys AA*=I4, AA^T=0 and b=Aδ. F8^d=:I8(A(j_sea+δ/z))/(96sqrt140): is a neutral even CAR current composite of the same source with original point splitting and finite derivative counterterms. Full correlations and i0 are retained; no E8 root/spinor vertices are needed. Fold energy8 equals source energy64.",
      "scopeEN": "Given reference dictionary; local eight original arcs, no c1/c8 point-net identity or P1 selection. No naive fermionic degree16 normal order.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:native-symmetric-quartic-and-erasure-constructors"
      ],
      "attemptIds": [
        "contract:native-octic-seam-origin-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9abbdd1d97ecab558a6beb99",
        "source:fa9bc910b6619512584e0e80"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-geometric-source-jet-and-partial-p1-seed-closure",
      "titleEN": "Geometric source jet and actual positive parts of the P1 interface",
      "statementEN": "U_phi=√phi′ pullback derives the original source jet, twisted dotB=i(v′∂+v″/2), periodic additionally−αv′. Same CAR source has positive OS histories, Euclidean gap clustering and SF+1. Correction25Oct: a compatible local image suffices for the boundary mechanism; a global W is a stronger full-presentation equivalence test.",
      "scopeEN": "Actual P1 image with collar domains/relative action remains open; diagnostic zeta reference does not replace Dref. New paper audit explicitly corrects the earlier global-W requirement. Profiles/strengths remain intervention data.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:declared-p1-p2"
      ],
      "attemptIds": [
        "contract:native-octic-seam-origin-20261025",
        "contract:paper-source-reconstruction-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:be81e5ec75e57cf4e18cd1aa",
        "source:69d937d054c2805a0442233a",
        "source:99ebc62c0e2789b54bd45265",
        "source:13162607e3ce1f3d388a33eb",
        "source:970d138a6d4a43d092e93cd4",
        "source:a0a02c8724ef5d21a8a66f63",
        "source:17eb50b8cbc171310fc470fd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-root-ope-has-normalized-native-octic-component",
      "titleEN": "Full root product contains the normalized octic component",
      "statementEN": "In the supplied E8 vertex closure, the phase-correct dual-root product has a full weight8 coefficient S8 with all22 oscillator partitions. Exactly <F8hat,S8>=sqrt140/56=sqrt35/28 and ||S8||²=15600. Actual polarization gives moments2,4,6 zero and moment8=(15/2)I8.",
      "scopeEN": "Assumes the additional full E8 algebra; no exclusivity, executed projection or physical preparation. The classical invariant identity is not claimed as new. This extension is unnecessary for the original CAR mechanism.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:original-displayed-j-equivariant-cartan-root-isometry"
      ],
      "attemptIds": [
        "contract:native-octic-seam-origin-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:395b95a0e6b14380dbdefc6c",
        "source:72429b7e1be81f9b075dd7f6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:paper-microscopic-car-composes-with-native-octic-ward",
      "titleEN": "Existing microscopic CAR theorem closes the neutral octic Ward interface",
      "statementEN": "The original QWZ field/state/time theorem composes with the unitary fold of that same channel and fixed A=U+^T O^T M. Direct CAR gives KΩ=Σδ_k h_(k,-1)Ω and [K,h_(k,-n)]=n h_(k,-n-1), K=Lcal_-8/8. The neutral source-energy64 amplitude is sqrt35(16250979+56071008i)/128≠0.",
      "scopeEN": "Fixed original QWZ regulator and fold dictionary; no eight new source copies or E8 spinor field required. N≥4096 contains the whole E≤64 comparison sector. No pure preparation, P1 image or 3+1D derivation. Historical suite with stale pin is not reported passed.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-microscopic-qwz-integer-car-edge-limit",
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "attemptIds": [
        "contract:paper-source-reconstruction-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5108b907082fe61904b9d4ca",
        "source:a614cc47888fed7cd5be7eee",
        "source:f0a047be695a92dd82b09571",
        "source:fb7604c3a4946b0f29497ac4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:microscopic-neutral-octic-has-controlled-smeared-limit",
      "titleEN": "Neutral octic and adjoint have a controlled microscopic smeared limit",
      "statementEN": "On every actual positive source-energy cutoff, ||F8_m P_E||≤C(1+E+|m|)^11. Smooth mode sums converge absolutely and field/adjoint are closable. Global E-independent CAR approximants give N→∞ before mode-cutoff removal. The local route with the SAME Wick polynomial/counterterms gives N→∞, then separate field mollifier removal, then point-split removal.",
      "scopeEN": "The full energy contains Hosc+Σ(q²/2+δq)≥Hosc+Σq²/32, so P_E is finite dimensional. P_E is a comparison projection, not executed. Local regulators retain the eight arcs. No simultaneous diagonal UV limit, bounded point field or complete stress-unitary limit.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-microscopic-qwz-integer-car-edge-limit",
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "attemptIds": [
        "contract:paper-source-reconstruction-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:224dc6efc9398c17a1d02c45",
        "source:48a8402676deb1c5d929f946",
        "source:23402f5a13d47af8632c9007",
        "source:97ae711f063a5a961209bc65",
        "source:85e3bac592bf00b481494e1c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:paper-seed-source-needs-local-image-not-global-equivalence",
      "titleEN": "Original paper allows a local boundary image and does not prove full source rigidity",
      "statementEN": "Seedop requires complete local data; global unitary intertwiners are morphisms, not object-membership conditions. A state/time/reflection covariant local star monomorphism induces an OS isometry onto its cyclic image. QWZ parameters may be regulator coordinates once that source comparison holds. v464 tests a chosen sin(k) chain, not a classification of original Dcoll from SF1.",
      "scopeEN": "Actual local image, elliptic collar domains and finite relative action remain open. SF/APS/Quillen do not replace the operator comparison. One-particle K and many-body H remain distinct. The old global-W test survives only as a sufficient full-presentation equivalence test.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:declared-p1-p2"
      ],
      "attemptIds": [
        "contract:paper-source-reconstruction-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a0a02c8724ef5d21a8a66f63",
        "source:17eb50b8cbc171310fc470fd",
        "source:255991a12c0720e3dfb7b359",
        "source:ae7495ef419938987ba3c501",
        "source:a9e0479abeec3c6a6739d295",
        "source:9c357e73469f6f6cbe5c4626"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-car-positive-time-forces-source-vacuum",
      "titleEN": "Full CAR and the same positive time force the source vacuum",
      "statementEN": "For FULL CAR, antilinear a(f), same Bogoliubov time with gapped K and H≥0,HΩ=0, one gets a(P+f)Ω=0 and a(P−f)*Ω=0. CAR forces P−=1_(K<0), gauge invariance and Wick. After this operator/time identification, the quasifree vacuum is not an independent premise.",
      "scopeEN": "Conditional on the full odd-CAR image in the same OS representation and time. Even CAR alone is insufficient: one-mode CAR_even=C⊕C has trivial dynamics and arbitrary ground-state occupation. The reduction does not construct the missing P1 image.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:full-graded-car-with-original-positive-time",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions"
      ],
      "attemptIds": [
        "contract:paper-source-reconstruction-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:75e8260aa0dd042d49813333",
        "source:66c658f0f385ed1b4304a791"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-winding-theorem-does-not-select-seam-ray",
      "titleEN": "Original winding statement does not construct the subsequently named seam line",
      "statementEN": "The archived primitive seam theorem supplies a K1 class and stated spectral flow but no eigenvector or rank projector. EM subsequently calls psi_Sigma selected by it. For PuP, S*S=P-Pu*(1-P)uP; index -1 gives rank one only with further operator conditions. Exact countercontrols retain the same index; a smooth orientation-preserving circle symbol with the same winding and quarter offset has leakage 15/4096.",
      "scopeEN": "Source audit of the specified original step and mathematical countercontrol. Not two complete P1 models or a general no-go. The separate Calderon repair remains conditional on zero leakage and the same index.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-seam-pair-and-full-moment-os-statements"
      ],
      "attemptIds": [
        "contract:primitive-seam-operator-reconstruction-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:14a6379bf83a02bde5dcb691",
        "source:7589bb4e3dd762ee4cb81e4b",
        "source:115e9d6aab1278cf4f87df7a",
        "source:c2180b69a7386c00d46a7fe0",
        "source:5c61437cd63469d035e8172f",
        "source:9f67301df027819f385648b7",
        "source:d3c2e9d2b03451ca2d0ef673",
        "source:89f7775090fe1302c613ef0a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel",
      "titleEN": "The same B,u pair conditionally reconstructs the entire channel and canonical seam line",
      "statementEN": "Strong covariance and actual index -1 make S=P_BuP_B isometric and Pi=P_B-uP_Bu*=1_(0,1](B) rank one. Spectral bands u^n Pi u^-n sum strongly to I; on all H one gets basis u^n psi and B=-i partial_theta+epsilon with H1 domain and 0<epsilon<1. Actual monodromy i fixes epsilon=1/4. No external Hardy space or new source is chosen.",
      "scopeEN": "Complete infinite-dimensional theorem within the explicit operator hypotheses, independently reviewed. Original B_Sigma/u_Sigma time and index identification remains open; coordinate arcs are not spacetime localization. Additional phase, CAR quantization and the original source functional do not follow from index one.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:strong-seam-covariance-and-same-pair-index"
      ],
      "attemptIds": [
        "contract:primitive-seam-operator-reconstruction-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9f67301df027819f385648b7",
        "source:d3c2e9d2b03451ca2d0ef673",
        "source:1784ffd7a8b89bb6db5b34a6",
        "source:a013c6d716bdbe839f1e7568"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-os-step-needs-full-moments-not-connected-cumulants",
      "titleEN": "OS step requires full moments rather than connected cumulants",
      "statementEN": "Archived sources define S_n^T=delta^n log Z and use it directly as the full OS family. An RP Gaussian functional gives full Gram determinant 2c²>0 for 1,X², but cumulant replacement gives -a²<0. Repair: Z/Z0=exp W and the full graded moment-cumulant expansion, followed by RP on all reflected words. A unital graded reflection/time compatible word map preserving the full functional induces an OS isometry.",
      "scopeEN": "Exact counterexample and mathematical repair of the specified OS step. The original full Z_adm and its boundary word transport are not thereby constructed. Uniform growth and symmetric contraction time hypotheses must actually hold for full reconstruction.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-seam-pair-and-full-moment-os-statements"
      ],
      "attemptIds": [
        "contract:primitive-seam-operator-reconstruction-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5f68beab2336e69cb6e05eb6",
        "source:3773e2df55f804d81286a192",
        "source:80ebe48a5da95a61ff8dbcad",
        "source:a7e841d5fe8f267135a523ff",
        "source:89f7775090fe1302c613ef0a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:graded-field-image-precedes-physical-observable-restriction",
      "titleEN": "Graded field image precedes admissible observable restriction",
      "statementEN": "Original OS/CAR reconstruction concerns graded fields; A_adm instead restricts operators and their adjoints preserving the admissible space. Odd charged CAR fields therefore need not themselves lie in A_adm. Neither P_C=P_B nor an antiunitary P_C complement relation is a general requirement for complex CAR. Active modular closure induces D_rel from already supplied C_Sigma, which does not derive C_Sigma in reverse.",
      "scopeEN": "Typing correction of the required original interface. No assertion that the original full fermion/boson functional has been constructed; reviewed passages assume it. The existing full-CAR ground-state reduction remains conditional and unchanged.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-seam-pair-and-full-moment-os-statements",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions"
      ],
      "attemptIds": [
        "contract:primitive-seam-operator-reconstruction-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:748b7940e88d21a0f908d8c7",
        "source:986cf4d8dfadc1e70b10e5b5",
        "source:55b11f2500858ef542c732b6",
        "source:b2e5cc82888fa744942ad173",
        "source:80ebe48a5da95a61ff8dbcad",
        "source:a7e841d5fe8f267135a523ff",
        "source:9f67301df027819f385648b7",
        "source:d3c2e9d2b03451ca2d0ef673"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:older-original-circle-representative-already-realizes-ward-and-index",
      "titleEN": "Older concrete circle representative already realizes Ward covariance and index pairing",
      "statementEN": "fullv21 already contains concrete twisted circle domains, D_Gamma and u=exp(i theta). Its printed positive eigenvalues belong to B=-D_Gamma=-i partial_theta. After this common orientation repair, strong covariance, SF+1, index -1 and Pi=|psi0><psi0| are exactly realized for every fixed interior twist. The recent abstract operator construction need not be reinvented on this older representative.",
      "scopeEN": "Explicitly supplied older one-particle representative, not reconstruction from the later operational seed. Zero endpoints require a convention. M_z is not an involution; sheet exchange and clutching differ. Quarter phase, physical time, actual EM projector and later B_Sigma identification do not yet follow.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "attemptIds": [
        "contract:older-paper-source-recovery-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c16376818e95bd565a31d2aa",
        "source:817c7fdd68d4bd6989b874f3",
        "source:fe6c9765e34de6e777d43682",
        "source:e83c65f7417c484e475b56d3",
        "source:a313752b66179d423382bf6f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:old-quarter-heat-transfer-has-controlled-rank-one-limit-and-odd-product",
      "titleEN": "Old quarter-circle heat transfer has a controlled rank-one limit and full odd product",
      "statementEN": "On both original quarter circles |B_a| has simple energies(2m+1)/4. R_t=e^(t/4)exp(-t|B_a|) has eigenvalues1,r,r²,... and ||R_t-Pgap||_1=r/(1-r),r=e^-t/2. Thus det(I-Q R_t)→1-Q with explicit log-error bound. At finite q=e^-t/4, det(I-T_t)=prod_m(1-q^(2m+1)). Full opening qD(q)^(-5/4) first differs by5q^4/4 from q(1-q)^(-5/4). An odd-divisor recurrence fixes all coefficients.",
      "scopeEN": "Infinite-dimensional analytic proof and independent review, exact coefficient control through degree20 normal/-OO. No free psi line; ground-normalized limit is not yet the original physical EM prescription. Full finite transfer is not rank one. q_heat versusq_EM and source/trace/original time remain distinct; no new alpha prediction.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-quarter-circle-full-heat-transfer-comparison",
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "attemptIds": [
        "contract:older-paper-source-recovery-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f7a643ced62d0ac16465871b",
        "source:f5ec7eaf0f85d822809e80c0",
        "source:fe6c9765e34de6e777d43682",
        "source:e83c65f7417c484e475b56d3",
        "source:a313752b66179d423382bf6f",
        "source:2361212303ee140fc632f740"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:historical-em-rank-one-and-full-heat-traces-have-different-contracts",
      "titleEN": "Historical EM single-mode expression and full heat transfer have different spectral contracts",
      "statementEN": "fullv21 EM response uses scalar defect-sector weights with J1=1. v31 defines full heat transfer and its cosmological companion assumes lowest multiplicity48; v32 calls the route a future conjecture. v42 uses ordinary admissible eigenvalue traces and treats rank one as extra. The later1-q is not already the exact full finite heat determinant.",
      "scopeEN": "Source-reviewed version chain with distinct sectors. Not exclusion of every common underlying source; multiplicity48 cosmology and a scalar EM branch cannot be identified without the actual projection.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "attemptIds": [
        "contract:older-paper-source-recovery-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c720ea9584c4885f3ca8025d",
        "source:b2a85f708a14a77185389e81",
        "source:622c204f9932fb157429a329",
        "source:52736b18790c2780cc73eeb4",
        "source:d2d4cba8adf919447d83cf0e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:older-frg-functional-already-supplies-formal-full-moment-parent",
      "titleEN": "Older FRG functional already supplies a formal full-moment generator",
      "statementEN": "v42 defines exp(W_k[J]) as a regulated functional integral and gives the Hessian propagator. Formal full moments follow by differentiating exp(W_k[J]-W_k[0]); no new general Z template is required. STr permits collective graded field/source notation, so missing separate eta symbols do not prove exclusion. Concrete graded action/measure, seam map and joint RP are not established there. Direct OS use of expressly truncated cumulants still needs correction.",
      "scopeEN": "Recovered formal definition, not an existence proof of an infinite mixed measure. Full moments, symmetric positive time and uniform OS growth remain actual requirements; no specific source notation is mandatory.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:original-seam-pair-and-full-moment-os-statements"
      ],
      "attemptIds": [
        "contract:older-paper-source-recovery-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0f0877c5b4346959c8f074a7",
        "source:15ba296fa366878a2b8513c9",
        "source:2806246b98151c76a1838191",
        "source:52c9d27c5cb91531d9ba32e7",
        "source:e98836a0fff57c2525b15eef",
        "source:003e51077702db1f91183558"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:earliest-c3-route-quantizes-level-but-needs-physical-kinetic-normalization",
      "titleEN": "Earliest c3 route quantizes a level and needs physical kinetic normalization",
      "statementEN": "V1.06 chooses M4×Y7 with integral forms, quantizes g_top=n/(8pi²) under printed period/flux conventions, then defines g_top=8c3². n1 and positive root yield1/(8pi). Canonical fields instead give coefficient n g4²/(8pi² F_a), before trace/embedding factors; the kinetic integrals are not supplied there. For dynamical a, dC also contains da∧omega3 and local CS reduction has mixed terms.",
      "scopeEN": "Historical source audit of a best-effort PDF extraction, not a new derivation or numerical change of P1. First geometry choiceY7/forms, n1 selection and c3 parametrization remain explicit. Local factor3 modulo derivative is not a global c3 correction; global patch data and da0 special case are separate.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:declared-p1-p2"
      ],
      "attemptIds": [
        "contract:older-paper-source-recovery-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2f212594e1c9649410225383",
        "source:e03bc91e4844928284334f01",
        "source:6126477372ec74fb452d7cbe",
        "source:02afee48920c75d10b680bf8",
        "source:7d24cd9d15a12d61f52619eb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:canonical-positive-circle-half-selects-the-toeplitz-line-and-sixth-order-correction",
      "titleEN": "Positive half of the old circle selects the same defect line and first differs at sixth order",
      "statementEN": "For canonical P+=1_(0,infinity)(B_a), exp(ta)P+exp(-t|B_a|)P+ on P+H has eigenvalues1,s,s²,...,s=e^-t. For every0<a<1 its limit is exactly the Toeplitz defect Pi with trace-norm error s/(1-s). At a1/4 D_full=D_+D_- with exponents1 and3 modulo4. Opening qD_+^(-5/4) first differs by5q^6/4 from the single-mode form; the full q^4 term comes from the negative q^3 mode.",
      "scopeEN": "Analytic consequence on the supplied old circle, independently reviewed. Zero block outside P+H adds no trace norm or Fredholm contribution. P_adm=P+, EM parameter, exponent5/4, physical time and state identification are not derived by compression. Orders4 and6 concern different traces and are conditional diagnostics, not an alpha prediction.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "attemptIds": [
        "contract:older-paper-source-recovery-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a45e2029d50fbd5438428cf3",
        "source:6d2d6c1a6e715f675e3250ad",
        "source:3b5e8ce447418c51a6d636f2",
        "source:2361212303ee140fc632f740"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:old-seam-shift-canonically-gives-relative-car-line-and-fredholm-factor",
      "titleEN": "Old seam shift gives a direct CAR defect line and relative Fredholm factor",
      "statementEN": "On the old circle uP-u*-P-=Pi0 and [u,P-] has rank1. Under the same full CAR and positive time the existing SOURCE W1 is this mode shift: UOmega~c0*Omega with energy a. Directed relative Fredholm determinant det[(I-z(C+Pi))(I-zC)^-1]=1-z gives the exact minimal factor without a heat limit. Full finite-word responses follow from a rank1 update of existing Wick determinants.",
      "scopeEN": "One-particle identity is exact on the given old representative. Fock statements need the actual full CAR/time image; then no free state choice. SOURCE W1 is reused, not novel. Pi and Fock density are related by explicit isometry Vf=c(f)*Omega, not identified. Neutral full words U*AU need no individually neutral U observable. Scalar matching proves no physical permission,locality or EM-response identity.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:full-graded-car-with-original-positive-time"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ba664f1241d0ad63679209f2",
        "source:d1c41fb4b9c7289563d56e56",
        "source:ac37e52c68cdc1272327583c",
        "source:65cc134694fcc95b5253d7b2",
        "source:7eac7e134f04fbab80096219"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:old-index-coupling-removes-heat-map-and-has-sharp-residual-ward-test",
      "titleEN": "Old index coupling replaces heat matching and has a sharp residual Ward test",
      "statementEN": "fullv27/v28 already contain J=d SF and give q=delta_top e^-2alpha for d2,SF1 under their relative defect contract. For complete sectors q=e^-alpha*d*s R(alpha),R=Z_s^0/Z0^0 exactly. Fixed prefactor holds precisely for constant R, differentiably equivalent to partial_alpha logR=0 throughout the interval. With fixed measures this is the difference of residual action responses; moving measures add score terms.",
      "scopeEN": "No new identification J=E,Q,N or Q². No q_heat=q_EM needed on the direct defect route. Intended old pure relative reweighting is exact with fixed residual normalization. Positive diagnostic Zdef=e^-2alpha,Ztriv=e^-alpha shows only the omitted condition in the generally read lemma,not a TFPT countermodel. SF normalization and original positive orientation remain.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:historical-sf-sector-action-and-relative-normalization"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2467d309877acdd144cbba2f",
        "source:5ee0b7ab81dd45152f348fbb",
        "source:ef177cf489a7ad4e2e40ec2e",
        "source:c9fdc6ce09e1ade5fa71f61c",
        "source:ba664f1241d0ad63679209f2",
        "source:d1c41fb4b9c7289563d56e56"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-admissibility-requires-image-membership-not-positive-half-or-commutation",
      "titleEN": "Original admissibility needs image membership rather than a positive half or mere commutation",
      "statementEN": "Original later P_adm is primitive seam/Cauchy and gap selection with color and determinant upgrades. It is neither P+(B_a) nor the rank1 EM projector. Historical u=M_z is clutching,not already a local observable. Actual line membership is P_adm R0=R0; commutation alone is insufficient. An original local or reducing image isometry suffices; global Hilbert equivalence is unnecessary.",
      "scopeEN": "Source-reviewed definitions and necessary image test,not a new proof of all original analytic reconstruction theorems. Failure of u* invariance for P+ excludes only an additional claim that u belongs to the same admissible star algebra; membership is not assumed. Odd fields and complete neutral response words remain distinct.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:original-admissibility-and-graded-source-interfaces"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f4d3d5a35d2087e635692f84",
        "source:c248c8f2e2e1068ad40a072e",
        "source:a0069d06826d9a1ef9bc6137",
        "source:dc9bef847d1f56efdf2faa62",
        "source:a38642efdd7cb8c4f5e56ac2",
        "source:ba664f1241d0ad63679209f2",
        "source:d1c41fb4b9c7289563d56e56"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:old-closure-already-assumes-car-but-does-not-map-the-geometric-circle",
      "titleEN": "Old closure already assumes a CAR kernel without identifying the geometric circle",
      "statementEN": "fullv21 supplies the geometric one-particle circle; v31 closure assumes an RP CAR kernel and v42 has exp(W_k[J]) as a formal full parent integral. Existence under those hypotheses need not be rederived from B. Actual local mode map,time/reflection and the same coupled action/measure contract do not follow. The master functional already contains a separate eta asymmetry term; only its squared determinant alone is sign blind.",
      "scopeEN": "Targeted v21/31/32/42 source review,not absence across every future text. Spectral action,positive geometric marginal and full graded source remain typed. No mandatory separate eta source notation or universal exclusion of other bosonic contours. Actual full CAR/positive-time image already forces the free sea.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:original-admissibility-and-graded-source-interfaces"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:65f400d85da17f18671b1e87",
        "source:4382961f2212f553f575f07f",
        "source:0f0877c5b4346959c8f074a7",
        "source:6349b7a427ed5cd82b53c04d",
        "source:ad4d497e6c55ede3cb76d60f",
        "source:96057e613162b6d9a652e231",
        "source:7022e323eec3726e8ca013b9",
        "source:bb612f2c195f2f7dc688b99d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:historical-uv-map-infinite-mass-exclusion-already-proved-and-recovered",
      "titleEN": "Historical UV-map exclusion was already proved and is recovered",
      "statementEN": "The original2026-10-13 audit already proves d(Tnu)/dt>=m*nu(total)/∫psi dnu>0,so output mass is infinite. Printed T is not an endomorphism of the asserted finite-measure cone and supplies no fixed point there. Current independent review confirms the same v42/tfpt45 wording. Positivity alone also does not preserve the moment slice.",
      "scopeEN": "Reuse of an existing exact source audit,not a new discovery or an all-TFPT/all-RG exclusion. A corrected original kernel needs at least integrability and actual moment preservation; no replacement kernel is chosen. Atlas navigation had exposed the old registered contract as pending rather than a curated conclusion.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:literal-positive-rg-map-on-finite-halfline-measures"
      ],
      "attemptIds": [
        "contract:original-source-functional-audit-20261013",
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:55b7e77193e5105e274b8e6e",
        "source:3d17021733a29cb6cdd707d6",
        "source:8672351679bca19425697630",
        "source:276ab24497c5635e883b929a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:a4-spin-lift-fixes-local-ns-and-unordered-quarter-pair",
      "titleEN": "A4 spin lift fixes local NS and the unordered quarter pair",
      "statementEN": "A4 requires the order-four lift of the same Moebius identification. The double-cover core loop is its square,so spin holonomy r²=-I gives NS. Both Pin-minus lifts r,-r and the base sign twist have the same cover holonomy. Full combined cJ_perp gives spin-reference phases{1/4,3/4}. The tentative R twist on the cover preserved only thin A2/A3 and violated A4; it is not a countermodel to the full original.",
      "scopeEN": "Local spin contribution in the original Moebius geometry; no choice of extra U1 Wilson holonomy,single quarter CAR channel or physical OS time. Not identity with separate P2 clock.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-a4-same-moebius-order-four-pin-lift",
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "attemptIds": [
        "contract:canonical-seam-fermionization-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:fa230915a3276c53bfdf7dae",
        "source:f6153693ab0949e80a906f61",
        "source:4f25eb0eba60fb62774fe34a",
        "source:da88031655d7917665ad3270"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:cover-winding-exchanges-quarter-sectors-before-its-square",
      "titleEN": "Primitive cover winding exchanges the quarter sectors",
      "statementEN": "Exact unitary Fourier decomposition including H1 domains: B_cov=2(B1/4⊕B3/4),T_pi=diag(i,-i),u_cov=[[0,u_base],[I,0]],u_cov²=diag(u_base,u_base). SF is1 and2=1+1; compressed Toeplitz index is-1 and-2. Full NS reference circle a=1/2 suffices for the prior relative EM line factor without extra quarter selector. In the descended Pinor space scalar u_cov changes lift c to-c at fixed J_perp.",
      "scopeEN": "Longitudinal spin-reference core; actual transverse boundary-kernel selection and original per-sheet operator map are not inferred from the index sum.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-a4-same-moebius-order-four-pin-lift",
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "attemptIds": [
        "contract:canonical-seam-fermionization-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4f25eb0eba60fb62774fe34a",
        "source:e86e26018a6d4ca961673d1a",
        "source:da88031655d7917665ad3270",
        "source:edc2bc84457e7e0ee5ff18f1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:retained-winding-preserves-local-support-and-neutral-time",
      "titleEN": "Retained winding preserves local support and neutral time",
      "statementEN": "For u=M_z,AdW1 preserves each original CAR interval. Exactly tau_t AdW1=gamma_t AdW1 tau_t; on the source U1 charge-zero net it commutes with given time. W1*QW1=Q+1,W1*HW1=H+Q+a,W1*J(f)W1=J(f)+fbar. Neutral current response and rank1 defect remain visible; old bounded Cartan four-word is not projected away.",
      "scopeEN": "Supplied full CAR and positive time; source U1 neutrality is neither the whole parity-even algebra nor physical EM/hypercharge identification. W1 remains global charged transport,not a claimed local individual element.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:full-graded-car-with-original-positive-time",
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "attemptIds": [
        "contract:canonical-seam-fermionization-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e125bba39cfa3e85a994135a",
        "source:c7c5ea590d1c7d6922e5a66c",
        "source:e5e9894a6aa10ccb7e9c00e4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:marked-glue-square-is-the-e8-fermionization-character",
      "titleEN": "Marked glue square is the E8 fermionization character",
      "statementEN": "The marked Z4 glue character squared fixes grades0+2 with52+60=112 D8 roots and negates grades1+3 with64+64=128 spinor roots. At lattice level K union(K+2g)=D8. Thus the non-anomalous E8 to D8 Z2 action of standard fermionization is already in the original marked glue.",
      "scopeEN": "Exact charged-root action in the marked compiler frame. Does not identify geometric deck involution,CAR parity or gauging of a physical source.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-marked-glue-and-retained-source-d8-frame"
      ],
      "attemptIds": [
        "contract:canonical-seam-fermionization-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ff101a72dcda96d8fb70e9b9",
        "source:f6153693ab0949e80a906f61",
        "source:2e3478c9960e4bd8e7a78f1e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-canonical-d8-is-not-transported-source-d8",
      "titleEN": "Fixed canonical D8 is not transported source D8",
      "statementEN": "With O/M held simultaneously fixed,canonical compiler D8 and D8_F=M(D8_CAR) each have112 roots but share only48 with64 exclusive each. Charged Z2 signs differ on128 E8 roots; actual quarter-time phase multisets differ. Identity of these marked subsystems is false.",
      "scopeEN": "Only fixed relative identity excluded. Common Weyl transport remains a valid coordinate change; affine connection works in actual D8_F without equality. Previously known extra zero-energy line is not counted as new discovery.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-marked-glue-and-retained-source-d8-frame"
      ],
      "attemptIds": [
        "contract:canonical-seam-fermionization-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9aca508a4dcd3b920f5d5470",
        "source:30f97dba0703e1250f4b4587",
        "source:66b5bf2798ae5368c2ec5683",
        "source:de68a2e162fae14c8891976f",
        "source:1cd18291e9db1fccd9767b5a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-winding-has-four-module-e8-defect-extension",
      "titleEN": "Actual winding has a complete four-module E8 defect extension",
      "statementEN": "On supplied four-module AIA parent p=n+c0s,W_ext=E_e0 Rhat gives the exact old NS winding with CAR Klein factors and compatible E8 cocycle restriction. It swaps0↔v,s↔c,preservesNS0+v/Rs+c and mapsE8 0+s to twistedv+c. For all integer/half-integer p,K_delta(Rp+e0)-K_delta(p)=(Q+a)/8 and W_ext*HW_ext=H+Q+a; M transports every datum together. Li Delta gives the associated inner-twisted field functor.",
      "scopeEN": "Complete finite-energy operator and formal punctured AIA/VOA field transport on supplied parent. Not ordinary local odd embedding or a bounded localized endpoint in the physical OS net. Parent and physical source are not identified from P1.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:standard-four-d8-module-parent-with-retained-subtheories",
        "premise:fixed-marked-glue-and-retained-source-d8-frame",
        "premise:full-graded-car-with-original-positive-time"
      ],
      "attemptIds": [
        "contract:canonical-seam-fermionization-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:fc019ac4856e124bedb6de4d",
        "source:57cc1c34adbd507f4f0d9f74",
        "source:32cfbd9bd6d510ad287b67b7",
        "source:9f48de5ac53ccef4fe5d0791",
        "source:2d56e56a5496ec40ee39ea8f",
        "source:f9af229e9891846961b288f3",
        "source:3d82c1bf9478f30be1651019"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:ramond-lift-sign-is-common-intertwiner-basis-gauge",
      "titleEN": "Ramond lift sign is common intertwiner-basis gauge",
      "statementEN": "The two extensions kappa=±i are equivalent by U_tau|n+c0s>=(-1)^(c0Qn)|n+c0s>. U_tau is pointwiseI on both supplied0+v and0+s,sendsW_kappa toW_-kappa and transports X=E_s onlyonv↔c. With additional fixedX,W_kappa XW_kappa*X*=(-i kappa)I; under full transport the word is unchanged. No independent physical kappa parameter. Geometric Cartanlift(+,+,-,-) and standard defect(+,-,-,+) are different operators despite agreeing onE8 0+s.",
      "scopeEN": "Common completion up to intertwiner basis; an independently original-marked mixed junction would be stronger input. No identification of physical clock operators or localized spinor vertex with global charge shiftX.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:standard-four-d8-module-parent-with-retained-subtheories"
      ],
      "attemptIds": [
        "contract:canonical-seam-fermionization-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d6b4b00d291086b6d8e36c67",
        "source:687b1dac4b5f95a8c0c441e4",
        "source:836de075deccb8519ab4c119"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class",
      "titleEN": "Old seam factor remains exact in faithful KMS polarization class",
      "statementEN": "Trace-class C-P implies det_F[(I-z uCu*)(I-zC)^-1]=1-z on|z|<1 by exact three-factor cancellation; u^m gives(1-z)^m. C_beta is faithful with trace-class C_beta-P and h(C_beta)=beta B_a on DomB_a. D_beta is positive trace class,infinite rank and trace1; its product telescopes at every finite beta. Full A4 NS cover winding gives1-z,its square(1-z)^2 without a single-quarter choice.",
      "scopeEN": "Proved operator persistence on the same circle,no fitted thermal scale or limit. Physical seam kernel,time,OS and EM readout still need identification. No full-E8 quasifree state.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:same-original-circle-trace-class-covariance"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ec9e14b9ff9dc9923215d61a",
        "source:e8a875d33b32c78219c109bb",
        "source:1042e04c218b1e449165b25a",
        "source:4d463944dba563e6d0bd6adc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor",
      "titleEN": "Finite circle compression cannot retain the whole thermal factor",
      "statementEN": "For pure C=P the compressed relative determinant is1-z<v,(I-zC_F)^-1v>,v=Fpsi0. It equals1-z on an open set iff psi0 lies in RanF,forcing endpoint eigenvalues0/1 and singular log odds. For C_beta,D_beta>0,TrD_beta=1 and Tr(FD_betaF)<1 for every finiteF. Already its derivative at0=-Tr(FD_betaF)>-1 rules out1-z.",
      "scopeEN": "Only naive finite-rank compression on the same circle. Not exclusion of the entire carrier program,infinite spacetime fibers with finite internal index,or another justified original source map.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:same-original-circle-trace-class-covariance",
        "premise:existing-finite-orthogonal-carrier-on-same-source"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1e6789865348ba36e9c05819",
        "source:3dba1f5a55731c5757e11de1",
        "source:cd46991ef798790ffb4db31d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:schur-carrier-plus-complement-preserves-original-relative-determinant",
      "titleEN": "Schur transport with carrier and complement preserves the relative determinant",
      "statementEN": "For A=I-zC,A'=I-z uCu*,Q=I-F,QQ and Schur blocks are invertible on|z|<1. Exactly1-z=det(S'_F S_F^-1)det_F(A'_QQ A_QQ^-1),with S_F=I_F-zC_F-z²C_FQ(I_Q-zC_QQ)^-1C_QF. Unipotent factors are finite rank with determinant1; the QQ difference is trace class. The complement comes from the same supplied source.",
      "scopeEN": "Sufficient exact operator transport once actualF and source intertwiner are supplied. Does not construct an unknown physicalF,infer autonomous carrier time,or assume multiplicativity of arbitrary separate zeta determinants.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:same-original-circle-trace-class-covariance",
        "premise:existing-finite-orthogonal-carrier-on-same-source"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:411120cbda538239f28969b7",
        "source:f9cac57a5ac6adf6ca4739a2",
        "source:24e972115f307b89fccef322",
        "source:9115f585fe3c788056b4c172"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:v258-forward-source-gap-is-reused-not-solved-by-inversion",
      "titleEN": "v258 forward-source gap is reused rather than closed by inversion",
      "statementEN": "v258 starts from supplied Dirac/Yukawa/Majorana data,computes Fermi C_F and inverts. P_F and C_Sigma are not computed inputs; physical compression is check(...,True). The September provenance audit already established this and is reused. Without T:H_circle→H_Sigma and carrier isometryV_F,P_F Pi P_F is untyped; with them the update is|V_F*Tpsi><V_F*Tpsi|. Finite strict-domain criterion:<v,(I-C_F)^-1v><1.",
      "scopeEN": "Source-reviewed reuse,not a new nonderivability theorem. Valid KMS/log-odds inversion is retained and does not prove forward origin.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:original-admissibility-and-graded-source-interfaces",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:57d11a463f3d1c56b88eeddf",
        "source:527f48ca37ebc72416ec8e8b",
        "source:5d52ec597926c790dd39c828",
        "source:579330e91b928b5c50cef8ad",
        "source:b2e5cc82888fa744942ad173"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:one-sided-source-and-real-em-norm-need-response-map-not-chiral-phase",
      "titleEN": "One-sided source and real EM norm need the actual response map",
      "statementEN": "v42 starts one-sided and defines one minimal EM transfer; it prescribes no full inverse physical pair trace. For the actual assumed inverse covariance pair,ordinary determinant and norm equal1;a Quillen square root changes nothing. Phase cancellation does not disprove real Dirac EM susceptibility. tr_adm on H_adm⊂H_OS is not identified with a collar-face marginal. Infinite-rank thermal jump and rank-oneU_min share only a determinant; source-functional equality is still required. Relative EM comparison needs(1-q(alpha))/(1-q(alpha_*)),sinceq(0)=delta_top≠0.",
      "scopeEN": "Type and reference control within the reviewed originals. No extra chiral measure as a general EM prerequisite,no physical marginal identity from the one-sided name alone,and no completed fermionic measure.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:original-admissibility-and-graded-source-interfaces",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1b0a94b369bf77c9bc6ee368",
        "source:2197fccbe166f721b9c4813a",
        "source:64f8c5aaf35adeee8f108694",
        "source:6c31104a97e0a5a4aaccbb86",
        "source:1624cad630678ebf27e3c14f",
        "source:bfebbfaf79f2c302a2ae2155",
        "source:9659b062d98af1fe00d523cc",
        "source:1703ffcd270e20f3b3640f0c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:trace-class-pair-index-fixes-relative-factor-without-primitive-ray",
      "titleEN": "Pair index fixes relative factor without a primitive rank-one ray",
      "statementEN": "Orthogonal P,Q with Q-P in L1 and k=Tr(Q-P) obey det_F[(I-zQ)(I-zP)^-1]=(1-z)^k on|z|<1. Exactly R_prime R^-1=(I-zQ)(P-Q)/(1-z)(I-zQ)^-1. For Q=UPU* and any positive contraction C with C-P in L1,three-factor cancellation yields the same factor. Pair index therefore suffices even for indefinite or infinite-rank defects; this scalar response needs no preferred ray.",
      "scopeEN": "Extension of the existing fixed-shift theorem,no new general index mathematics. Ordinary relative Fredholm determinant on the same space; no selected physical kernel,transfer spectrum,5/4 index or EM Ward derivation.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:trace-class-polarization-pair-with-restricted-unitary",
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c793581086682a49e1c04ece",
        "source:539d8815a0a34a57cc3df6d1",
        "source:e6aa81815d1874d6df54d3f4",
        "source:a6c5c56b05837b4e42355678"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:matrix-clutch-degree-connects-weak-determinant-class-without-ray-selector",
      "titleEN": "Weak determinant class carries index one independently of internal rank",
      "statementEN": "On the negative vector Fourier sea Q-P is trace class and Tr(Q-P)=sum_j j tr(g_j* g_j)=wind detg for smooth g. Thus det_rel=(1-z)^(wind detg). uI_r has indexr,while an actual degree-one U2 clutch has indexone. Originals v31/v32/v42 already contain the weak degree-one line and its assignment to total seam twist. S(U3×U2) is a fiber stabilizer and does not force a globally trivial determinant line. A common realization on the same source covariance therefore yields1-z without a rank-one choice.",
      "scopeEN": "Analytic matrix-index theorem proved; original class is reused as a branch statement,not newly derived from P1/P2. Normal S2 clutch equator is not automatically the tangential field-source circle. Ordinary admissible EM trace and relative pair response still require an original intertwiner.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:trace-class-polarization-pair-with-restricted-unitary",
        "premise:smooth-matrix-clutch-on-original-negative-fourier-sea",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:900fad547c72289277c77c29",
        "source:c5ed3844208c82ca7363fffd",
        "source:73edb3328eddc35d394011ea",
        "source:fe3ee0dbc105f391f94a821a",
        "source:9d315d3c56588e1a024b7f4a",
        "source:df76b28cdce90ab5cec928a9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index",
      "titleEN": "Finite NS circle contains a UV partner and gives no determinant limit1-z",
      "statementEN": "Sampling original M_z gives exactly the diagonal site phase and the cyclic shift in the actual v519 NS Fourier window. Negative sea obeys U_N P_N U_N*=P_N+Pi0-Pi_-M. Hence the complete ordinary finite relative determinant equals1 for everyN. Pi_-M escapes strongly but retains trace normone; a Fredholm determinant limit1-z is therefore invalid. Canonical sampling becomes exact on every fixed Fourier core; finite cyclic u_N admits no exact intertwining with bilateral M_z.",
      "scopeEN": "Excludes only passage from ordinary finite NS determinants by strong convergence. Positive full sampling proof for all evenN plus directN8/16/32 controls. Does not exclude separately defined original infinite relative factor,a justified different UV rule or all P1 sources. Finite alias,carrier complement and reflected physical pair stay distinct.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:actual-finite-ns-kernel-and-sampled-original-winding",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:trace-class-polarization-pair-with-restricted-unitary"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bc731fd4d74b50b543822058",
        "source:8adad8ebd93d270f30d55a8a",
        "source:87046d93b2c7f458549165d3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:inner-carrier-is-infinite-spacetime-module-not-finite-circle-cut",
      "titleEN": "Internal carrier retains all circle frequencies rather than a finite Fourier cut",
      "statementEN": "The explicitly available factorization H=H_circle tensor K with internal projection I tensor p,rankp=r has infinite total rank. Its trivial extension gives C_p=C_beta(B_circle) tensor I_r and U_t=e^(it B_circle) tensor I_r; scalar clutchuI_r yields(1-z)^r. It creates no finite96×96 covariance or Yukawa/Majorana dynamics. v177 maps H1 to generation rankthree,v210 uses a Fourier truncation,and v252 inserts internal field labels and Yukawas. Inspected originals do not construct symbolicK_car as a Hilbert bimodule with operator connection.",
      "scopeEN": "Exact typing and forward test of the original factorization; not exclusion of all nontrivial carrier connections. New matrix-clutch formula replaces a purported general rank law by actual determinant winding. Earlier v258 provenance gap is reused.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9176e6618cfc87c98d824209",
        "source:96db757fe437016a7f1e5d67",
        "source:21e2011bdb3fda6a923f70d2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:normal-spin-determinant-line-exactly-transports-whole-circle-in-given-product",
      "titleEN": "Normal spin line carries the entire circle source in the given product",
      "statementEN": "On spin S2,D_N twisted by L2=O(1) has one positive zero mode:H0(K^(1/2) tensor L2)=H0(O)=C,H1(O)=0. For the given graded product,V_chi f=f tensor chi exactly reduces it:B_prod V=V B_a and Fh(B_prod)F=Vh(B_a)V* for all bounded Borel h. All circle frequencies,time,polarization and finite-beta covariances remain;F has infinite total rank. Nonzero pairs +/-lambda never cross zero,hence SF=ind D_N^+. This does not identify the original bosonic operator or weak doublet H0(O(1)).",
      "scopeEN": "Sufficient operator transport in the explicit product class,not physical source selection. First additional input is the spin operator on det E2 rather than the bosonic original,then the genuine normal family and horizontal connection. Reuses existing Bott class route and Higgs/carrier audit.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-normal-spin-line-and-genuine-circle-product",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2dcb5053aef20ecafbb0c1db",
        "source:2bf6380d7bf8b40692d26167",
        "source:4677d8e3472c65279e2418da",
        "source:73e9ccfb54e8a82fb969907c",
        "source:34c29b9a96a5af990fedd659",
        "source:d2d1d3b89ce6e6c4ab045793"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:normal-index-line-source-match-is-holonomy-condition-not-vertical-degree",
      "titleEN": "Exact index-line source requires matching horizontal holonomy",
      "statementEN": "For an already exactly reducing rank-one source B_A=-i partial_theta+A and the same u=M_z,a periodic smooth multiplier g with B_A M_g=M_g B_a exists iff mean(A)-a is integral. g=e^(i chi),chi_prime=a-A transports the full domain and functional calculus. Horizontal tensoring by a flat line changes the induced circle phase while normal D_N,c1 and kernel stay fixed. Vertical degree-one data alone do not determine this phase.",
      "scopeEN": "Applies the already classified scalar first-order case at fixed time unit and exact reduction. Not two complete P1 countermodels,a newly selected Wilson factor or an adiabatic assertion of exact reduction. A4 NS/quarter origin remains;original reflection and clock marks need joint transport.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-exact-reducing-indexline-with-horizontal-connection",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:03b39f079a6a24cc42a06358",
        "source:4677d8e3472c65279e2418da",
        "source:b587f0919f97419214d0132d",
        "source:34c29b9a96a5af990fedd659",
        "source:d2d1d3b89ce6e6c4ab045793"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-normal-product-polarization-change-is-not-trace-class",
      "titleEN": "Full product polarization lies outside the ordinary relative trace class",
      "statementEN": "In the genuine circle times S2 product,the change P_(x+1)^lambda-P_x^lambda of negative projections has trace norm at least1/(2lambda) for large lambda already at a fixed circle index. The positive two-dimensional Weyl sequence lambda_j asymptotic to const sqrt(j) makes the sum divergent. Degree-one monopole values lambda_l=sqrt(l(l+1)) with multiplicity2l+1 even yield a lower bound greater thanone per level. Thus UP0U*-P0 is outside L1. Since C_beta-P0 lies in L1,finite thermal smoothing does not alter this.",
      "scopeEN": "Excludes only the unsupported extension of the ordinary one-dimensional relative Fredholm determinant to the full unprojected product. Exact reducing circle retains trace class and factor1-z. Does not exclude other justified relative regularizations or all P1 sources.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-normal-spin-line-and-genuine-circle-product"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e95af0bb0395229cad04f729",
        "source:ed139067c705d8e3ee6216c3",
        "source:34c29b9a96a5af990fedd659",
        "source:d2d1d3b89ce6e6c4ab045793"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:massive-transverse-zero-index-retains-positive-determinant-response",
      "titleEN": "Massive transverse zero-index channels retain positive determinant response",
      "statementEN": "For lambda>0,det_zeta(B_a^2+lambda^2)/det_zeta(B_a0^2+lambda^2)=[cosh(2pi lambda)-cos(2pi a)]/[cosh(2pi lambda)-cos(2pi a0)]. Its logarithmic a derivative is2pi sin(2pi a)/[cosh(2pi lambda)-cos(2pi a)],strictly positive at a=1/4. Yet the corresponding +/-lambda block has zero spectral flow. Zero index therefore justifies neither constant positive response nor dropping the complement.",
      "scopeEN": "Explicit individual positive channel with actual two-dimensional block multiplicity. Spectral a is not electromagnetic alpha;not a refutation of the original alpha Ward identity. Full source must retain complement,measure,renormalization and Quillen connection,or prove cancellation. No supertrace replacing tr_adm or unjustified zeta multiplicativity.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:positive-determinant-response-of-transverse-product-channels"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:28269643ee6920c82e6c90c5",
        "source:5560d3b7362589f61f31d928",
        "source:90040e62bb520ffded8a8155",
        "source:34c29b9a96a5af990fedd659",
        "source:d2d1d3b89ce6e6c4ab045793"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel",
      "titleEN": "Original Callias doublet count does not supply one complex source channel",
      "statementEN": "An actually closed normal Fredholm A and its true adjoint give an exactly reducing circle L2(S1) tensor ker A through the selfadjoint double;the particular compact spin realization is not required. For r=dim_C ker A,scalaru I_r has factor(1-z)^r in the ordinary complex relative source contract. Later original v42 sets H0(O1)=C2 and counts these two components as one weak doublet with bosonic indexone. This species count is not complex kernel rankone. For a retained irreducible SU2 doublet,Hom(C,M)=0,r=2 and factor(1-z)^2. det M is an SU2 singlet of hyperchargeone,but not a linear subspace of M.",
      "scopeEN": "Entire closed normal operator class in the explicitly given genuine product;original-source check of counting and adjoint/domain gap. Not a new discovery of the old Higgs/carrier type audit. No physical EM no-go,boson/CAR identification or exclusion of nonscalar U2 clutches with actual determinant windingone. No transfer of compact thermal trace class to a noncompact Callias slice.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:closed-normal-fredholm-with-retained-complex-kernel-representation",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:eeaffed68563e51de6b1baa4",
        "source:44f0101f5f84c392080bf348",
        "source:ce9f7c58bac93bac482b4909",
        "source:6ea92be1fe1c8f07ff0a16ab",
        "source:3acf62a86d119d723e073692",
        "source:76c28699e00a92fbecae3074"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection",
      "titleEN": "Exact moving-kernel reduction forces the off-diagonal Kato connection",
      "statementEN": "For the entire given matrix first-order class,P reduces selfadjoint B_A iff -iP_prime+[A,P]=0,equivalently A=i[P_prime,P]+PAP+QAQ. Both Hermitian diagonal blocks remain free. For rankone and smooth periodic frame chi,V f=chi f gives the exact whole-H1 intertwiner with a_eff=chi* A chi-i chi*chi_prime,hence full Borel functional calculus. For unchanged scalar A=aI,reduction forces P_prime=0.",
      "scopeEN": "Complete classification at the explicitly fixed scalar principal symbol,not all P1 sources. Applies standard Kato structure;no general mathematical novelty. Neither the term nor its diagonal phases is physically selected. No adiabatic approximation is declared exact reduction;normal domains and field statistics remain separate prerequisites.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:smooth-matrix-circle-source-and-moving-projector-with-fixed-scalar-symbol",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2a47d64c9d19beb71a6fa333",
        "source:e9ebb5c16ae25bbb520bc5a7",
        "source:b5867de843a621bbaf47b3bd",
        "source:2856de4a155b07420414f1fa"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:tetrahedral-quarter-face-phase-does-not-identify-original-quarter-marked-curve",
      "titleEN": "Tetrahedral quarter face phase does not identify the original quarter curve",
      "statementEN": "In the existing Bloch comparison,all ordered tetrahedral faces have tr(p_a p_b p_c)=plusminus i/(3sqrt3),hence normalized phase plusminus i. Yet the full four-point orbit is{(1+i sqrt3)/2,(1-i sqrt3)/2},j0. Original quarter marks have orbit{2,1/2,-1},j1728. Disjoint orbits exclude every direct marked Mobius identification even after relabeling. Holomorphic automorphisms have order12 for tetrahedral A4 and8 for square D4;a four-cycle is antiholomorphic in the tetrahedral chart.",
      "scopeEN": "Excludes only direct biholomorphic identification of these given quartets. Normalized three-point phase is a positive exact result,not a clock or physical event sequence. Original AXIOM A4 is not the tetrahedral group A4. Existing native E8 field conjugation and C12 clock dictionaries remain valid;other families or correspondences are not excluded.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:oriented-d3-tetrahedron-in-bloch-chart-versus-original-quarter-marks",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bfe44641c3010ae2a979ead9",
        "source:040f493c845b9992afcead42",
        "source:167223d6d2cc10f06a36214f",
        "source:62c52119f01e82212b983d42",
        "source:1e3132f530e4a4d2bc6d24cd",
        "source:b5867de843a621bbaf47b3bd",
        "source:2856de4a155b07420414f1fa"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:existing-elliptic-cover-correspondence-has-exact-c6-image-and-retained-mixed-clock",
      "titleEN": "Existing elliptic cover correspondence has exact C6 image and retains mixed clock12",
      "statementEN": "Existing C3:w^3=x^4-1 has elliptic quotient(u,v)=(x^2,w),u^2=v^3+1,j0,degree2. Its branch quartet has the tetrahedral Bloch cross-ratio orbit;an explicit ordered Mobius map is supplied. Existing C2:y^2=x^4-1 has j1728. From C12,pi_i=(x,s^6) and pi_omega=(x^2,s^4) have degrees6 and8. Their combined image field is exactly C(x,s^2),namely C6;the paired map loses s to minus s and therefore the C4 field s^3. Pure deck drops to order6,while already marked mixed R12=Q12 Delta12^4 still acts faithfully with order12,retaining its fourth and ninth powers.",
      "scopeEN": "Explicit reconciliation of existing curves and marks,not global novelty or a new cover. Tetrahedral image lies in the v quotient chart,not original x base. Does not identify internal D3 sphere with physical normal sphere. Compact curve maps establish neither punctured local-system transport nor fields,measure,EM response or full polarization. Previous maximal Phi12 module and integral-form boundaries remain preserved.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images",
        "premise:oriented-d3-tetrahedron-in-bloch-chart-versus-original-quarter-marks",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6ea3472858ed58f20fdb9aa1",
        "source:f48c98a26ea733b4feefd28b",
        "source:3a391623543ad301768ff929",
        "source:4857a66a1ba220a93cc01739",
        "source:8de3d87ca82282d21ac55e1e",
        "source:b5867de843a621bbaf47b3bd",
        "source:2856de4a155b07420414f1fa"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
      "titleEN": "Global natural Spin family lift and connection formula were already proved",
      "statementEN": "September22 already constructs every natural iota_m with sum m=-2 and W_m=LambdaEven E tensor sum(det E)^m without a global square-root bundle. Its continuation supplies A_Wm from a given A_E. The global mathematical quotient construction is therefore not an open construction in current research. A source intertwiner and selection of A_E,Phi,domain,state and time are not supplied.",
      "scopeEN": "Recovered existing result,not a new discovery. Fixed ordinary U5 Spin projection;no claim about every nonnatural bundle assignment or actual original source selection.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:natural-joint-spin-family-lift-with-given-split-connection",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0b6a34e08216429530800b2e",
        "source:1209163bb9ad19f5827d7b39",
        "source:ec4f2b07704032568f2c0602"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:global-split-joint-carrier-admits-parallel-native-c12-clock",
      "titleEN": "Split joint carrier admits a parallel representative of the whole native C12 clock",
      "statementEN": "For every natural m and given block U3xU2 connection,sigma0 from b=(1,1,1,0,0,0,0,1)/3 acts on W_m exactly as LambdaEven(diag(omega I3,I2)) tensor diag(omega,omega2,omega2,omega). It centralizes every transition and the entire induced connection. With central glue quarter kappa,c0=kappa sigma0 gives global parallel automorphisms with c0^9=kappa,c0^4=sigma0 and the complete native C12 character. The old complete torus Weyl theorem gives full inner VOA conjugacy including the common clock tuple. Exactly12 of243 thirds in the fixed toral centralizer match:two color orientations times six A3 vector weights.",
      "scopeEN": "Conditional mathematical closure for a GIVEN split connection,not selected from P1. Original marked chat is not automatically parallel on unchanged A_E;conjugator must transport connection and all marks or preserve them. An extra nonabelian family connection needs its own commutator,potential and closed domain their own invariance. Vertical bundle action identifies no base transport,time,CAR,state or EM response. Twelve counts marked torus points before further quotients,not physical sources. The2+2 action supplies no dictionary to original SU3 flavor on H1.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:natural-joint-spin-family-lift-with-given-split-connection",
        "premise:fixed-kappa-toral-third-centralizing-split-carrier",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e7213f196d9d3451e87a3448",
        "source:16100a13c722b377e2f157f9",
        "source:3d8b88b31420eee806e60375",
        "source:befce9ad84844122aebbedc4",
        "source:89640f3f9865fe6a7edd3f45",
        "source:1209163bb9ad19f5827d7b39"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:pure-weak-clutch-clock-identification-fails-despite-quarter-matches",
      "titleEN": "Pure weak clutch as whole native clock excluded despite quarter matches",
      "statementEN": "Under the extra same-angle identification,64 m residues contain exactly8 native quarter characters,permutations(2,2,2,0) and(1,1,1,3),with minimum h norm12. Earlier simple A/B lifts fail this quarter test. For whole C12 every pure weak clutch fixes at least32 weight-one directions versus22 native;all1728 classes fail. All20736 weak toral classes also fail the full character. Generally,sum k=1 prevents a clutchquarter from fixing its own original D5 factor pointwise:all k_i+-k_j=0mod4 would force sum k=0or2mod4.",
      "scopeEN": "Only direct same-angle identification in the specified clutch class or its own fixed D5 marking. Does not exclude a separate parallel clock,all connections or every clutch representative of the same topology. Full quarter character alone does not prove fixed-frame or source identity.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:natural-joint-spin-family-lift-with-given-split-connection",
        "premise:same-angle-evaluation-of-primitive-determinant-clutch-as-native-clock",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8f0e44f59be18ba645c9b737",
        "source:c5173084a1cd75b42f1327d5",
        "source:617c1545da55f19dae0f05ca",
        "source:4883c40de916d5bfdbf2047e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:same-chern-clutch-native-compiler-does-not-select-physical-connection",
      "titleEN": "Same Chern class can carry the whole clock without selecting physical connection",
      "statementEN": "The toral diagnostic k_color=(-6,0,6),k_weak=(0,1),m=(-5,1,1,1),h=(k,3,3,3) has the same block Chern classes0,1 and complete native C12 character. Norm100 is minimal in the specified integer toral class:an existing candidate bounds every better search,all6939 allowed canonical tuples through100 are checked exactly;155 match,all at100. These classify marked weight representatives,not a physical selection. The entire joint64 carrier still has determinant winding0.",
      "scopeEN": "Unbounded minimum proof in this toral class via exhaustive finite lower search. Norm is not energy;155 is neither physical-source count nor full E8 conjugacy-class count. Nullhomotopic color loop and clutch class select no connection or holonomy. In the ordinary circle CAR contract,the whole64 clutch has index0 rather than1;no identification of bosonic E8 VOA with CAR. The simpler parallel-clock closure makes this loop optimization unnecessary for mathematical compatibility.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:natural-joint-spin-family-lift-with-given-split-connection",
        "premise:same-angle-evaluation-of-primitive-determinant-clutch-as-native-clock",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:smooth-matrix-clutch-on-original-negative-fourier-sea",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:17b96f3bdfbe583d6ebf1df4",
        "source:5aa4df1e5786aa6bde75dff3",
        "source:f67e14bf6609144f64dfacf9",
        "source:19cb275bf2f4dd4c24eca719"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-gaussian-four-is-cartan-subspace-in-whole-sixtyfour",
      "titleEN": "Gaussian four is Cartan subspace in whole64 with actual G31 action",
      "statementEN": "Every real E8 root restricts nontrivially to H+. A generic point is regular semisimple,so H+ is a maximal commuting semisimple Cartan subspace in g_i. Existing whole-clock conjugacy carries it into the appropriate64 half-spin times family branch. Its normalizer quotient is exactly C_W(E8)(J)=G31:Weyl lifts can be corrected through surjective torus isogeny1-J to centralize the quarter clock. Old degrees8,12,20,24 are invariants of this same theta representation.",
      "scopeEN": "Exact fiberwise identification and group action;no numerical fit. Current orientation puts H+ in dual64. Conjugator exists but is not preferred. GIT quotient describes closed semisimple orbits,not physical orbit or state selection. Reuses v634,v690 and whole-clock conjugacy.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-cartan-four-in-full-clock-conjugate-source",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:15962368fa48549e8132fe07",
        "source:efcef0aa99ccb8eafb2ebfb2",
        "source:5f8abcfed12df29927377660"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-family-factor-is-not-gaussian-four-despite-symmetric-coincidences",
      "titleEN": "Family factor remains different despite symmetric-product coincidences",
      "statementEN": "For the same sigma=chat^4,H+ has C3 character(2,1,1). All480 toral representatives of the WHOLE native C12 class have character(0,2,2) in the unique order3 SU4 lift,and(4,3,3) in Spin10 vector. No direct sigma isomorphism identifies the fours. Nevertheless Sym2 andSym3 agree;in general Symn agree precisely for n not1mod3. Exterior2 gives(2,2,2) versus(4,1,1). All-degree trace generating-function difference is3t/(1-t^3)^2.",
      "scopeEN": "Excludes direct factor identity under the same actual third action. Positive Cartan-subspace inclusion and full inner E8 conjugacy remain valid. Product equality is only C3 character equality,not full G31 or Spin10 times SU4 equivalence. The480 belong to old complete classification and are not new physical sources.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-cartan-four-in-full-clock-conjugate-source",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:999299c47798955280a46927",
        "source:686d441f18270849307ca1f0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice",
      "titleEN": "Primitive class2 sphere prevents global whole Cartan-subspace choice",
      "statementEN": "Pointwise centralizer of whole Cartan four is T^J=F2^4;setwise normalizer N has order16*46080=737280. An everywhere smooth Cartan-subspace choice reduces the K_C bundle to N. On simply connected S2 this would trivialize it,contradicting old class2 in Z4 for every natural m. Separately,a whole Cartan four parallel under the same K connection forces curvature0.",
      "scopeEN": "Topological exclusion only for whole Cartan-subspace choice in fixed quarter sector over precisely the same primitive normal base. Needs no connection. Does not exclude single vectors,arbitrary rank4 carriers,punctured bases or allowed defect and degeneration sites. Previous parallel-clock theorem remains valid. No splitting of old sign-lift extension claimed.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-cartan-four-in-full-clock-conjugate-source",
        "premise:primitive-normal-sphere-joint-k-bundle-class-two",
        "premise:natural-joint-spin-family-lift-with-given-split-connection",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7e93ed9dfda7a808e44fa094",
        "source:e3be14e79135fe15aade9c2b",
        "source:343057040b773b7ca7b4573e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:even-degree-pullback-removes-cartan-topology-without-selecting-clock-cover",
      "titleEN": "Even cover degree removes topology and selects neither C12 nor connection",
      "statementEN": "An actually supplied degreeq pullback to the same normal base sends class2 to2q mod4. Every even degree removes this topological obstruction,smallest positive degree2;on compact S2 only branched or as a general degree map. Existing C2,C6,C12 do this only with proved same base and bundle map. Parity does not select C12. A given nonflat smooth connection remains nonflat under branched pullback. Sequence1 to Z4 to pi1(K/N) to N to1 explains why trivial N or G31 monodromy can hide class2.",
      "scopeEN": "Conditional repair with existing covers. Identity of normal S2 and original punctured source base is unproved. No freely chosen double cover as P1 selection. Full relative C12 monodromy retains its own global criterion.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-cartan-four-in-full-clock-conjugate-source",
        "premise:primitive-normal-sphere-joint-k-bundle-class-two",
        "premise:given-same-normal-base-degree-pullback",
        "premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:28a192e3892b21641de55367",
        "source:ae358cd388349dad993f7890"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:global-cartan-choice-is-optional-for-original-scalar-source-fields",
      "titleEN": "Global Cartan choice is not an original scalar-source obligation",
      "statementEN": "Original boundary data do not demand an everywhere smooth whole Cartan four. Normal geometry and flavor quotient have the same boundary-kernel origin;this supplies no actual base or bundle map. The class2 theorem remains an exclusion of the stronger Cartan choice. Any K-invariant classical polynomial value already glues across associated bundle transitions;an operator completion requires its own test. Current physical priority is corrected accordingly.",
      "scopeEN": "Source correction and elementary associated-bundle consequence. Does not contradict the preceding scoped Cartan theorem or identify Calderon reflection with elliptic deck.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-cartan-four-in-full-clock-conjugate-source",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4652edbfc9df66f947aea54b",
        "source:345288eb849e9c21e4cfaaf0",
        "source:4ee42bf6b9423cd4dfa6910a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:bare-native-octic-is-not-whole-e8-zero-mode-singlet",
      "titleEN": "The bare native octic is not a whole E8 zero-mode singlet",
      "statementEN": "For every E8 root,I8(alpha_+)=1. Its actual root zero-mode action on F8hat has nonzero PBW partition(7) coefficient alpha(-7)e^alpha/(672sqrt140). Thus the valid old neutral CAR field F8hat is not itself an E8 zero-mode singlet. Classical invariant-theoretic extension and this bare operator polynomial cannot be identified.",
      "scopeEN": "Excludes only bare full E8 invariance. Old F8 existence,correlations and stress responses remain proved;no unproved physical E8 gauge symmetry is imposed.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6b83d5943119d734b50321a7",
        "source:a016926429597e04355e9916"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:explicit-primary-e8-invariant-octic-completes-same-neutral-car-source",
      "titleEN": "Explicit primary E8 octic completion in the same neutral CAR source",
      "statementEN": "The simultaneous rational system of actual root zero mode,L1 and L2 has1600 coefficient rows,rank16 and precisely one solution in the17 dimensional ansatz with H8 leading coefficient1. All16 contraction coefficients are explicit;||W8||²=65028096000/43. Weyl invariance transports the root equation to all240 roots;L1 throughL8 vanish. W8 is therefore a horizontal E8 zero-mode-singlet weight8 primary. Its internal subline in the given K-associated VOA bundle is canonically trivial,including class2. It uses only the old neutral CAR currents,derivatives and point-splitting counterterms.",
      "scopeEN": "Uniqueness only in declared ansatz. Internal scalar retains conformal weight8 and its geometric weight line. No affine-vacuum invariance,local E8 gauge physics,new source,preparation or novelty claim. Concretely connects the known W(E8) spin8 generator to the native source.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:479e440277351fe1e757a4db",
        "source:0a7834dd6b1aed71ed7e2b94",
        "source:1caa49b37af795b8515f042c",
        "source:85923346da4d0f2c8fae5df9",
        "source:4e343d9a34ab0afee0dde1f1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:completed-octic-has-exact-old-root-ope-component-and-quarter-source-value",
      "titleEN": "Completed octic is connected to old root OPE and quarter source",
      "statementEN": "Original240-root isometry and Gaussian polarization give |<F8hat,W8/||W8||>|²=43/896. In the old full22-partition OPE coefficient S8,<W8,S8>=48384000/1333 and proj_CW8 S8=W8/41664;normalized overlap squared30/537199. For both actual quarter sources1/4 and3/4,z8<Y_d(W8,z)>=25123488075/357824462848 is nonzero,using old O/M transport and the same single shift.",
      "scopeEN": "W8,F8hat andS8 remain different. Component is not a physical projection rule,preparation or progress percentage. Equality of a quarter one-point value does not identify whole modules,states or reflections. Original grades and eight-arc support are retained.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4d4135894d6ff6362cb54e38",
        "source:a60d788abbc53ce285428c30",
        "source:58e2dbebf80b5b31a328a1fb",
        "source:395b95a0e6b14380dbdefc6c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:elliptic-normal-spin-pullback-doubles-index-and-deck-quarter-lifts-anticommute",
      "titleEN": "Elliptic normal spin pullback doubles index and deck-quarter lifts anticommute",
      "statementEN": "On old E:y²=x⁴-1,the spin Dirac twisted by p*O1 has ordinary complex index2 for every spin. In q-fixed even spin alpha=O(T-O),u=(y+i)/x²,kernel is span(1,u). Genuine deck and quarter lifts have D=[[0,-1],[1,0]],Q=a diag(1,-1),so D²=-I and QD=-DQ independently of scalar phases. Quarter exchanges the two deck eigenlines;no common rank1 kernel sector.",
      "scopeEN": "Excludes only index-one and quarter-compatible single-line pullback in this normal spin factor. Actual normal-base identity and original field transport are absent;an actually existing further tensor factor may compensate the projective cocycle. Does not exclude original bosonic doublet count or whole TFPT. Does not identify Calderon projector with deck projector.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-elliptic-curve-with-specified-normal-spin-factor",
        "premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:cb36611f14eba01e18364256"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:exact-separated-w8-twopoint-in-original-quarter-current-source",
      "titleEN": "Complete separated W8 two-point response in the original quarter source",
      "statementEN": "For both original quarter charges, z^8 w^8 <W8(z)W8(w)> is exactly sum_(r=0)^8 A_r X^r, X=q/(1-q)^2. Bosonic exchange, homogeneity and the sole pole at q=1 of order at most16 prove completeness. Nine rational Fock norms determine all coefficients without a fit. A0 is the squared old one-point value, A8=65028096000/43, and an independent stress Ward test forces A7=2(85/256)A8=43182720000/43. All A_r are positive. Regular and optimized checker outputs are byte-identical.",
      "scopeEN": "Exact theorem in the given positive neutral CAR current source with the already fixed W8. No P1 target operator, measured value or absolute time calibration.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:21456661e45a9f073054862a",
        "source:3d754f9a80cd87793d137817",
        "source:a4aebcd83a251c22a978a3c7",
        "source:ac984dbc7cadc8479a2419a8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:unshifted-vacuum-fails-same-w8-source-state-time-dictionary",
      "titleEN": "Unshifted vacuum fails the same W8 state and time dictionary",
      "statementEN": "The supplied quarter source has positive W8 spectral norm A1=93237295693374937125/15629680934138150912 at N level1. The unshifted vacuum has exactly A8 X^8 and no response at levels1 through7. No intertwiner can identify this same W8 insertion, state and time generator between those specified data. On the folded neutral sector N=(Lcal0^alpha-1/32)/8=K_alpha and H0=8N. The first shifted response has H0 grade8; the homogeneous unshifted W8 state has H0 grade64.",
      "scopeEN": "Excludes only the unshifted vacuum replacement with this same W8 and time. No general exclusion of P1, other operators or other actually derived sources.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:555390f1246aeadea8ca5a7e",
        "source:81e2d957bcd12a0c14c2eafd",
        "source:4034805713f9717f6936c814"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:local-current-phase-and-conditional-cyclic-p1-w8-image",
      "titleEN": "Local current phase test and conditional cyclic P1 image of W8",
      "statementEN": "On a proper interval choose real compactly supported chi, kappa=(1/(2pi))integral(chi_prime)^2, f=chi and g=-2chi_prime/kappa. The original level1 current cocycle is c(f,g)=-2i; the Weyl commutator is exp(2ist)I. A normal unital local current embedding must preserve this identity. If it also preserves state, time, reflection and original eight-arc support, GNS gives an isometry onto its cyclic image. On that image the same point-split products and counterterms fix W8. A global unitary onto the entire P1 space is unnecessary for this subfield. Reviewed original passages give C_seed from an already supplied local seed to boundary data and assume the positive CAR kernel; they do not supply the concrete reverse current embedding.",
      "scopeEN": "Sufficient conditional current route and necessary test within that route. Actual P1 image and full target comparison remain open. A single Weyl pair is insufficient; charged seam fields and closed collar/reference domains require additional original transport. No universal P1 no-go claim.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3a09f07020dd144720b49379",
        "source:30ccc046ad3d863287baad84",
        "source:a9e0479abeec3c6a6739d295",
        "source:912aae15bde2499d7f250c0a",
        "source:4034805713f9717f6936c814"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:all-neutral-w8-correlations-identify-the-two-original-quarter-charges",
      "titleEN": "All neutral W8 correlations agree for the two quarter charges",
      "statementEN": "The actual root automorphism g=-M R M^-1 with coordinate reversal R maps d_1/4 to d_3/4, fixes W8 and preserves N. Its Fock intertwiner therefore identifies every separated pure W8 correlation function in both real charge modules. The exact two-point calculation verifies this explicitly. W8 alone cannot select these original quarter labels.",
      "scopeEN": "Pure neutral W8 subalgebra in the given charge sources. Does not identify entire CAR modules, charged seam operators, geometric supports or the full marked clock tuple.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9de98a51a5079320f99b9664",
        "source:711693cecbc11ce35cf022c4",
        "source:4034805713f9717f6936c814"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-w8-response-has-infinite-same-time-spectral-support",
      "titleEN": "The actual W8 response has infinitely many time levels",
      "statementEN": "For every ell>=1 the connected spectral norm is a_ell=sum_(r=1)^min(ell,8) binom(ell+r-1,2r-1) A_r >=ell A1>0. Smoothing by the existing positive generator exp(-epsilon N) makes the insertion norm finite and only multiplies these spectral contributions by exp(-2epsilon ell). For every epsilon>0 the cyclic time subspace remains infinite dimensional. No finite spectral-support model with this same time reproduces the exact two-point response.",
      "scopeEN": "Exact dynamics in the same source/time contract. Does not exclude finite approximations or finite native observer codes; does not fix absolute physical time.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:da29da892b1e9b2fc81edccb",
        "source:3d754f9a80cd87793d137817",
        "source:4034805713f9717f6936c814"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:older-seam-equivalence-verifications-do-not-supply-marked-local-p1-map",
      "titleEN": "Older seam verifications do not supply an already closed marked local P1 map",
      "statementEN": "Reviewed originals retain the old circle, concrete microscopic neutral CAR field route and conditional E8 net extensions. v366 sets inclass=True and tests supplied copy counts and target constants; v464 uses a chosen sin(k) chain. v469 gives the extension route under its subnet hypotheses. v994 explicitly labels C7 cited/open; v1030 explicitly leaves microscopic generators and local word/adjoint tails unproved. The current SEAM.EQUIV.01 parent is open and its MMST branch conditional. The earlier complete Dirac vector cocycle cancellation is retained in its Lagrangian/CAR scope. None of these passages constructs the actual marked local P1 W8 image.",
      "scopeEN": "Targeted original-source review of the named claims, not an exhaustive archive theorem or rejection of positive compiler/microscopic results. Charged E8 extension and stronger typeIII exhaustion are not imposed as prerequisites for neutral W8.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:28e6fcea78899a2a8333d1fc",
        "source:ac64c73876d86fc18d095513",
        "source:dbd2b4df16ea657c38543c07",
        "source:586b5c24b61e3c93d8271d3e",
        "source:5f5c64f397ba554a5b677662",
        "source:27632f5968430a732e6a1df9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-original-c1-stress-cycle-reconstructs-neutral-w8-response",
      "titleEN": "The full original c1 stress cycle reconstructs the neutral W8 response",
      "statementEN": "For the same original quarter CAR source,p=alpha-1/2=plus or minus1/4 and c1 lowest weight h1/32. This is not a Kac weight m²/4. The injective Virasoro Verma map and equal partition characters prove at each grade that the full original stress cycle generates the entire fixed relative-charge sector. All W8 response components and their positive-semigroup smoothing are therefore in it. At original grade8 the first response is explicitly reconstructed by22 literal CAR stress words: all rational coefficients,residual0,full rank22 modulo three primes,and the identical complete Gram from independent c1 Sugawara calculation. All original modes and intermediate states are retained.",
      "scopeEN": "Complete mathematical cyclicity in the GIVEN original source; concrete application of standard representation theory, no general novelty claim. No actual local P1 map, specified single physical intervention or local-net equality. A matching c1,h1/32 P1 stress module would conditionally give the cyclic state intertwiner but still needs original identification.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:066e0b573b49dfc6460e2141",
        "source:2f2f957c1f7256d2691d9eff",
        "source:876299245555accf07467678",
        "source:874a98d02ba8ed5509ac6076",
        "source:2fa901dfd965e89d91c23459"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:folded-c8-cycle-misses-intrinsic-w8-tangent-without-obstructing-original-stress",
      "titleEN": "Only the smaller folded stress cycle misses the intrinsic W8 tangent",
      "statementEN": "In the folded c8 space the Virasoro cycle at N level1 is span(d.h_-1 Omega). The actual first W8 response has perpendicular component v_perp=grad_tan H8(d),norm²51311452775625/9345848836096 in both quarters. All16 O8-invariant quantum Q_ab corrections contribute only radially at this level. An independent240-root enumeration reconstructs the whole first coefficient and one-point value from all17 old ansatz coefficients. The entire smoothed response is outside the closed Lhat cycle. This restricted exclusion is consistent with the positive full original c1 reconstruction.",
      "scopeEN": "Excludes generation by Lhat_n=Lcal_(8n)/8+constant alone. Does not exclude the full original stress source,the old F8 overlap or P1. Introduces no extra nonstress source or physical gate.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8a1704f08ad7e1f41c210dd7",
        "source:a9210f25f45f0c462dabeb99",
        "source:ed0a315a5777fb68bc9681b6",
        "source:688450eaee329a9ecb34c437"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-source-first-nonuniform-moment-is-four-with-literal-five",
      "titleEN": "The fourth original root moment reconstructs the five after three uniform moments",
      "statementEN": "The actual60 complex E8/J root lines obey exactly M1=I4/4,M2=Pi_sym2/10,M3=Pi_sym3/20 and40M4=Pi_C+Pi_sym4. Extracting40M4−Pi_sym4 without a five-dimensional target literally recovers the original code projector. The preexisting parent I−20M4 has spectrum0^5,(1/2)^30,1^221. Rebuilding the identity from the original Gaussian roots gives byte-identical normal/-OO results and two firing negative controls. Algebraically(20M4)^n=Pi_C+2^(−n)(Pi_sym4−Pi_C) for n>=1.",
      "scopeEN": "Finite original root lines,given J/metric and four native registers; no novelty claim for the old parent. First nonuniform projective moment does not exclude arbitrary nonlinear recognition. No physical time,dissipation,preparation,P1,3+2,clock or48c3^4 selection; E8 and J are not derived.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors"
      ],
      "attemptIds": [
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bcd11890c5da0736ed79c74a",
        "source:b4eaa75dcbeab0f103610f0e",
        "source:862729e1721e3d859baa89fe"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-whole-five-ground-space-needs-four-register-interaction",
      "titleEN": "Equal actual three-register marginals exclude exact whole-five ground spaces from at-most-three-body terms",
      "statementEN": "rho_C=Pi_C/5 andrho_S=Pi_sym4/35 have exactly equal reductions on all4+6+4 subsets of sizes1,2,3; each three-register reduction isPi_sym3/20. Their global trace distance is6/7. Every Hermitian at-most3-local Hamiltonian on the same four registers therefore has equal mean energy. If the ENTIRE codeC has minimal energyE0, positivity ofH−E0I forces the full35-dimensional symmetric space to be ground as well. An exact five-dimensional code ground space is impossible. The existing4-local moment parent attains the necessary interaction order.",
      "scopeEN": "Only exact energetic selection of the ENTIRE original five-code on the same four registers. Arbitrary Hermitian terms and frustration allowed. Does not exclude one selected code state,ancillas,thermodynamic systems,effective four-body interactions,open dynamics or approximate selection. Marginal equality is for the two mixed states,not all pure code inputs. No physical-origin derivation.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors"
      ],
      "attemptIds": [
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bcd11890c5da0736ed79c74a",
        "source:b4eaa75dcbeab0f103610f0e",
        "source:862729e1721e3d859baa89fe"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:old-cover-winding-reconstructs-local-quarter-current-net",
      "titleEN": "Old cover winding reconstructs the local quarter current net",
      "statementEN": "The old stress formula gives J_n=2(L_n^(3/4)−L_n^(1/4)) on the same CAR generators for every n including0. The comparison within the existing cut-cover source is not free: u_cov W0=W1 and u_cov W1=W0 u_base give U=[[0,u_base],[I,0]],rank[C,U]1 and phase-independent adjoint Fock transport AdGamma(U). The first arrow preserves factor seas and Wick ordering. Hence on factor0 J(f)=2(AdGamma(U)^−1 T_(3/4)(f)−T_(1/4)(f)). Existing self-adjointness/energy bounds and the stable unitary Trotter sequence show that this transported stress pair generates exactly the local U1 current net on every base interval. The full winding remains charged and is not globally vacuum-preserving because of the second arrow.",
      "scopeEN": "Complete operator and local-net theorem in the GIVEN original cut-cover CAR realization. Support is the two-preimage region, not a single cover arc. The later eightfold fold, cross-arc CAR transporters and original P1 support/Theta/collar/reference map do not follow from this scalar current-net theorem alone. No time interpretation of product parameters or physical gate closure.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-cut-cover-car-with-actual-winding-and-sea",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9377a51d7d19d598c16ca625",
        "source:7852f47ffeb160c13a411ab8",
        "source:0177b63bec75b7a037d99971",
        "source:df868371721af19a636bfec6",
        "source:f49242905b7895760167fbdb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:untransported-independent-quarter-stress-pair-is-not-current",
      "titleEN": "Untransported independent quarter stress pair is not a current",
      "statementEN": "For the untransported two-factor difference D_n=2(L_n^+⊗I−I⊗L_n^−),c±1,h±1/32,the ground-state commutator is exactly n(4n²−1)/6. Values1/2 and5 at n1,2 contradict a level1 current with1,2;no common rescaling works. Every real self-adjoint linear combination aLplus+bLminus has cubic coefficient(a²+b²)/12 and thus can yield a Heisenberg algebra only trivially. The proved actual winding transport above avoids this false replacement.",
      "scopeEN": "Complete exclusion of the named real linear class of independent stress factors. No exclusion of the transported common CAR factor,general nonlinear source operations or P1. Finite CAR checks are not asserted to be full finite CCR representations.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-cut-cover-car-with-actual-winding-and-sea",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c6ec1f1a3022d3bb6cfbfb72",
        "source:84025a2264497db86a87667b",
        "source:c482dec3543d280eeed472c0",
        "source:8ed8047595b33651542791c4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:current-public-paper-bytes-and-binding-source-gaps-recovered",
      "titleEN": "Current public papers and binding source boundaries checked",
      "statementEN": "Directly downloaded current public introduction and tfpt_research_contracts PDFs are byte-identical to website/public/papers,with SHA256 d564ea7b…c7b9 and5c08d585…9b93. Old search-engine views return differing earlier editions and do not prove a deployment defect. The reviewed current TYPEIII.CHARGED original remains open. Its binding ALG2 correction withdraws the Vandermonde inference to the microscopically generated algebra and requires FE-GEN or the precise projected-algebra route. The old technical companion CMB section does not supply this P1 field map either. The positive old stress/winding composition is instead reused as F1.",
      "scopeEN": "Targeted current public sources and original passages on26October2026. Not a theorem that every archive lacks another solution. Neutral W8 retains positive older results;the charged TYPEIII extension is not imposed as an extra prerequisite.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0cc473cd2bb31eb3e952a502",
        "source:f81df2db04fdeab090bc2644",
        "source:3664d50bfe7d1ad5ef1bbbfb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:winding-charge-conjugation-descends-fixed-pin-domain-but-not-full-dirac-sea",
      "titleEN": "Winding and charge conjugation preserve a fixed Pin domain with a decisive Dirac correction",
      "statementEN": "In the given flat Moebius comparison,A=e^(i pi x)sigma1K is an antiunitary involution of the same fixed(c,b) H1 domain and preserves cover support. Exactly A D A=−D+pi sigma1. Centering D−(pi/2)sigma1 would change flat/Pin data. For the full D sea the PH polarization mismatch has at least n/4 frequency contributions of4/(13n²) on every n≥4;the HS level sum≥1/(13n) diverges. Thus this PH Fock lift does not exist in this full two-dimensional sea. The old transverse zero branch instead retains its finite rank1 defect. A is not a bulk D solution intertwiner;Calderon boundary-range invariance follows neither positively nor negatively from that and remains separately open.",
      "scopeEN": "Positive fixed-domain descent;proposed Theta/state/same-time identification excluded in the named full flat D-sea contract. No exclusion of all P1 kernels or reduced circle sources;no new physical Theta or general Calderon theorem.250 finite grid controls accompany the analytic divergent lower-bound proof.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:517b6ea745253e449087eef5",
        "source:df765a0afa918c954b23f7bb",
        "source:f5d28627e8ef3f969edcdc03"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-fourth-root-frame-has-signed-collective-sixty-mode-dual",
      "titleEN": "The actual fourth-order frame has a phase-sensitive sixty-mode dual",
      "statementEN": "Columns z_a^tensor4 define F and K=F*F with spectrum3^5,(3/2)^30,0^25. F/sqrt3 literally identifies its top five with the native code. Each row contains1 once,1/16 thirty-two times,−1/4 twelve times and0 fifteen times. Actual triangle0,1,2 has invariant product−1/64. Magnitude replacement |K| instead has a unique Perron mode at6;|K|² is strictly positive.",
      "scopeEN": "Finite duality of the same supplied frame; no physical sixty-site world or coupling. Only the magnitude replacement is excluded,not all classical/nonlinear self-organization. Central J acts trivially in quartic degree.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors"
      ],
      "attemptIds": [
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8c700b5b49acd42ce3e1cb6d",
        "source:984d71caaac4dd5e4bb093d6",
        "source:29019dc1bf23d73cfd99d814"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-root-gram-spectrum-is-not-canonical-source-energy-selection",
      "titleEN": "The root Gram is a source metric rather than canonical energy selection",
      "statementEN": "Normalized local quartic fields have the actual vacuum two-point functionK_ab/(z−w)^8. YetL0F=4F andF*L0F=4K,so the generalized energy problem hasE=4 on all35 source directions. ExactlyK+=(7K−2K²)/9 andFK+F*=Pi_sym4. Positive candidatesL_t=(3I−K)(I+tK),t>=0,share the five-kernel with different remaining rates;the finite correlation alone selects no physical generator.",
      "scopeEN": "Only identification of this covariance spectrum with canonical c8 stress energy is excluded. Intrinsic frame anisotropy remains. No executed whitening,no identification ofL0 with P1 time,no exclusion of original quarter states,other interactions or full P1 models. The older full W/Gamma generating functional remains available.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:literal-native-positive-cartan-quartic-fock-embedding"
      ],
      "attemptIds": [
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8c700b5b49acd42ce3e1cb6d",
        "source:984d71caaac4dd5e4bb093d6",
        "source:29019dc1bf23d73cfd99d814"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:identical-overlapping-native-five-codes-have-no-common-state",
      "titleEN": "Identical overlapping native five-codes have no common state",
      "statementEN": "ForA=V_1234 tensorI andB=I tensorV_2345,exactlyA*B=(1/4)S for a factor permutationS. Their image intersection is0. The auxiliary projector penalty2I−AA*−BB* has minimum3/4;the actual native parent sum is>=3/8. Since overlappingS4 groups generate symmetry on the union,the same zero intersection follows for identical code constraints overlapping in1,2 or3 registers.",
      "scopeEN": "Only rigid identical code constraints in a shared register frame. No new P1 code-closure axiom. No classification of differently rotated codes,disjoint blocks,approximate/open processes,frustrated phases or the full E8 field. The auxiliary penalty is not presented as a native extensive Hamiltonian spectrum.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors"
      ],
      "attemptIds": [
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8c700b5b49acd42ce3e1cb6d",
        "source:984d71caaac4dd5e4bb093d6",
        "source:29019dc1bf23d73cfd99d814"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:horizontal-e8-invariant-octic-cannot-isolate-native-five-ground-space",
      "titleEN": "A horizontally E8-invariant octic cannot isolate precisely the native five ground space",
      "statementEN": "For the actual normalizedf0=sum(u_a.h(-1))^4/sqrt96 and original rootalpha=sqrt2e0,E_alpha(0) has charged PBW componentalpha.h(-3)|alpha>/(3sqrt96) with squared norm1/144,outsideC5. Thus an operator commuting with horizontal E8 zero modes cannot have preciselyC5 as an isolated eigen/ground space on the full grade4 source. The existing screenedW8 obeys[E_alpha(0),o(W8)]=0 and therefore fails this necessary condition as a sole exact-five selector.",
      "scopeEN": "Finite canonical c8 source with the same positive Gaussian polarization;no claim of full affine invariance. Does not exclude W8 contributions to larger E8 multiplets,broken symmetry,quarter references,state responses or full TFPT. The observer code need not be a full-source ground space and this is not imposed.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:declared-original-octic-quantum-completion-ansatz"
      ],
      "attemptIds": [
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8c700b5b49acd42ce3e1cb6d",
        "source:984d71caaac4dd5e4bb093d6",
        "source:29019dc1bf23d73cfd99d814"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea",
      "titleEN": "Longitudinal reflection preserves the fixed Pin domain and full Dirac sea",
      "statementEN": "Theta_x=K R_x is an antiunitary involution of the same(c,b) H1 domain for both c=±i and b=±1. Deck inversion compensates conjugation:bar(c)^−1=c. Exactly D Theta_x=Theta_x D;all real spectral functions,the complete D sea and quasifree vacuum ray are preserved. Block-diagonal antiunitary Fock implementation needs no PH mixing or HS repair. D time and longitudinal translations are reversed. Original operational Theta is distinct from normal deck lift and Calderon polarization;longitudinal reflection is a correctly typed candidate,not yet an identified P1 field map.",
      "scopeEN": "Concrete flat boundary family and its given D sea. State invariance does not imply Green reflection positivity;P1 locality,time and kernel need an actual map. Do not identify the three reflection types.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9e846147c5ce4ed41964e91f",
        "source:1a2d891720ffef7d9802ef25"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity",
      "titleEN": "A single fixed Pinminus Green kernel fails the neutral OS word",
      "statementEN": "The actual invariant simple transverse branch has D0=−i b partial_x,q=cb=±i. Its exact Green kernel Gq is q/(q−1) for0<s<1 and1/(q−1) for−1<s<0. The equivalent normalized one-mode trace has z=−q^−1 and omega(N)=1/(1−q)=(1±i)/2. The neutral number word is phase-independent under standard antilinear charge-exchanging word reflection. Its smeared positive-time OS square is not real. Thus the complete free Green realization in one fixed Pinminus sector is not RP. Linear Clifford reflection sends c to−c and is not an endomorphism there;K R_x as D-sea symmetry does not replace it.",
      "scopeEN": "Only this given charged Gaussian Green realization and standard charge-exchanging word reflection on a single fixed Pinminus sector. No P1 no-go,no exclusion of the positive NS cover source or arbitrary other kernels. Sector exchange prevents transporting the neutral witness as an isolated OS square in the cover state.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:32e7209bf21a337083acd9e7",
        "source:75597e1ff68f6b2e3a02f75a",
        "source:afca0f750c8f90774c51bff2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp",
      "titleEN": "Full original NS orientation cover has charged Green RP in all modes",
      "statementEN": "Original doubled Pin deck action forces beta2 in the existing length convention. H=i sigma3 partial_w is selfadjoint on the same b boundary domain,with simple spectrum nπ/2,n inZ. For L=partial_x+H,S(t)=e^(−tH)(1+e^(−2H))^−1 is the entire antiperiodic Green kernel. Both charge blocks factor exactly:−S(−t−s)=B_t*B_s and S(t+s)=Btilde_t*Btilde_s,with B_t=e^(tH)(1+e^(2H))^−1/2 and Btilde_t=e^((1−t)H)(1+e^(2H))^−1/2 for0<t,s<1. Both are bounded. Explicit source-order minus and charge-exchanging word reversal give full free CAR RP through Wick/Gibbs limits. Relative thermal Z=2 product_n≥1(1+e^(−nπ))² converges. Linear Clifford reflection exchanges the actual c=±i deck spaces;their zero kernels jointly give NS value±1/2. Every transverse excitation is retained.",
      "scopeEN": "Proved for the given free charged Green quantization on the existing whole orientation cover. No additional field-species doubling,no mixture of independent complex states,no identification with P1 kernel or previous W8 vacuum. Cover trace period2 is not the global relative C12 cover result. Jaffe/Ritter is not applied with unchecked boundary hypotheses;the concrete proof is direct.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c219ec0e96519b4a451144f6",
        "source:d70c5d292abae84715e3e51f",
        "source:1ec86de4dd20200840aa3ed6",
        "source:b97cc6cb8be69454eefa9544"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum",
      "titleEN": "Cover Green state and quarter Hardy vacuum require an actual time and state map",
      "statementEN": "The full cover Green realization quantizes x as Euclidean time and has thermal covariance C=(1+exp(2H))^−1 on the w-section L2 space,with simple zero-mode value1/2. The D sea on L2(x,w) and old quarter Hardy state on the longitudinal circle are spectral projections. Mere covariance-preserving one-particle unitary identification is impossible:projections have only0,1 while C has1/2. Spaces and time coordinates must be transported. Enlarged purification or local net embedding is not excluded. v526 already assumes the chiral NS kernel and half algebra;its thermal success does not supply this original two-dimensional P1 identification.",
      "scopeEN": "Type check of the specified free sources. No ban on local state maps in enlarged cyclic spaces and no requirement of surjective full Hilbert-space identification. Same geometry or numerical temperature is not yet same field action and time.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover",
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:09f3dd9c0d34a9ee9e1f8237",
        "source:a8696b2ad3d67606e81deae3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:declared-recursive-native-som-is-u35-equivariant",
      "titleEN": "Declared recursive SOM update alone prefers no absolute code orientation",
      "statementEN": "For every U in U(35),the stipulated update is exactly covariant under X->XU,W->WU: norms,distances,winners,means and normalization are preserved. After5000 directly executed steps the relative signal error is1.36e-14. Original code weight.9809168 becomes.1324321 for actively rotated input with FIXED readout; passive readout transport restores.9809168.128 orientations transported by the proved covariance give mean.1417688 near5/35. Three generic complex starts also compress without the high native code weight.",
      "scopeEN": "Exact mathematical symmetry of the chosen update plus finite numerical checks. Generic U(35) does NOT preserve native tensor powers/field products;not a countermodel to full TFPT origin. Given native initial alignment may be justified upstream.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-recursive-native-som-update",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d33883e7974bd19e0baf6ce2",
        "source:7b239bd8b5d134037889613e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:declared-recursive-native-som-clocks-depend-on-chosen-rates",
      "titleEN": "Recursive SOM oscillations depend on chosen learning rates",
      "statementEN": "Nine prescribed beta/eta pairs around the original settings were executed5000 steps each. Three reach numerical rest,six retain motion. At beta=.25,changing eta=.15 to.075 changes frozen-response periods from11201/64540 to18551/106907 iterations. For all9 states,the observed frozen120x120 response reproduces the next1000 nonlinear steps with relative error<8e-14. Normal and-OO runs produce identical result bytes.",
      "scopeEN": "Finitely tested property of the expressly chosen learning rule. Frozen response is not the full Jacobian;no general attractor theorem,no identification with physical time or an original TFPT Clock.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-recursive-native-som-update",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d33883e7974bd19e0baf6ce2",
        "source:7b239bd8b5d134037889613e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower",
      "titleEN": "Existing C2 real forms yield the concrete annulus and Moebius quotient",
      "statementEN": "The complete affine census of eight h^a Q^b kappa has precisely two dividing members:hQkappa and hQ³kappa. With O=(0,i),T=(1+i)/2,Qz=iz,hz=−z+T,kappaz=−i bar z+T. Their halves have width1/2,circumference1 and Q exchanges them. Delta=hQ² is the unique free involution among h,Q²,hQ²;on the annulus it acts(t,s)->(1/2−t,s+1/2),with Moebius quotient. The earlier kappa-only nondividing statement is correctly scoped. v507 half-period origin,v510 free-deck/Fock class and v519 free RP are reused results.",
      "scopeEN": "Exact theorem only in the named h,Q,kappa subgroup and its eight-member anti coset. There the unordered OS annulus pair is canonical. Full already marked D4 lift has16 antiholomorphic members and an additional equatorial dividing pair;earlier unqualified full canonicity is narrowed by finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots. No square-modulus derivation or physical P1 cover identity. Free-deck uniqueness only among h,Q²,hQ².",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:03da850d46042ef43eb76e84",
        "source:b7a477f1bf7ac018088a6186",
        "source:03209c6e391c44a354f0780d",
        "source:285354614601bca72a8657dc",
        "source:fdbfc6dffc7130bf50c52b96",
        "source:897e300272ae674cdb6844a6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent",
      "titleEN": "Raw NS pullbacks yield the spin central commutator and quarter descent",
      "statementEN": "For the untwisted NS NS line and raw complex-linear coefficient pullbacks,U_delta²=chi(1+i)=+I and U_rho U_delta=−U_delta U_rho,because universal lifts differ by the A cycle. The glide g=delta_E rho=−bar z+T has g²=z+i and U_g²=−I. With fixed sigma_s²=I,A=sigma_s U_g is Dirac covariant,A²=−I,and has c=±i spaces with involutive c^−1 A descent. Anti-linear Real j_g is distinct:(sigma_s j_g)²=+I and has no complex ±i eigenspaces. Q invariance allows only(+,+),(−,−);a genuine transported A4 Spin/Pin relation forces(−,−),without a separate no-zero-mode rule.",
      "scopeEN": "Raw flat spin pullbacks with explicit Clifford convention. Additional spin minimality requires genuine Spin/Pin bundle transport up to real central sign;an arbitrary projective U1 phase is another linearization. Do not identify Q,half translation,Pin operator and OS Real structure.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e8229bdce434838c74017e1f",
        "source:94e192e3b6f2755cf7d1e10c",
        "source:51dfd050a3721013170e9938",
        "source:32cc1ec4fd13eeb70a68b36d",
        "source:0c1934259baa50fb13ecaf94"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms",
      "titleEN": "Canonical elliptic cut reproduces the original quarter boundary tuple and KMS normalization",
      "statementEN": "Unitary theta=2pi s identifies domains and actual operators:B_Sigma/(2pi)=Bcov=2(B1/4 direct_sum B3/4),V=T_pi,u_cov=[[0,u_base],[I,0]]. Q rotates cut charts and is not V. At canonical width W=1/2,the second chiral Calderon compression is C_A=(1+exp(2pi Bcov))^−1,hence geometric beta_angle=2pi without fitting. C_A is a mixed traceclass perturbation of the Hardy sea at distance<0.086590;relative covariance/Fredholm factor remains1−z,and(1−z)² for double winding. Known two-boundary graph reconstruction is specialized to the actual existing C2 cut. The old full flat Moebius test has modulus1,this one1/2;units cannot identify their full Dirac problems.",
      "scopeEN": "Proved for the given one-particle boundary tuple and declared free chiral CAR interpretation. No equality with Hardy vacuum,original P1 measure/time identification,or EM/Quillen response from the relative covariance determinant. v813 index-four response normalization remains open;E8 compiler and existing W8 are not relabelled as new. Continuation:This boundary-tuple identity is not literal identity with the full marked equator pullback,which is a ramified V4/E8 graph. Retain full Real group and both original slots.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:801b8d7eccc89956a1d1149b",
        "source:1bbcb16092fec5e2bf5afe6d",
        "source:cf9582228ef3c7d7d9dc36e3",
        "source:16aa855809b1b0313a03a068",
        "source:51dfd050a3721013170e9938",
        "source:5ac46d1713bcaaf4794fa66a",
        "source:2aa965e8745f86d1f035bb34",
        "source:897e300272ae674cdb6844a6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:finite-crosscap-cauchy-state-is-not-original-quarter-vacuum-by-normal-filtering",
      "titleEN": "Finite crosscap Cauchy state does not yield the quarter vacuum by normal filtering",
      "statementEN": "In the declared flat Pin model,the crosscap Cauchy covariance on each lambda,−lambda pair is the graph with t=−c exp(−2Llambda). Its commutator with signed boundary B has norm lambda/cosh(2Llambda)>0. Fock energy variance is lambda²/cosh²(2Llambda),so the finite-L state is nonstationary. Further normal collars filter in trace norm to the tree NS vacuum,which loses c,b marks. The loop quarter operator still follows from cb=±i,but this limit supplies neither its Hardy state nor W8 source dictionary. Cauchy data remain free before imposing physical local b boundary conditions;imposing them would instead solve the different zero-kernel problem.",
      "scopeEN": "Only identifying this finite crosscap state or its normal tree vacuum limit with the original quarter Hardy state under the claimed same time is excluded. No P1 no-go and no exclusion of actual open/closed sewing maps with appropriate state/time transport.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:00c83f8827bb904bd8117e87",
        "source:668841b4fbf113d20efb1055",
        "source:ad7ee5629f30616eeb912c5e",
        "source:5ac46d1713bcaaf4794fa66a",
        "source:2aa965e8745f86d1f035bb34"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-quartic-relative-arc-charge-excludes-additive-density-stress-insertion",
      "titleEN": "Native quartic requires relative charge transfers among source arcs",
      "statementEN": "In the actual M/O/quarter dictionary,each degree8 CAR arc-charge Gram has rank5 and determinant498159/262144,normalized166053/4294967296. All four index-difference classes have rank5. Every nonzero native quartic responds to every nonconstant real infinitesimal arc phase;the common phase remains trivial. These phases pointwise fix the restricted additive scalar density/stress subnet. Native field distributions cannot be generated there. The full original CAR algebra already contains the required transfers.",
      "scopeEN": "Exact highest CAR degree;subnet conclusion assumes the expressly restricted insertion algebra. Closed-operator affiliation needs an appropriate realization and common core. No exclusion of full CAR or arbitrary P1 maps,no claim for every finite phase,and no physical event selection.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:typed-source-structures",
        "premise:original-eight-arc-additive-density-stress-restriction"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ac9f27a70ec861a235ddb47c",
        "source:f574e44dc5cd8180a84d6ff6",
        "source:a3bc69ae699f2079c90a2e7b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:retained-quarter-sea-finite-modular-transfer-preserves-integrated-native-cartan",
      "titleEN": "Finite source modular mixing preserves integrated native Cartan matrices",
      "statementEN": "The actual source class was restricted on rings64 and128 for both quarter phases to eight equally spaced arcs. h=log((1-C)/C) has nonzero interarc transfers but numerically commutes with all four actual integrated native Cartan matrices. Removing interarc covariance removes the witness while changing the state. Normal and-OO produce byte-identical results.",
      "scopeEN": "Finitely tested modular one-particle response. No continuum reconstruction,pointwise quartic-field invariance,physical-time identification,or F_a to delta D_rel map.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a94ab70379a555312e9b43d0",
        "source:fcd15f969f60d55454d0e150",
        "source:50e3ba90dc3d9eea50a7abd8",
        "source:a3bc69ae699f2079c90a2e7b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-neutral-interarc-fields-have-exact-connected-current-vertex-reconstruction",
      "titleEN": "Original neutral interarc fields have exact current reconstruction",
      "statementEN": "In the original Q0 Maya/current dictionary,B(z,w)=w/(z-w) exp(sum(z^m-w^m)J_-m/m) exp(sum(w^-m-z^-m)J_m/m). CAR current commutators,infinite-sea vacuum contraction and cyclicity determine all finite-energy matrix elements. The actual quarter factor(z/w)^alpha follows from field powers. Independent exact checks test every matrix element through degree4/8 with12/67 states at two point pairs;normal and-OO are byte-identical. The connected current-net/fixed-point theorem places neutral interarc bilocals in a larger connected interval,and locality puts them in the complement-current commutant onQ0. The additive separate eight-arc net remains strictly too small. Substitution into actual A_a and unchanged point-split prescriptions reconstructs native currents and existing quartic/W8 composites without a new elementary coupling.",
      "scopeEN": "All-degree formal or finite-energy matrix-element identity;localized bounded bilocals use the separate net theorem. Unbounded native limits retain old core/smearing/affiliation hypotheses. No equality of dual net with full neutral CAR,no finite smooth pulse,new time flow,or original P1 net embedding proved. F_a to delta D_rel remains relevant to a claimed particular primitive interaction,but is not an extra existence requirement for an already neutral composite.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures",
        "premise:full-existing-local-e8-field-hull-observer-code"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:47d7d1a5e11ad8c530190f68",
        "source:8e50f3982fb3da4fbef8f1a7",
        "source:3e89eb12fa75cb7ef3cd4d54",
        "source:a809da6ab9fde6a466e5471e",
        "source:a9e0479abeec3c6a6739d295",
        "source:748b7940e88d21a0f908d8c7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-pin-zero-branch-retains-quarter-car-state-time-but-no-uniform-scale-return",
      "titleEN": "Actual normal zero branch preserves quarter CAR state and time,but uniform scale gives no return",
      "statementEN": "Vf=(1,b)f/2 is isometric on the original Pin fundamental region and obeys D0V=V b(-i partial_x),q=cb. Spectral projections,all quasifree CAR words and Theta_x transport. This explicitly composes the known zero branch. For every uniform a>0,QD_aP0=0. Exact nonlocality witness ||Q M_w phi0||²=1/3 shows P0 is not an automatic thin seam/collar projector.",
      "scopeEN": "Given pure D sea,correct b orientation and actual domains. P0 is normal zero branch,not native five. No full P1 locality/admissibility identification or equality with thermal C.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a0c68a626a1e009ae73373eb",
        "source:97e94e6f7674136085a2e3a2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:conformal-pin-source-geometry-fixes-exterior-return-and-unitary-memory",
      "titleEN": "Conformal original geometry fixes exterior return form and actual memory recursion",
      "statementEN": "deltaD[h]=-(hD0+D0h)/2 gives exactly ||Q deltaD psi_k||²=k²Var(h)+<h_prime²>/4 for every smooth real even normal profile,zero precisely for constant h. Full Fourier/zeta check yields4k²/45+1/3 for h=w². Actual bounded U=exp(i dt D_e)gives memory(P0 U Q)(Q U Q)^j(Q U P0),without resets. For the same collar-preserving probe,400 steps agree with full257-mode evolution to2.11e-13;129/257 curve difference<3e-10. Wrong adjoint feedback differs by.02084. Normal/-OO byte-identical.",
      "scopeEN": "Exact return form/block identity;long trajectories are finite Galerkin tests. Profile/epsilon are diagnostic inputs,not P1-derived. Second responses are forms,no unproved higher domain powers. No Fock implementer or3+1D/P2 closure claimed.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:typed-source-structures",
        "premise:given-pin-source-conformal-normal-geometry-probes"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a0c68a626a1e009ae73373eb",
        "source:dcc2568be6388e7c02e2e1f5"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:geometric-exterior-schur-response-transfers-proper-native-arc-charge-but-is-compact",
      "titleEN": "Geometric exterior Schur response transfers relative arc charge but is not a local native current",
      "statementEN": "Exact second geometric Schur response at z0 contains R_h(k)=k/8 sum_m h_m²(pi*m)²/[k²+(pi*m)²]. Between actual disjoint quarter preimages I=(1/32,3/32),J=I+1/2,every nonzero cosine coefficient contributes a strictly positive multiple of(1-i). Thus transfer is nonzero for every nonconstant smooth real even profile. Concrete probe gives.001720549637597(1-i)as epsilon² coefficient;independent Fourier error7.09e-12. R_h(k)->0 is compact and cannot itself be a nonzero local folded multiplication current.",
      "scopeEN": "Transfer is necessary structure for the existing native arc-charge test,not sufficient quartic/P1 identification. Second spectral Schur response is not new physical time or Hessian;full fields/composites,domains and profile/history selection remain needed.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:typed-source-structures",
        "premise:given-pin-source-conformal-normal-geometry-probes"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:be682d267b94fec65a05e32b",
        "source:b5031494e0225cedbef73052"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-ns-half-cover-cauchy-graph-purifies-green-state-with-neutral-ground-time-obstruction",
      "titleEN": "Half-cover Cauchy graph realizes given Green covariance but not positive ground-state time",
      "statementEN": "Actual NS half collar0..1 has graph(exp(-H))projection[[1-C,sqrt(C(1-C))],[sqrt(C(1-C)),C]],C=(1+exp2H)^-1;other NS half is complement. Pure quasifree boundary extension restricts under j=(0,I)state/time faithfully to given source. Neutral A=a0* a_m nevertheless has frequency-m*pi/2 and norm1/[2(1+exp(m*pi))]>0. Thus even a nonsurjective embedding of this entire neutral observable class in a positive ground source with same time is impossible;m2 also preserves spatial J parity.",
      "scopeEN": "Given free Green quantization and actual x-time cuts,not P1 seam or old circle time. Cauchy trace space is a mathematical extension,not new physical species. No exclusion of other P1 states,admissible subalgebras or differently derived local time maps.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a0c68a626a1e009ae73373eb",
        "source:97e94e6f7674136085a2e3a2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots",
      "titleEN": "Full marked C2 lifts distinguish equatorial seam and OS Real structure",
      "statementEN": "The old base inversion x->1/x lifts to r=(1/x,i y/x²),r²=h,rQr^−1=hQ^−1. The full group has32 elements,16 holomorphic and16 antiholomorphic. The anti coset has12 involutions,4 each dividing,nondividing and empty,plus4 order-four maps. The old eight-map hQkappa stratum was complete only in its subgroup. New dividing S=rkappa and hS project to the pointwise equatorial Real structure and are Q paired;old hQkappa/hQ³kappa remain the correct midpoint OS lifts. v519 explicitly requires distinct Real slots. The unlinearized NS spin class remains invariant under the full lifted action.",
      "scopeEN": "Complete exact census for the already marked base D4 and its actual central deck extension. No selection of a physical boundary circle or identification of pointwise equatorial circle with an OS half-space. Previous canonical pair applies only in its explicit old subgroup stratum.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:843f9927f24520fa136999ec",
        "source:e08293a0cc4b37a83d3a4d68",
        "source:df630651d804edc93ce64781",
        "source:8fae7a5ddff68a3ae79e2f2d",
        "source:e2a1bc7c46e6cb3cd1390223",
        "source:4659ed522720bc56274c2b8a",
        "source:4f5db69532bb5fe01897f3fc",
        "source:60183d300f4c618b038e9993"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-marked-equatorial-pullback-is-ramified-graph-not-smooth-seam-circle",
      "titleEN": "Full marked equator pullback is a ramified graph rather than a smooth seam circle",
      "statementEN": "For Gamma=|x|1,exactly p^−1(Gamma)=Fix(rkappa) union Fix(hrkappa). Two horizontal and two vertical square-torus ovals at1/4,3/4 intersect at the four ramification points. Full pullback is a connected torus graph V4,E8,F4,b1=5,with local valence4. The old single smooth NS circle has valence2,so a marked collar homeomorphism cannot identify it with this full pullback. Normalization gives4 circles,radial push-off2 components. Selection,smoothing or vertex domain does not follow from the bare lift. Retain both source/Real types.",
      "scopeEN": "Only literal geometric identification of the full ramified equator pullback with the old single smooth seam circle preserving local marks is excluded. No ban on proved pushforward,local field intertwiner or originally derived smooth readout. No freely chosen vertex scattering and no P1 no-go.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8fae7a5ddff68a3ae79e2f2d",
        "source:e2a1bc7c46e6cb3cd1390223",
        "source:b75ad6f8ce3898175afa2bf7",
        "source:4659ed522720bc56274c2b8a",
        "source:4f5db69532bb5fe01897f3fc",
        "source:60183d300f4c618b038e9993",
        "source:689ff4b765b83ed80db6a20a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:same-elliptic-szego-green-functional-has-all-word-free-rp-and-calderon-marginal",
      "titleEN": "Same elliptic Szego Green functional has full free RP and the Calderon marginal",
      "statementEN": "On actual NS NS E,S(t)=exp(−tB)(1+exp(−B))^−1 for0<t<1 is the Green operator of partial_t+B,B=−i partial_s,and equals the elliptic Szego kernel with prefactor i/(2pi). Pole,NS multipliers and H0(alpha)0 determine the identity. Both charged blocks factor for0<t,u<1/2:−S(−t−u)=X_t*X_u,S(t+u)=Y_t*Y_u. Fixed source-order/Clifford minus and anti-linear word reversal give RP of every free Gaussian CAR polynomial by Wick expansion. Time-slice covariance C=(1+exp(B))^−1 is precisely the labelled second Calderon marginal on the same annulus;the full graph is its canonical two-face purification. Q transports B to−B,C to1−C,u tou^−1 between cuts.",
      "scopeEN": "All-word theorem only for the expressly free Gaussian CAR source on the same elliptic carrier. No two-point argument for interaction,no equality of full graph and marginal state spaces,no primitive P1 measure/physical-time identification,no Hardy W8 replacement or EM/Quillen response. Reuses earlier positive-full-cover method,now on the actual square curve.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e1c45caa1d64782bdb6afa4c",
        "source:ac648ed7ba4b3f8d92b4eb0f",
        "source:fe3c17f29e4ae7a4a9a3ec96",
        "source:5c34f152d213ec5657634f4f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:elliptic-scalar-spin-pushforward-has-original-holomorphic-p2-anchor",
      "titleEN": "Elliptic scalar and spin pushforward has the original holomorphic P2 anchor",
      "statementEN": "Existing p_*O_E=O+O(−2) and p_*alpha=O(−1)+O(−1) give Vell=(p_*O_E/O)+p_*alpha=O(−2)+O(−1)^2. Thus rank3,degree−4,H0=0 and original splitting anchor a=(1,1,2) are exact. Both natural and P2 target residue triples have trace1 per mark,explaining the common degree. This relates actual holomorphic bundle isomorphism classes,not mere dimensions.",
      "scopeEN": "Bundle isomorphism class for the named tracefree scalar deck term plus whole untwisted spin pushforward. No original physical selection of this direct sum as flavor carrier or connection intertwiner. Keep previous normal spin-twist calculation distinct.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:68b0bafe3cf815aca7795810",
        "source:eb52ed9cf83b5371a8bf9291",
        "source:900652cae40b11928b781d47",
        "source:7b8e9d19c76fe3d8ffcea6dc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:natural-elliptic-anchor-connection-is-not-original-p2-cusp-connection",
      "titleEN": "Natural elliptic anchor connection is not the original P2 cusp connection",
      "statementEN": "Natural induced connection on Vell has residues0,1/2,1/2 at each ramification mark,monodromy1,−1,−1,polynomial(lambda−1)(lambda+1)^2,order2,trace−1. Original P2 target has residues0,1/3,2/3,spectrum1,omega,omega²,polynomiallambda³−1,order3,trace0. Thus no local connection intertwiner exists. Nonzero scalar twists preserve the repeated eigenvalue and cannot repair it. Natural direct sum is also reducible,while stated original <U,M0> is irreducible. v499 already separates the Z2 pillowcase from the Z3 weight cover. Another connection on the same bundle remains additional data to derive.",
      "scopeEN": "Excludes only the natural scalar/spin direct connection as the actual original P2 connection,including scalar-twist repairs. Does not exclude other originally derived nonabelian connections on the common bundle. Separate exact v117 matrix properties from numerical ODE identification.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:68b0bafe3cf815aca7795810",
        "source:eb52ed9cf83b5371a8bf9291",
        "source:900652cae40b11928b781d47",
        "source:7b8e9d19c76fe3d8ffcea6dc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-elliptic-gaussian-source-determines-full-quarter-current-functional",
      "titleEN": "Existing elliptic Gaussian source determines full quarter current functional",
      "statementEN": "The actual labelled Calderon/Szego covariance gives C_r=(1+exp(4pi(r+alpha)))^-1 and rho=Z^-1 exp(-4pi Halpha),Halpha=N+Q²/2+(alpha-1/2)Q per quarter. The full current functional is omega(Wf)=Theta_alpha(f0)/Theta_alpha(0) exp[-1/2 sum_m m coth(2pi m)|fm|²],with exact original BCH phase for every finite ordered Weyl word. Theta retains all charges. The explicit normal representation is left action on the rho^(1/2) cyclic space;its subspace for currents alone,the full HS space for full CAR. Previously reconstructed neutral vertex products give the same Wick field correlations in this state. Finite fermion determinants and grouped1/2/4/8 pair comparisons independently check the analytic derivation;normal and-OO are byte-identical.",
      "scopeEN": "Complete free current source on existing elliptic midpoint annulus under expressly given Gaussian quantization. b4pi belongs toHalpha,2pi to2Halpha,32pi toKalpha=Halpha/8;the same density operator. No physical temperature,primitive P1 measure,marked equator-graph/collar intertwiner,or interacting Wick theorem. Native unbounded limits retain old domains/smearing/normal-order hypotheses.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e8e683594febda1ab5930596",
        "source:aa757cb96e6e8503d992b3b1",
        "source:9d759cb012e4e441d4a3d647",
        "source:2e4e0d8741c9e5db47a592a8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:elliptic-current-state-differs-from-hardy-on-every-proper-current-interval",
      "titleEN": "Elliptic current state differs locally from Hardy even at Q0",
      "statementEN": "Exact telescoping of the actual Fermi covariance gives omega(J_-m J_m)=m/(exp(4pi m)-1),hence omega_Q0(J_-1 J_1)=0.00000348735451780811656...>0 versus0 in the old Hardy state. Q0 conditioning removes only the theta factor. Every nonzero real smooth mean-zero profile supported in a proper interval obeys omega_ell(Wf)/omega_Hardy(Wf)=exp[-sum_m m|fm|²/(exp(4pi m)-1)]<1. States thus differ already on every such local neutral current net under the unchanged original current dictionary.",
      "scopeEN": "Exact state witness whose positivity is not inferred from finite regulators. No exclusion of other originally derived P1 states,admissible subalgebras,or properly transported current/time maps. Q0 conditioning is a mathematical comparison,not claimed physical selection. Purification leaves these marginal expectations unchanged.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:67920b821f324b256fdba72f",
        "source:aa757cb96e6e8503d992b3b1",
        "source:2e4e0d8741c9e5db47a592a8"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:primitive-geometric-force-retains-coupled-reference-and-parity-variation",
      "titleEN": "Primitive geometry response retains reference split and parity mixing",
      "statementEN": "Exactly deltaA=-({h_plus,A}+{h_minus,B})/2 and deltaB=-({h_plus,B}+{h_minus,A})/2. Even/odd relative heat responses and chi variation are derived;moving measure,R,eta and domain terms remain. Original reference source-independence does not imply geometry-independence. Independent noncommuting matrix differentiation with odd profile and chi agrees to3.1e-92.",
      "scopeEN": "Typed variation identities;no Pin comparison identification with D_rel,no automatic odd-profile admissibility,no asserted infinite trace contract or quantum completion.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:primitive-reflection-split-and-controlled-geometric-variation",
        "premise:original-admissibility-and-graded-source-interfaces",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:167e9c78488d1d09746ddaae",
        "source:10191e7b4c6f5620c41212f3",
        "source:1154c19b6d10f9963edabc8b",
        "source:e993abf4a3f9753255772a5c",
        "source:ac74219b3331369a1aff4089",
        "source:f62e926f379876bbdf8e994d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:equal-finite-positive-heat-channel-values-do-not-fix-geometric-force",
      "titleEN": "Equal finite positive channel values do not fix geometry force",
      "statementEN": "Two strictly positive normalized four-atom heat measures have exactly the same F(0),F(A),F(B),S(0)=.8675847696814872,but opposite derivatives±.0027432473040925574 on the same common scale path. Rational null relations,prime logarithms and an interval certificate prove this beyond rounding. Recursing equal endpoint data cannot reconstruct the difference. Finite stationarity for every positive heat profile forces equal nonzero squared spectra and a constant scale orbit. The already fixed scalar transferT(q)=(1-q)^(-5/4)keeps its unique derivative;the actual geometry insertion and complete source terms remain required.",
      "scopeEN": "Counterexample only to force selection from finite endpoint values and heat positivity. No replacement P1 or exclusion of a fully specified transfer,dynamical chi,quantum measure or restricted geometry paths.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:finite-positive-heat-channel-endpoint-selection-test",
        "premise:typed-source-structures",
        "premise:historical-sf-sector-action-and-relative-normalization"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:167e9c78488d1d09746ddaae",
        "source:10191e7b4c6f5620c41212f3",
        "source:1154c19b6d10f9963edabc8b",
        "source:8067142a64f5a6a222687b05",
        "source:a7dde74a7b4eb98aa2e3223c",
        "source:ba664f1241d0ad63679209f2",
        "source:41250acad9fae15e9acdc927"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:elliptic-ns-spin-trace-has-complete-global-quarter-kernel",
      "titleEN": "Complete elliptic NS spin kernel splits globally into quarter pair",
      "statementEN": "Partition{1,−1}|{i,−i} is exactly the supplied Q fixed nontrivial spin-line class by divisor D_A and H0 test. With g⁴=(x²−1)/(x²+1),S_alpha=sqrt(dx dz)[g(x)/g(z)+g(z)/g(x)]/[2(x−z)] is the actual normalized Szego kernel. Its complete two-sheet matrix has constant unitary diagonalization to diag(g(x)/g(z),g(z)/g(x))/(x−z),without an undetermined elliptic remainder. dlogg=x dx/(x⁴−1) has alternating residues±1/4;four central spin meridians square to−I and multiply toI. Q exchanges both character lines. Pole,spin divisor,conjugate-sheet cancellation and H0(alpha)0 prove the global identity;theta3 numerical checks are only diagnostics.",
      "scopeEN": "Exact holomorphic half-form Green kernel on named four-mark C2 source. Uniqueness concerns underlying spin-line class,not an extra Q linearization phase. No automatic positive equal-time CAR covariance,smooth quarter circle or physical time/action normalization. Raw coefficient monodromy remains order2.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5530cb4b89e99e80d6ed963b",
        "source:32dd6762e6d1ecedf45f8f2a",
        "source:a6880d0a804fe2d42c5ac906",
        "source:c48ec4f6cfe66f05cc73c2a1",
        "source:ff16c39195a77d03f6418a0d",
        "source:6c41c32c5848984dd3936eaa",
        "source:3ec643623a73dc474e87c68d",
        "source:d1c43c1e4106d8e636ae54c2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-induced-ramified-resolutions-do-not-select-quarter-circle-domain",
      "titleEN": "Actual ramified resolutions select no single quarter-circle operator",
      "statementEN": "Supplied detours give T_out=I,T_in=P,without a free U2 choice. Common raw flat meridians(P,−P,P,−P) split into two characters exchanged by Q. Both radially pulled-back scalar operators have spectrumZ with multiplicity2. Literal ramified pullback is(1+z²)partial_z/(2z);smooth ambient continuity has only one isotropic trace dimension instead of maximal2. Moving-tangent spin phases±iP are not a circle boundary condition. No single deck character remains Q invariant. A closed real trace with C_base=T C_E T*,0<=C_base<=I still needs proof.",
      "scopeEN": "Excludes only automatic single smooth quarter domain from named raw flat connection and ambient continuity. No ban on an originally derived other real trace,joint boundary source or field map. Full holomorphic kernel in F1 remains established;earlier RP on a smooth annulus cut remains separately valid.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:db67cdff30159fdd3711b939",
        "source:476d91ccb1ad4b78e1f8e3de",
        "source:53a14b92efc4e1fd959bf516",
        "source:5530cb4b89e99e80d6ed963b",
        "source:32dd6762e6d1ecedf45f8f2a",
        "source:6c41c32c5848984dd3936eaa"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-native-and-fermat-c3-carriers-do-not-identify-marked-v117-pair",
      "titleEN": "Fixed native and Fermat C3 carriers do not supply the marked v117 pair",
      "statementEN": "Fixed P_nat and v117 M are unmarked regular C3 modules,but ZP_nat=P_*Z together with ZQ=QZ or ZG=GZ has rank9 and only Z0. Natural Fermat deck has H10 multiplicities(0,2,1),H1(0,3,3);scalar cubic twists never give(1,1,1). Existing C12 Phi12 bridge has rank4 with(0,2,2). Same abstract C3 class or existing rank4 intertwiner does not replace a common marked rank3 dictionary.",
      "scopeEN": "Excludes only explicitly tested fixed carriers and marks. No exclusion of all native E8 modules,other original transports or existing exact C12 theorem. P_nat/Q comparison is a named ansatz,not an assumed physical module identity.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:fixed-three-slot-permutation-and-original-compiler-comparison",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f4b141f95cba11a6f71040a3",
        "source:c69ae907609b6569507a8522",
        "source:a974f3bc8c57e469cd7d0bdd",
        "source:4e07c45400d403da9601f369",
        "source:1d9149a9f539a56f467d2549"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:theta-square-modular-pair-reconstructs-v117-with-distinct-geometric-q",
      "titleEN": "Modular theta-square pair reconstructs v117 with a different geometric Q mark",
      "statementEN": "Standard theta squares give raw group96,central mu4 and projective PSL2(Z4)=S4. Spin labels alone see onlyS3. For UTheta=−i A_T,MTheta=i A_S A_T, X=[[-1−i,0,0],[0,i,−i],[0,1,1]]/sqrt2 satisfies exactly XUThetaX*=U_v117 and XMThetaX*=M0_EXACT. Same X intertwines both generators;normalized group has24elements. Geometric Q:z->iz at tau=i is modularS with projective order2 and eigenmultiplicity1+2,whereas U_v117=T has order4 and three distinct eigenvalues. Isotrivial v493 supplies no elliptic T path. Origin needs an actual level4 family/sewing transport with distinct spatial mark and derived phase section.",
      "scopeEN": "Exact joint representation equivalence after expressly named phases. No original P1/P2 origin proof or identification of spatial with moduli monodromy. New moduli path is an additional changed premise and specifically does not repair the fixed Q identification.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:theta-square-modular-transport-with-distinct-geometric-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0528722ca9cec0912e620f8e",
        "source:8a8a993b75346bf1c6b1341f",
        "source:6c41c32c5848984dd3936eaa",
        "source:3ec643623a73dc474e87c68d",
        "source:d1c43c1e4106d8e636ae54c2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:archived-d4-puncture-formula-fails-and-existing-v117-repairs-existence",
      "titleEN": "Archived D4 puncture formula fails; existing v117 repairs existence",
      "statementEN": "Literal TFPT45 archive section004 assigns D,PDP^-1,P²DP^-2 and their inverse product as fourth monodromy. Printed matrices have triple productI,so fourth monodromyI instead of cusp spectrum(1,omega,omega²). P³I does not implement a quarter turn. Unchanged v117 gives exact existence repair M_k=U^kM0_EXACTU^-k,k0..3 with productM_k=I and every required local class. This does not prove uniqueness from local spectra,det and abstractD4 alone. Active TFPT2 already states bare Z4 nonrigidity and global parabolic additional data. Two independent original-source reviews separate archive defect from current theory.",
      "scopeEN": "Concrete mathematical erratum of archived TFPT45/42 formula. Preserve originals. Exact v117 representation remains valid;analytic ODE match and later anchor/resonance premises retain their own status. No blanket P2 exclusion or silent paper edit.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4e07c45400d403da9601f369",
        "source:1d9149a9f539a56f467d2549",
        "source:f4b141f95cba11a6f71040a3",
        "source:c69ae907609b6569507a8522",
        "source:a974f3bc8c57e469cd7d0bdd",
        "source:3ec643623a73dc474e87c68d",
        "source:d1c43c1e4106d8e636ae54c2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:geometric-square-clock-is-not-theta-v117-quarter-generator",
      "titleEN": "Geometric square clock is not the modular v117 quarter generator",
      "statementEN": "On actual tau=i torus,Q:z->iz induces modularS on theta squares. It has projective order2 with eigenvalue ratio1:1:−1. U_v117 and its exactly conjugate normalizedT have projective order4 and three distinct eigenvalues. Thus no invertible linear or projective intertwiner sendsQ toU_v117. Positive joint dictionaryT->U andST->M remains valid.",
      "scopeEN": "Excludes only unchanged geometricQ mark in actual theta-square representation. No refutation of an originally derived family/sewing transport explicitly retaining distinct paths and central phases. No general exclusion of elliptic flavor sources.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:theta-square-modular-transport-with-distinct-geometric-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0528722ca9cec0912e620f8e",
        "source:8a8a993b75346bf1c6b1341f",
        "source:6c41c32c5848984dd3936eaa",
        "source:3ec643623a73dc474e87c68d",
        "source:d1c43c1e4106d8e636ae54c2"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:canonical-conformal-boundary-trace-fixes-existing-elliptic-cauchy-state",
      "titleEN": "Canonical conformal boundary trace preserves the existing elliptic Cauchy state",
      "statementEN": "The conformal Dirac law and boundary density give V_sigma=e^((d-1)sigma/2), which exactly cancels the harmonic-spinor factor:V_sigma Tr psi_sigma=Tr psi0. Thus V_sigma P_sigma V_sigma*=P0 for the orthogonal closed Cauchy-data projection. Both marked faces and regional supports are preserved. In common bulk L2 the required trace is T_sigma=e^-sigma_boundary/2 Tr for Dtilde=e^-sigma/2 D e^-sigma/2. Quarter/fold are transported afterwards. The existing labelled marginal and full free current source are identical for all compatible metrics on the same complex curve. An unweighted raw trace produces an exactly detected spurious covariance change.",
      "scopeEN": "Analytic smooth massless conformal Cauchy-data theorem, not a regulator-limit claim. The free state consequence uses the existing CAR quantization premise. Newly metric-defined stress, spectra, resolvents, APS projections, full marked graph traces, P1 origin and physical time are not identified; previous nonzero Schur/sea responses remain intact.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures",
        "premise:same-marked-elliptic-annulus-massless-conformal-metric-family"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a1d32ea509c78e7b29ad8496",
        "source:90e66d31973d3edf533bd785",
        "source:468a3582e7b6a5ab5ef2a6b4",
        "source:dba6b332a389db3ae297237c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:conformal-factor-averaging-preserves-given-free-boundary-wick-words",
      "titleEN": "Averaging the conformal factor preserves the given free boundary Wick words",
      "statementEN": "After the derived boundary transport, each given conditional free CAR word on the same marked curve is independent of sigma. Its identical normalized source functional therefore factors out of any source-independent integrable total geometric weight of nonzero normalization, including determinants, reference, Jacobian and anomalies. The connected fermion four-point defect stays exactly zero, as do all higher Wick rules. No particular geometric measure is selected or discarded. Pure conformal geometry variance is therefore not evidence of an interacting boundary source. With other varying data, integrating out this factor may change their effective weight; their covariance requires a separate test.",
      "scopeEN": "Only the given conditional free quantization and correctly transported CAR observables; no Gaussian theorem for original S_prim/P1 measure and no assertion that connected current correlations vanish. Z_ref[0] cancels in Z_rel[J]/Z_rel[0], not automatically from geometric forces. The next decisive four-field test requires an original covariance-changing variation or higher fermion vertex.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures",
        "premise:same-marked-elliptic-annulus-massless-conformal-metric-family"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a1d32ea509c78e7b29ad8496",
        "source:90e66d31973d3edf533bd785",
        "source:468a3582e7b6a5ab5ef2a6b4",
        "source:dba6b332a389db3ae297237c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:retained-seam-defect-has-derived-causal-geometric-response-with-contact",
      "titleEN": "Retained seam defect has a derived causal geometry response with contact",
      "statementEN": "On the same source R_h(s,t)=Tr(DeltaC_s(t)partial_sD_s) and exactly partial_sR_h|0=k<h²>+integral_0^t chi_hh. Full mode sum weights are(E±k)^3/(16E),chi(0)0,chi_prime(0)=-k<h_prime g_prime>;it converges for smooth profiles. At t1 the retained collar-preserving probe gives contact+.3861727422,causal part-.4054682615,total-.0192955193. Direct commutator error<3.6e-13,independent full-family derivative after extrapolation<3.3e-8. Omitting contact gives error.386. Actual400-step machine computes the same relative response;129/257-mode difference<5.4e-7.",
      "scopeEN": "Exact relative response form of the given source;no assertion of separately defined infinite vacuum quadratic operators or geometry-change Fock implementers. Long curves finitely tested. No identification with primitive action variation,selected history,native quartic words or physical time.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:retained-zero-branch-defect-on-common-pin-geometric-history",
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:given-pin-source-conformal-normal-geometry-probes",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:551fad346a5c2cfef41ab80c",
        "source:bfd9f5e2a1df9579bbcbbd86",
        "source:f4223a0d11d7d5b2af0f3b42",
        "source:4ac005d726ae5c59a76865c2",
        "source:484d1276c7a740674c56927f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:same-final-pin-geometry-retains-history-while-relative-index-factor-is-fixed",
      "titleEN": "Same final Pin geometry retains history with an unchanged index factor",
      "statementEN": "For the two actual commonly evolved states P_t=U C0 U*,Q_t=P_t+Pi_t and exactly(I-zQ_t)(I-zP_t)^-1=I-zPi_t,determinant1-z,without requiringC_t-C0 inL1. After50 pulse steps and50 steps with exactly restored D0,the t1 relative readouts differ:no pulse-.4739486483,positive+.01-.4701253569,negative-.01-.4780397086. Recursion matches direct evolution to4.8e-14. Causal kernel predicts pulse derivative.3956885828,finite symmetric difference.3957175880. Complete historical sector weight remainsQ_full=e^-2alpha R(g,alpha);its geometry response at fixed alpha comes fromR and is not calculated by the index.",
      "scopeEN": "Exact transported pair identity on the full given source;pulse values from a finite129-mode run with chosen duration/amplitude. No cyclic cutoff shift as an index proof. Full P1 measure/reference Ward identification remains open;the relative CAR response is not substituted into delta logR without proof.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:retained-zero-branch-defect-on-common-pin-geometric-history",
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:given-pin-source-conformal-normal-geometry-probes",
        "premise:typed-source-structures",
        "premise:historical-sf-sector-action-and-relative-normalization"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:551fad346a5c2cfef41ab80c",
        "source:bfd9f5e2a1df9579bbcbbd86",
        "source:4ac005d726ae5c59a76865c2",
        "source:f8fb3b006002c8b49f2252fe",
        "source:d8fa7eb1eba8c44fc9ece585",
        "source:b7128221ebbb69c815860676"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-projector-covariance-and-positivity-force-all-car-words",
      "titleEN": "Full projection covariance and positivity force all CAR words",
      "statementEN": "For an arbitrary positive CAR state with full covariance C=P=P*=P²,GNS zero norms force a(f)Omega=0 onkerP and a*(f)Omega=0 onranP. CAR normal ordering uniquely determines all finite words and hence the full state as the pure Fock/Slater state omegaP. Quasifreeness,gauge invariance and zero anomalous pairs follow instead of being assumed. This is the charged application of Araki1970 Lemma4.3. A positive ensemble mean with projection covariance P forces that same covariance and state almost surely;complex weights are outside this ensemble argument.",
      "scopeEN": "Exact infinite CAR-state theorem under actual full projection covariance,not a new general CAR theorem and requiring no extra Gaussian premise. GNS uniqueness gives no implementability in an arbitrarily prechosen old Fock representation. A geometric Cauchy projection is not automatically presented as a physical covariance;P1 and its real joint field carrier remain to be identified.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:positive-joint-car-source-tested-against-full-geometric-projector",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d8cdf210465eadc80591e139",
        "source:9eb1c9ffa08477c6c8b58ddf",
        "source:111f994133b65773c1a893f7",
        "source:79ead05a614011c7e0145e7b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-two-face-projector-reduces-free-source-test-to-cross-coherence",
      "titleEN": "Actual two-face projection reduces the free-source test to joint coherence",
      "statementEN": "The original closed annulus graph has P_A=[[I-C_A,X_A],[X_A,C_A]],C_A=(I+exp(2WB_Sigma))^-1,X_A=(2cosh(WB_Sigma))^-1 and X_A²=C_A(I-C_A). Its full kernel is a projection,a single face is not. An actual positive P1 CAR source with this joint kernel would therefore inherit all previous free current/Weyl/native-composite correlations under the old domain/subtraction dictionary without an extra Gaussian premise. The missing physical cross equation is omegaP1(aL*(f)aR(g))=<f,X_Ag>. Three positive source controls share the same face marginals;dephased and product states even share the full diagonal covariance but have four-point values0 andp(1-p). On an actual finite P reducing block,delta=Tr[(I-P)C]+Tr[P(I-C)] gives ||rho-rhoP||1<=2sqrt(delta) for arbitrary positive states. All256 ordered four-field words are independently checked;normal/-OO byte-identical.",
      "scopeEN": "Sufficient identification test for the existing chiral scalar two-face source;no physical purification freely selected from C_A,no complete Dirac vector source or new time. Nonprojection marginals still require higher-word comparison. Quantitative error only inside the tested reducing block;no global control from finite samples. Original P1 measure,joint closed real graph trace/domain and physical cross equation remain open. Prior four-field requirement is sharpened only for the full projection case.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:positive-joint-car-source-tested-against-full-geometric-projector",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d8cdf210465eadc80591e139",
        "source:9eb1c9ffa08477c6c8b58ddf",
        "source:111f994133b65773c1a893f7",
        "source:79ead05a614011c7e0145e7b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:retained-marked-quarter-compiler-has-no-local-geometric-wick-correction",
      "titleEN": "Retained marked quarter compiler has no local geometric free-Wick correction",
      "statementEN": "Four marked branch points have one complex modulus lambda. The original cyclic Q acts by lambda to1/lambda;at lambda=-1 its tangent action is minus1,with no invariant modulus. The explicit curve family y²=x⁴+a x²−1 confirms this by F_a(ix)−F_a(x)=−2ax². Thus rho nonzero is excluded from the existing supplied P1\\mu4 parity compiler. Combined with the proved correct conformal boundary trace,fixed spin/connection and given free quantization,the whole normalized transported Cauchy/Wick source is unchanged by nearby compatible geometry changes. Source-independent averaging adds no connected fermion four-point correction. Existing clock-given square rigidity is reused;its primitive physical derivation is not claimed.",
      "scopeEN": "Local theorem in fixed marked C2 and massless free annulus with fixed spin/connection,canonical boundary transport and source-independent integrable weights. No assertion for full ramified equator graphs,other bundle insertions,bulk sea response or primitive P1 admission. QGEO.REALIZE.01 remains C/O.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:same-marked-elliptic-annulus-massless-conformal-metric-family",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0e58b51ad74ce5e802d7d411",
        "source:206497dadfc169e6635727ec",
        "source:4f0832236cdf73348a7d67cf",
        "source:3dfcdcab44665666eacf5737",
        "source:a1d32ea509c78e7b29ad8496",
        "source:16db7042fd884c205ee31d24"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:changed-elliptic-modulus-has-derived-cauchy-response-and-neutral-fourfield-variance",
      "titleEN": "Changed elliptic modulus gives derived boundary response and conditional neutral four-field variance",
      "statementEN": "Under the expressly changed modulus-family premise,both real structures and free Moebius quotient persist,but Q exchanges rho and minus rho. Actual primitive periods give I(rho)=2K((2−rho)/4),r=I(−rho)/I(rho),W=r/2,tau=ir and r_prime(0)=2Gamma(3/4)²/Gamma(1/4)². Free boundary covariance is c_n,alpha=[1+exp(4pi r(n+alpha))]^-1,alpha1/4,3/4. Its first variation is fixed and trace class;the original global holomorphic spin kernel independently confirms a nonzero variation. For actual lowest opposite NS modes,any positive shared geometry law gives exactly kappa4=−Var(c). Diagnostic averaging at rho plus/minus.1 yields−8.133849897e−6 with positive normalized two-mode density. In the retained original fixed-Q compiler rho0 disables this mechanism.",
      "scopeEN": "Exact conditional free Cauchy/CAR family calculation and finite70-digit checks;not an admitted original compiler branch,derived P1 law or variance,common physical time or spacetime interaction. ModularS differs fromT;complex structure differs from flat U1 Quillen moduli;holomorphic spin kernel is not directly positive boundary covariance.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:real-marked-elliptic-complex-structure-family-with-transported-spin",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0e58b51ad74ce5e802d7d411",
        "source:206497dadfc169e6635727ec",
        "source:4f0832236cdf73348a7d67cf",
        "source:9347b82e833c7db9fa37d992",
        "source:476cfa85bca433e4a5611980"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-equatorial-half-form-trace-fixes-orthogonal-hardy-range",
      "titleEN": "Actual equatorial trace fixes orthogonal Hardy range",
      "statementEN": "Actual measure is |dz|=|dx|/(|c||y|). Closed half-form trace is L2 unitary to |dx|. The two bounded Cauchy idempotents gP_Hg^-1 and g^-1P_Hg, |g|²=|tan(theta)|^1/2, have exactly closed range H² by outer cyclic factors. Their orthogonal range projector is P_H⊕P_H. Integrable branch singularities do not remove H1 vertex coupling. Intrinsic boundary generator has variable speed 4K(-1)sqrt(|sin2theta|), failing constant base-winding Ward relation.",
      "scopeEN": "Actual full equatorial trace for supplied metric. No equality with old quarter state, positive annulus KMS state or physical time. Preserve smooth annulus results and original W8 Hardy comparison.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:actual-elliptic-half-form-l2-trace-on-full-marked-equator",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bf00ff528bee75bb35c73631",
        "source:008323e5ea3fcb2b0b47a30c",
        "source:dfef15f701461ce339559ba9",
        "source:d97f536a79cd679b5f70f706"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-holomorphic-quarter-cauchy-idempotents-are-not-positive-car-covariances",
      "titleEN": "Holomorphic quarter Cauchy idempotents are not positive CAR covariances",
      "statementEN": "In actual L2 measure gP_Hg^-1 and g^-1P_Hg are not self-adjoint. Range and kernel have exact nonzero overlap integral |tan(theta)|^1/2 exp(-2i theta)dtheta/(2pi)=-1/sqrt2. An additionally chosen channel metric could orthogonalize them but would change the source.",
      "scopeEN": "Excludes only unchanged oblique idempotents as CAR covariance in actually induced measure. Orthogonal analytic range is constructively fixed; no general exclusion of positive elliptic sources.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:actual-elliptic-half-form-l2-trace-on-full-marked-equator",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bf00ff528bee75bb35c73631",
        "source:008323e5ea3fcb2b0b47a30c",
        "source:dfef15f701461ce339559ba9",
        "source:bc188f0e12526556332711a9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-equatorial-checkerboard-free-algebra-fails-fixed-reflection-positivity",
      "titleEN": "Full free equatorial algebra fails one fixed reflection",
      "statementEN": "The two components of p^-1(|x|<1) lie on opposite positive and negative time halves for each fixed S or hS reflection. Actual NS Green kernel gives a globally U1 neutral even normal-ordered word :barpsi(f+)psi(g-): with strictly negative reflected norm for compact supports in both faces. Analytic interior witness is independent of boundary and vertex choices.",
      "scopeEN": "Only full globally neutral even free CAR algebra on the union under a fixed reflection. No automatic claim about local gauge invariance in original admissible algebra. Separate parity/gauge per face is additional data. Positive annulus source remains valid.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:actual-elliptic-half-form-l2-trace-on-full-marked-equator",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:44cfac9c05ff0e446798290c",
        "source:3fe6ae72d31ffef5f72c70a6",
        "source:0d557f006cf175e563f7a782",
        "source:cada94c77beaa070ac369608"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:genuine-d4-orbifold-branch-has-unique-irreducible-v117-class",
      "titleEN": "Genuine D4 orbifold branch has unique irreducible v117 class",
      "statementEN": "J_D4=1/2-(x⁴+x^-4)/4 generates C(x)^D4. For genuine unitary SU3 descent on(infinity,2,4), c=diag(1,i,-i), regular cubic M=a², four half-meridian branches have traces0,2,2omega,2omega². Trace2 is impossible; complex branches are reducible. Unique survivor is a³=1,p=(1/2,1/4,1/4), the v117 matrix orbit. For genuinely linearized stable parabolic object canonical MS descent follows from uniqueness of adapted metric. Treat concrete A0* connection separately.",
      "scopeEN": "Complete theorem in exactly specified genuine D4 class. Same abstract matrix class does not identify different marked base paths. Do not infer full D4 connection symmetry from C4 rotation. No physical P1 origin.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:genuine-d4-unitary-stable-parabolic-orbifold-descent",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7792746d6b33b73d8100e216",
        "source:1df4c9d91ad5b8ed8570d79b",
        "source:39cda68d2987ff3ecc1330b2",
        "source:72e098f0e58a4eef4d5cbfb5",
        "source:3db6d78cad5808925d865061",
        "source:dfef15f701461ce339559ba9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:wall-weight-additivity-does-not-exclude-stable-v117-parabolic-bundle",
      "titleEN": "Wall weight additivity does not exclude stable v117 bundle",
      "statementEN": "Section011 row-sum argument assumes complete flag splitting along three global BG summands. W_wall is then direct sum of three parabolic degree-zero lines, a different reducible wall point. Four exact v117 meridians generate irreducible A4 order12; compact kernel cover has genus5. H0(E)=V^A4=0 and degE=-4 give exactly O(-2)+O(-1)^2. MS object is stable. Equal weight sets do not identify relative flags.",
      "scopeEN": "Excludes universal wall forcing and identification of W_wall with irreducible v117. Declared split A0* raw-flag test is separately exactly stable; without concrete Levelt/Birkhoff lattice its affine flags are not automatically ODE Deligne extension. No paper edits.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e72287ad74da5daf8fc9a054",
        "source:cfc6badd2359a45f369f5f46",
        "source:6da3b6bce13fa3a06a7a58d6",
        "source:0000da0130762e2f30bb5ed2",
        "source:df547eea96f9c100c0f90ab9",
        "source:e8481567dec474ca379ce174",
        "source:54256a508e1557e0f2daa4b7",
        "source:d4cbf56e2fd181c96b997946",
        "source:9ac525ec658464cb29809406"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:recovered-september-c4-triangle-closes-original-a0star-monodromy",
      "titleEN": "Recovered September proof closes original A0* monodromy",
      "statementEN": "The28Sept synthesis already contains analytic identification of unchanged v117 ODE: t=z⁴ and diag(1,z,z³) give three Fuchsian points of orders4,3,2; sole infinity resonance coefficient is exactly zero. Alternative frame diag(1,z,z^-1) gives semisimple exponents -1/2,0,-1/2 without resonance. Image is faithful S4 rotation representation; positive t0 meridian is U^-1. Marked pair is exactly v117 up to simultaneous basis change and remaining diagonal basis-sign convention. Diagonal0,-i/2,+i/2 follows analytically. Original four meridians have A4 image; U extends to S4. No new ODE fit needed.",
      "scopeEN": "Reused older analytic proof independently checked now. Closes ODE group identification incorrectly treated again as numerical-only. No new origin derivation selecting A0*, no complete field/state/time isomorphism. Physical gates remain open.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:80e93dc0e2701afc4efc1978",
        "source:c10ff6702f10df1c451a760e",
        "source:feab4dca4fbe43c1e99ffa0e",
        "source:7bb98421226ad6090801d9ca",
        "source:2ae019675e303e8522b39416",
        "source:c41d41ebfb66303a15bafa3d",
        "source:e7d30943f46a34056b49990d",
        "source:781ff295d6b7d38cce7173b9",
        "source:6733104c52e18bdb5e1088d1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-a0star-connection-does-not-have-rational-base-inversion-lift",
      "titleEN": "Actual A0* connection has no rational base-inversion lift",
      "statementEN": "For A0* local exponent analysis forces every rational z->1/z lift into finite polynomial ansatz. Transformation equation G prime=A(z)G+z^-2G A(1/z) has only zero solution. Actual C4 quotient connection has isotropy orders4 and2 at0 and infinity, exchanged by base inversion. It is not marked D4 pullback with orders4 at both, despite abstract S4 generator pairs occurring.",
      "scopeEN": "Only literal base inversion of unchanged A0* connection. Actual finite C4 monodromy is positively closed by old triangle proof. No exclusion of other base maps or other parabolic D4 objects. Same number or abstract group does not replace common clock marking.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d5bdd4d5a13e2c6d9bcf7935",
        "source:a52bd679d7c85f5e6592508f",
        "source:80e93dc0e2701afc4efc1978",
        "source:c10ff6702f10df1c451a760e",
        "source:feab4dca4fbe43c1e99ffa0e",
        "source:7bb98421226ad6090801d9ca",
        "source:2ae019675e303e8522b39416"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-v117-sign-lines-are-negative-weierstrass-triangle-two-torsion",
      "titleEN": "Actual v117 sign lines are two-torsion of negative Weierstrass orbit",
      "statementEN": "On C:eta²=1-w⁶ the correct lines are L_a=O(q_a-q_(a+1)),q_a=-omega^a. Kummer roots h_a²=(w+omega^a)/(w+omega^(a+1)) multiply to1. V4 cover Zq of w sphere ramifies only at three q points and has genus0. Actual quotient coordinate t=((1+w³)/(1-w³))² gives degree24 with uniform ramification orders4,3,2 over0,1,infinity. Thus Zq is regular S4 triangle cover of same marked v117 class. Fiber product with z⁴=t has ordinary A4 image; intersection field is C(z²), since S4 has no C4 quotient. Over C this is exactly unramified genus5 V4 kernel cover. Hence pi*E_v117 decomposes into three expressly written unitary two-torsion lines. Equality follows from actual Kummer cover and target marks, not fitted target matrices.",
      "scopeEN": "Exact flat coefficient lift with actual marked finite monodromy. No intertwiner of primitive CAR fields,state,positive time or support; no implicit selection of joint C2 NS field linearization. Older source already supplied curve and point intertwiner; line identification is separately proved here.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c1ff3dffc1d1a7f7e0ebc182",
        "source:ab7e7bac283bb079f3e8cfbc",
        "source:652d204a0e190503bed18988",
        "source:a3b534357d1ce6a5c52d0452",
        "source:2e7d4dec153b4fbf3d6bf0cf",
        "source:e62c9c946924591c99c5cf74",
        "source:7e2dbc123dd39d5ab8f6a284",
        "source:09348dcde2bb85e34c614204",
        "source:722d8a530b77d3baa4107eee"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:antipodal-and-positive-sign-packets-fail-actual-marked-v117-ramification",
      "titleEN": "Antipodal and positive sign packets fail actual v117 marking",
      "statementEN": "Initial natural packet O(p_a-q_a) is nontrivial unramified V4 two-torsion on C, but v_a=z u_a gives V4 field over w sphere ramified at all six Weierstrass points, genus3. Actual target orders are4,3,4 rather than4,3,2. Positive triangle O(p_a-p_(a+1)) gives2,3,4 with fixed target marks. Both are different marked connections. Comparing imported T and B_k matrices would have been circular; actual function field and ramification test decide.",
      "scopeEN": "Excludes exactly these packets for fixed v117 clock and target marking. Does not refute their mathematical existence. Equal dimension,A4 group and genus5 alone do not identify a flat source map.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c1ff3dffc1d1a7f7e0ebc182",
        "source:ab7e7bac283bb079f3e8cfbc",
        "source:652d204a0e190503bed18988",
        "source:a3b534357d1ce6a5c52d0452",
        "source:2e7d4dec153b4fbf3d6bf0cf",
        "source:e62c9c946924591c99c5cf74",
        "source:7e2dbc123dd39d5ab8f6a284",
        "source:09348dcde2bb85e34c614204"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:common-cyclic-twelve-cover-does-not-trivialize-v117-unramified-sign-lines",
      "titleEN": "Common cyclic twelve cover does not trivialize v117 sign lines",
      "statementEN": "Common cyclic fiber-product cover D:h¹²=(z²-1)/(z²+1) transports g=h³ and w=h⁴. Over C it is h⁴=w, totally ramified at two simple zeros and two simple poles of w. Its unique quadratic intermediate h² with square w is also ramified. Therefore D neither contains nor trivializes any of three nontrivial everywhere unramified actual v117 lines L_a. Geometric Q lift (z,h)->(iz,i/h) transports underlying curves but does not replace missing coefficients or a common field state.",
      "scopeEN": "Only specified cyclic mu12 root cover as automatic sign or field completion. Older general C12 monodromy/intertwiner contract is unchanged. Does not exclude other common higher covers or actual transported field maps.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c1ff3dffc1d1a7f7e0ebc182",
        "source:ab7e7bac283bb079f3e8cfbc",
        "source:652d204a0e190503bed18988",
        "source:a3b534357d1ce6a5c52d0452",
        "source:2e7d4dec153b4fbf3d6bf0cf",
        "source:e62c9c946924591c99c5cf74",
        "source:7e2dbc123dd39d5ab8f6a284",
        "source:09348dcde2bb85e34c614204"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:negative-sign-packet-has-source-selected-quarter-clock-lift",
      "titleEN": "Negative sign packet carries original quarter lift",
      "statementEN": "Original geometric lift Q(z,w,eta)=(iz,w^-1,-i eta/w³) preserves q orbit and satisfies Q²=(−z,w,−eta). Kummer roots obey Q*h_a=epsilon_a omega/h_(-a-1),product epsilon_a=1. Actual local marked inertia t proportional s⁴ at q_0 forces epsilon_0/epsilon_2=−1 and epsilon_1=−1. The two inverse lifts are V4 frame-conjugate. Determinant-one coefficient representation fixes the remaining line with+1,square has two minus signs,spectrum1,i,−i. Explicit simultaneous basis change identifies U; positive quotient monodromy is contravariantly U^-1. C4 equivariance of existing coefficient lift is closed.",
      "scopeEN": "Equivariant flat coefficient lines of unchanged v117 source with actual clock direction. No selection of CAR field quantization or state,no identification of modularT with geometricQ,no new base inversion symmetry.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ba2e3cf072f3c6c8a083e8ba",
        "source:127e6097098a88b0253422f1",
        "source:652d204a0e190503bed18988",
        "source:a3b534357d1ce6a5c52d0452",
        "source:722d8a530b77d3baa4107eee"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-root-and-sign-lines-have-minimal-degree48-common-cover",
      "titleEN": "Original root and sign lines have minimal common degree48 cover",
      "statementEN": "For D:H¹²=f(z),w=H⁴,g=H³ and actual unramified V4 cover Yq/C,function fields are linearly disjoint over C. D/C is totally C4 ramified at four points and has no nontrivial unramified intermediate. X=Norm(D times_C Yq) has degree16 over C,degree48 over z,group C12 times_C3 A4 isomorphic A4 times C4,genus41. Minimality holds among all connected common covers:g and w determine H=w/g;trivializing three lines forces Yq. Common C3 quotient is identified once. Accepted quarter lifts combine diagonally with order4.",
      "scopeEN": "Minimal common holomorphic carrier of expressly given root coordinates and flat coefficient lines. No new physical worldsheet,CAR state or full compiler field map. Geometric clock here inverts deck generator;it is not separate commuting compiler order12 clock.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5d8f2e210756ce796c5ed8c7",
        "source:330e842566bdeb2d8e8db45f",
        "source:92f196ed33597901f29c29e4",
        "source:b6a3e2c63fa491aa260a880b",
        "source:d56dee2abb8290249d03e894",
        "source:c1e5b63beca16b1ff0b4b1c1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:given-elliptic-flat-connection-family-has-explicit-quillen-norm-and-two-holonomies",
      "titleEN": "Given elliptic connection family has explicit Quillen norm and both holonomies",
      "statementEN": "Actual free elliptic operator has L_z spectrum4pi²[(m+.5+v)²+(n+.5+u)²] and relative zeta determinant N(z)=exp(-2pi u²)|theta3(z|i)/theta3(0|i)|². Relative heat integration of the same spectrum independently checks the standard torus identity at three nonsingular60-digit probes. Positive theta line has A=2pi i u dv,degree+1 and holonomies exp(-2pi i u),exp(2pi i v),including endpoint descent. Null locusz(1+i)/2 is retained;no global nonvanishing section. At the original point Hess logN=-2piI,and the vectorlike doubled real action has HessGamma=2piI,the chiral modulus half. This supplies an explicit continuum object on this given carrier;physical P1 and v472 comparison remain open.",
      "scopeEN": "Known Quillen torus calculation on the given mathematical carrier,with actual relative heat and line response. No new general theory of nature. Spacetime curvatureF_A0;parameter curvature/holonomy susceptibility is neither local4Da4 nor SMb1. No P1 law,joint positive CAR cross kernel,physical time or Berry-to-continuum limit.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-square-nsns-elliptic-unit-charge-flat-connection-family",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:19db256c3dd54fa62ffc0e23",
        "source:e53f136b3435074d1a750c90",
        "source:ac57070c47a74d4f5581e61b",
        "source:f9806d732bf4ca083d9c5943",
        "source:476cfa85bca433e4a5611980"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:bare-large-gauge-quillen-norm-does-not-equal-original-winding-counting-factor",
      "titleEN": "Bare large-gauge Quillen norm does not give the original counting factor",
      "statementEN": "Exactly N(z+1)=N(z+i)=N(z),so a large-gauge full spectral norm ratio is1. The retained old NS circle still gives det_F[(I-q uCu*)(I-qC)^-1]=1-q. Forq nonzero these differently inserted operator comparisons cannot be identified. Additionally:an ansatz using only this norm,fixed multiplicity,constant reference and smooth z(alpha)withz(0)0 has first derivative0,while W_min_prime(0)=-(5/2)delta_top/(1-delta_top) is nonzero. Alpha0 still hasqdelta_top and is not a seam-free reference. A derived different background or additional actual insertions is not excluded.",
      "scopeEN": "Excludes only the bare gauge-ratio identification or explicitly described smooth zero-twist ansatz. Original relative factor1-q and T(q)=(1-q)^-5/4 remain intact. Does not exclude physical EM response,other originally derived couplings or completeTFPT.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-square-nsns-elliptic-unit-charge-flat-connection-family",
        "premise:same-original-circle-trace-class-covariance",
        "premise:historical-sf-sector-action-and-relative-normalization",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:19db256c3dd54fa62ffc0e23",
        "source:e53f136b3435074d1a750c90",
        "source:ac57070c47a74d4f5581e61b",
        "source:33011e1b714efe2318c06712",
        "source:7b9bb25b000f54ee914fe50d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:existing-elliptic-half-period-has-canonical-graded-gns-intertwiner",
      "titleEN": "Existing elliptic half period has a canonical graded GNS intertwiner",
      "statementEN": "The already given actual NS Green kernel gives S(W)=−S(−W)=(2cosh(WB))^-1=X_A,also as both reflected charge Grams at t=u=W/2. In the existing thermal HS GNS,aR=L_a and aL=−Gamma R_a with aL*=Gamma R_a* give full double CAR and crossMij=Tr(sqrt(rho)ai*sqrt(rho)aj). For the same free rho,M=X_A,hence complete covarianceP_A. The previous projection theorem gives all words;the cyclic isometry to the given graph-state GNS is ontoHS. No new physical state or particle carrier is introduced. Bare Euclidean evaluations a(W),a(0) are not independent CAR families:their cross anticommutator is exp(−Wlambda),not0. Using onlyL_Pi instead of canonical HS parity produces false spectator factors,detected already with2modes.",
      "scopeEN": "Exact connection inside the already given free elliptic source and its faithful normal HS carrier. Its numerical cross kernel was not unknown;the previous cross gap still means its actual physical P1 operator/sewing identification. Geometric OSTheta is not presented as TomitaJ,nor the chiral scalar as a full Dirac vector. Domains/subtractions and previous state/time exclusions remain unchanged.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:normal-even-sea-car-source-and-canonical-graded-hs-double",
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e824212d52da9093d601a78c",
        "source:a183418e20ee9718a165fd7e",
        "source:139fb26bd03a7e83a334a0ee",
        "source:030751cbcd84232146f56d36",
        "source:28d5eaa4cb3f3c10938180c9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law",
      "titleEN": "Free projection sewing requires maximal coherence and linear half-modular field action",
      "statementEN": "For arbitrary faithful even rho,the actual canonical cross coherencemj=Tr(sqrt(rho)aj*sqrt(rho)aj) obeys0<=mj<=sqrt(cj(1−cj)). Equality holds exactly when sqrt(rho)aj=qj aj sqrt(rho),qj=sqrt((1−cj)/cj). On full finite CAR,saturation for all modes in a covariance eigenbasis is equivalent to a quasifree product density. On the existing normal all-mode HS carrier,actual all-mode saturation givesMij=qjCij,then full projection covariance and quasifreeness without uncontrolled density inverses. The already given H_int control has both deficits14745600/82945²>0 and half-modular factors2/32 and8/128 depending on spectator occupation. Positive standard doubling and its quarter clock remain,but projection coherence fails. The original property still to be tested is therefore a linear half-modular action on the actual odd fields,not merely existence of positive doubling.",
      "scopeEN": "Analytic finite saturation theorem plus separate all-mode theorem inside the explicit normal HS class. Finite checks do not prove all-mode saturation. The old interaction control is only an algebraic countercheck,not an admitted P1 coupling or new model study. No primitive law or physical odd-field/clock/reflection map is derived or freely chosen. For an actually nonlinear P1 half action,retain its operator contributions instead of forcing free saturation.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:normal-even-sea-car-source-and-canonical-graded-hs-double",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e824212d52da9093d601a78c",
        "source:a183418e20ee9718a165fd7e",
        "source:139fb26bd03a7e83a334a0ee",
        "source:030751cbcd84232146f56d36",
        "source:28d5eaa4cb3f3c10938180c9"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:declared-recursive-machine-baseline-controls-and-recovery-are-finitely-measured",
      "titleEN": "Baseline controls and perturbation recovery of the declared machine are finitely measured",
      "statementEN": "Six original10000-step controls are archived:baseline rank3.794/code.98067,no-feedback5/.99928,frozen-memory18.336/.63888,no-interaction1/.07348,magnitude-kernel1/.10458,no-initial-noise3.794/.98136.20starts of5000steps yield ranks3.458..4.99995 andcode.97952...98454. After perturbation.1,RMS falls from.09891 to.01182 after10steps and remains.01101 after5000. Stored states match measurements. Cold-load,identical random perturbation and continuation were reexecuted bit-identically during archiving.",
      "scopeEN": "Finitely measured expressly chosen learning rule and same runtime environment;no general convergence,physical dimension or fundamental selection. Long measurement runs were not rerun during archiving. U35 and rate qualifications remain;no fresh UI-running claim.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-recursive-native-som-update",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:47fea6af146a71126e712a52",
        "source:964b27ee4b7bb082eef525aa",
        "source:7218a3be7caf2001fc097bb8",
        "source:e9f0c4081c5aec3f1422d372",
        "source:f1f60c79d3476845e3bd1a24"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:declared-recursive-machine-long-run-retains-motion-at-stable-aggregate-rank",
      "titleEN": "Long machine run retains motion despite stable aggregate rank",
      "statementEN": "Archived run reaches100000steps with rank3.794077326,code.981093691 and signal change.000377118958 perstep. Reconstructed frozen120x120response has periods11201.2123 and64540.3822iterations and reproduces1000more actual nonlinear steps with relative error5.4759e-14. Stable aggregates are not a microscopic fixed point here. The100000checkpoint was checked against these measurements during consolidation.",
      "scopeEN": "One actual measured run of the declared rule. Frozen response is not the full Jacobian;no general attractor or physical clock. Rate dependence is separately retained.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:declared-recursive-native-som-update",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:47fea6af146a71126e712a52",
        "source:964b27ee4b7bb082eef525aa",
        "source:7218a3be7caf2001fc097bb8",
        "source:e9f0c4081c5aec3f1422d372",
        "source:f1f60c79d3476845e3bd1a24"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:recursive-kohonen-source-investigation-has-source-verified-atlas-handoff",
      "titleEN": "Complete Kohonen and source investigation has a source-verified Atlas handoff",
      "statementEN": "The common overview covers24 results or explicitly reused prerequisites in nine groups:native structural limits,executed machine and limits,Dirac return/state,primitive selection,causal memory,conformal boundary invariance,positive projector source,modulus admission and Quillen insertion. Early controls/long-run/perturbation evidence with code and checkpoints is added. All cited source hashes and extents of24 entries were verified;seven reports are preserved as unchanged text copies. Individual premises and scopes remain separate.",
      "scopeEN": "Coverage and source audit of this conversation investigation,not a fresh independent mathematical review of all proofs or unrelated parallel Atlas research. Finite measurements remain finite;conditional constructions remain conditional. Physical P1 insertion,law and completeTFPT solution are not closed.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:original-admissible-source-closure-20261025",
        "contract:collective-native-marginal-origin-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:63097796c620da4a59e08444",
        "source:47fea6af146a71126e712a52",
        "source:e687f28fc5b542685ee4dfbe",
        "source:11f46e2e88b7c00a2bd00e7c",
        "source:e17fda0df4dd897aad35afbf",
        "source:37a70843710663dd3eceb3bc",
        "source:7e4b9a399cba3d2c3424452e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:chat-algorithmic-comparison-native-pauli-code-and-scoped-information-loss",
      "titleEN": "Chat comparison connects native Pauli quartic code with scoped algorithmic information",
      "statementEN": "The initial exact original-source calculation is now archived in the repository and replayed normally,optimized,and at its archived location with byte-identical results. Pi_native=Q_Pauli Pi_sym4 holds in the unchanged frame;ranks16,35,5 remain distinct. All64 one-register matrix-unit conditions give the existing erasure property. The60 original source rays have frame potentials1/4,1/10,1/20,1/32;the fourth Haar value is1/35 and HS moment defect3/1120. For the already known pair Pi_native/5 andPi_sym4/35,relative entropylog7 and global distance6/7 disappear in all proper marginals. The external standard-gate control compresses to diag(0,0,i,i,i),leaking2directions. The original comparison and known Clifford-commutant literature retain all premises and the physical selection boundary.",
      "scopeEN": "Exact finite source identities and reconstruction of known mathematical connections. No proof of universal computation,physical noise,clocks,couplings,Born rule,or simulation. Marginal information loss concerns this mixed-state pair,not all pure codewords. A fully Clifford-invariant Hermitian generator is scalar on5/30 only in that class. Literature links toHamming/E8,QCA,transfer convergence and sufficient statistics remain background theorems under their own premises. The historicalF_a->deltaD_rel question was later sharpened for merely defining composites by the existing current reconstruction.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d2993423c57ab383ed63e16f",
        "source:c7b4d322a303ed993a2d487b",
        "source:a52f1b573a65eaadab3ee041",
        "source:8024f98de650fd21dd1dc5b2",
        "source:f839a41611561ee037011278",
        "source:920c9dea9a260816ba139448",
        "source:c63e6d8e9203bd2354404212"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:chat-20261026-results-consolidated-with-corrected-assumptions",
      "titleEN": "All results of this TFPT chat consolidated with corrected assumptions",
      "statementEN": "The common reading map and manifest connect the initial algorithm comparison with all11 previously stored findings from this chat:relative arc charge,finite modular control,neutral current reconstruction,elliptic current functional and local Hardy distinction,conformal trace and averaging,projection state and two-face coherence,half period and graded GNS,and modular saturation. Previous referenced source versions were checked against their current files. Seven explanatory PNG images and available SVG/source assets are preserved byte-identically in the repository. The historical first report remains unchanged with the laterF_a->deltaD correction identified. Final Atlas verification uses the complete finding IDs in the manifest,not scientific promotion inferred from graph paths.",
      "scopeEN": "Documentation and completeness reconciliation of this chat,not a new physical derivation. Images are explanatory aids,not proofs. The Atlas undersemantic_explorer remains the sole current map;the overview is an entry into its sources. All original P1/carrier/reflection/time/interaction boundaries remain visible;no ledger or empirical status is changed.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:native-arc-charge-source-interface-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5ccef3ac839348ea2d780cb7",
        "source:3d81987221fac6ecac2f21c1",
        "source:920c9dea9a260816ba139448"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-inversion-forces-six-line-theta-completion",
      "titleEN": "Original inversion forces six coefficient lines",
      "statementEN": "Original inversion forces six coefficient lines. s:w->−w exchanges q and p packets;their minimal s-stable closure is sum of both triples. Vq and Vp are orthogonal symplectic planes spanning Jac(C)[2]. Joint unramified elementary two-cover has degree16 over C,genus17. Explicit normalized Kummer lifts of c,s give order6 T=sc and old block M plus(−M). Lift choice remains a recorded deck torsor.",
      "scopeEN": "Flat coefficients and C6 action;T and Q remain distinct marked operators. Fixed hexagon symmetry at most D12 does not supply full Sp4(2). Following source theorem closes spin selection.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e3cf20fbe047b941950925c6",
        "source:8b5357ffc5005324f32d6721",
        "source:e1959ade82163b5268f13414"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:literal-geometric-quarter-is-not-central-gaussian-quarter-on-labels",
      "titleEN": "Literal geometric quarter is not central Gaussian quarter",
      "statementEN": "Literal geometric quarter is not central Gaussian quarter. On Jac(C)[2],Q acts by diag(A,A),A=[[1,0],[1,1]],rank(Q−I)=2. J=i acts identically on L/(1+i)L. Hence no invertible intertwiner with Q->J exists. Excludes only this literal generator identification;source already identifies Q with rank3 U,not J.",
      "scopeEN": "Named quotients and generator map. Code/context quotient is not correct theta translation target;positive Pauli bridge remains. A spin lift of Q² is a distinct correctly typed comparison.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:934226c33498bb69d052657d",
        "source:3bb36659ed2fed4278807122"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-cubic-and-quarter-select-even-theta-and-spin-half-turn-lift",
      "titleEN": "Original cubic and quarter select spin line and half-turn lift",
      "statementEN": "Original cubic and quarter select spin line and half-turn lift. S0=O(q0+q1+q2−K_C) is even,S0²=K_C,and equivalent to p definition. c has no nonzero fixed vector on Jac(C)[2],so S0 is unique c-invariant theta characteristic among16. Q preserves S0;at marked fixed point q0,Q*eta=i eta. Any compatible spin lift alpha has alpha^4=−I,order8. beta=alpha composed Q*alpha is order4 lift of h=Q²,independent of alpha->−alpha,with local phase+i. Previously open S0,beta selection is closed by existing data.",
      "scopeEN": "Spin bundle of actual genus2 source,not honest C2 linearization. Subsequent finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package closes complex module bridge for Wq. Physical choice of inverse point norm and state remains open.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e907433847678b37e901d588",
        "source:2e4ac2273137c4aa7c627f04",
        "source:867de85f0615b14f8e2aaf34",
        "source:18f7e576bcf807b88323806c",
        "source:d3c93d3c8fa9b3594c1a3ae9",
        "source:87538a78f45859406ca07071",
        "source:f49fd35ba7ffbe92349b7303"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-cubic-matches-native-pauli-translations-after-context-target-correction",
      "titleEN": "Source cubic matches native Pauli translations after correcting context target",
      "statementEN": "Source cubic matches native Pauli translations after correcting context target. v783 distinguishes code labels L/(1+i)L from P_nat=N64/mu4;full Sp4 modules admit no linear intertwiner. On P_nat original sigma is fixed-point-free with polynomial(x²+x+1)²,exactly as c on Jac(C)[2]. Phi with columns IY,YZ,ZY,YI is explicit symplectic intertwiner. Among35 planes exactly5 are sigma invariant,exactly2 symplectic and orthogonal,selecting same unordered triple pair natively. Exactly18 c-equivariant symplectic markings remain. Earlier0-versus2 fixed-space conflict concerns only wrong code/context target.",
      "scopeEN": "This lemma covers exact symplectic bridge. Full central and four-dimensional bridge for Wq is closed in subsequent finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package. Older v784/v796 objects and exclusions retain scope.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ae60bba7479604ceb76718db",
        "source:697ae1a2c618138fb372901a",
        "source:645320c5d610ae8fecdab898",
        "source:d8b5c731516fc64c2bcfc50c",
        "source:d3c93d3c8fa9b3594c1a3ae9",
        "source:87538a78f45859406ca07071",
        "source:f49fd35ba7ffbe92349b7303"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-source-clock-relations-have-one-native-clifford-gauge-class",
      "titleEN": "Joint clock relations have exactly one native Clifford gauge class",
      "statementEN": "Joint clock relations have exactly one native Clifford gauge class. Under explicit module condition beta->J=iI,no matrix in any64-element G31 fiber over the9 admissible Q actions squares to+iI;in zeta8 G31 each fiber has8. Original relation alpha sigma alpha^(-1)=sigma^(-1) leaves exactly alpha and−alpha. Explicit alpha=zeta8(XI)U has alpha²=J,alpha⁴=−I,and joint group order24. Actual C_G31(sigma) has order72 and is transitive on all9 sign classes. Thus one gauge class remains for fixed sigma,J,Pauli system.",
      "scopeEN": "Finite matrix construction with fixed central character. Geometric bridge for Wq is now separately proved by finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package. Conjugacy class is not automatically physical gauge;P1/P2 anchors,state and readout excluded.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:914fcfa5794f2fafc580a367",
        "source:70264022443cecac8f95cc8a",
        "source:ef5c4dd91d0bd066d09186f3",
        "source:b3295d52caaa00a608fb0d82",
        "source:d42b403744c25ea0920661c4",
        "source:d3c93d3c8fa9b3594c1a3ae9",
        "source:87538a78f45859406ca07071",
        "source:f49fd35ba7ffbe92349b7303"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:ordinary-theta-determinant-erases-selected-spin-central-character",
      "titleEN": "Ordinary theta determinant functor erases selected spin character",
      "statementEN": "Ordinary theta determinant functor erases selected spin character. Every E_L=S0 tensor L has chi=1+1−2=0. Scalar lambda acts on det RΓ(E_L) by lambda^chi=1. Thus beta²=−I becomes beta_D²=+I,and alpha⁴=−I becomes alpha_D⁴=+I. Dualizing or squaring cannot restore lost phase. All four standard H0(2Theta) functions are even;inversion acts+I. Direct untwisted functor therefore does not give beta->J=iI.",
      "scopeEN": "Only ordinary rigidified determinant and Kummer functor. Finite Clifford construction remains valid under explicitly required central character. Refinements and additional lines from marked source data are not excluded.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:ordinary-rigidified-genus-two-theta-determinant-functor",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:fa2c20b0573e27c91a4ed086",
        "source:b86f97d2500ff9fbf9c5ba22",
        "source:3d86b2a2067f958ef089fc98"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:marked-negative-point-norm-restores-required-spin-central-character",
      "titleEN": "Marked negative-point norm carries exactly missing central character",
      "statementEN": "Marked negative-point norm carries exactly missing central character. For Nq=tensor_a S0|q_a,beta on each fiber is+i,so beta_Nq=−i and beta_Nq^(-1)=+i. c acts trivially on Nq. Hence H0(2Theta) tensor Nq^(-1) has alpha²=+iI,alpha⁴=−I without fitted phase. Determinant of three fibers and norm line differ under Q only by transposition sign. p partner has conjugate−i character;s exchanges both. Using exactly one inverse point norm in actual field space remains candidate bridge.",
      "scopeEN": "Point norm and central character proved. Full family and complex module intertwiner are closed in following spin-rigidification findings. Original boundary selection of one inverse norm remains open. One complex four-space with scalar J does not also carry s exchange of conjugate characters.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9ae0bbde81665d64252bf3ec",
        "source:cd4175b3ba278f4a5ed6efa9",
        "source:8171e8cd4ff89037925caf45",
        "source:d3c93d3c8fa9b3594c1a3ae9",
        "source:87538a78f45859406ca07071",
        "source:f49fd35ba7ffbe92349b7303"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:point-normalized-theta-family-correction-fails-original-cubic-action",
      "titleEN": "With fixed q0 rigidification,direct point-norm correction does not preserve original cubic action",
      "statementEN": "With fixed q0 rigidification,direct point-norm correction does not preserve original cubic action. For E_L=S0 tensor L,evaluation line is Nq(S0) tensor P_delta,delta=Dq−3q0=q1−q2 nonzero in Vq. O(2Theta) tensor P_delta is a different marked line bundle. Since c has no nonzero fixed vector in Vq,c*delta differs from delta;no linear c lift exists on same theta line bundle. Imposing vanishing first on determinant line then performing usual squaring removes P_delta² but point phase becomes−1 rather than+i. Neither direct functor variant supplies required joint bridge.",
      "scopeEN": "Two explicitly defined q0-normalized variants. Following source-selected S0-relative normalization removes first family obstruction;boundary-first then square remains excluded. Not intrinsic obstruction of all Poincare families.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:ordinary-rigidified-genus-two-theta-determinant-functor",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9ae0bbde81665d64252bf3ec",
        "source:cd4175b3ba278f4a5ed6efa9",
        "source:8171e8cd4ff89037925caf45"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:source-spin-relative-poincare-normalization-closes-point-norm-family",
      "titleEN": "Source-selected spin rigidification closes whole point-norm family",
      "statementEN": "Source-selected spin rigidification closes whole point-norm family. O(Dq)=S0 tensor K=S0³. For any Poincare family P define P_spin=P tensor pi_A^*<P,S0>^(-1). Since deg(S0)=1,<P_spin,S0> is canonically trivial,so Nm_Dq(P_spin)=<P_spin,S0³>=O. Changing initial Poincare normalization cancels in P_spin. Scalars in S0 isomorphisms and O(Dq)≅S0³ vanish in pairing with degree0. Norm trivialization is c,Q covariant;constant Nq phase survives. Ordinary theta determinant is unchanged because chi=0.",
      "scopeEN": "Mathematical family bridge using already selected S0;q0 flat factor was rigidification artifact. No new free reference marking. Physical selection of exactly one inverse Nq copy remains open;boundary-first then square is distinct operation.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9ae0bbde81665d64252bf3ec",
        "source:cd4175b3ba278f4a5ed6efa9",
        "source:8171e8cd4ff89037925caf45"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package",
      "titleEN": "Spin-rigidified theta space is identified as complete complex Heisenberg and clock module",
      "statementEN": "Spin-rigidified theta space is identified as complete complex Heisenberg and clock module. For L=O(2Theta),N={g in G(L):g⁴=1} is canonical order64 group with mu4 center. Every symplectic Phi lifts to N≅N64;Stone-von Neumann identifies Wq=H0(L) tensor Nq^(-1) with native C4 module. c lift has no remaining Pauli shift because1−Sigma invertible. alpha gamma alpha^(-1)=gamma^(-1) and trace(Ad gamma)=1 force trace(gamma)=1,hence exactly gamma->sigma without cube-root phase. Same intertwiner sends alpha to fully classified joint Clifford conjugacy class.",
      "scopeEN": "Complex four-dimensional module closure for explicitly constructed Wq including full central action. Physical source selection of one inverse Nq copy remains open. Does not derive integral Gaussian E8 lattice,physical metric,W8 dynamics,or state rule.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d3c93d3c8fa9b3594c1a3ae9",
        "source:87538a78f45859406ca07071",
        "source:f49fd35ba7ffbe92349b7303"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:tfpt-origin-investigation-full-source-coverage-and-current-frontier",
      "titleEN": "Complete origin investigation from E6/E7/E8 through the spin theta bridge consolidated in Atlas",
      "statementEN": "A common overview and full manifest link all197 existing findings in the two relevant research problems. All1185 source references of388 stored findings were checked against497 current files for existence,SHA256 and line extents,with no discrepancy. Three previously local reports on real D4 comparison,conditional cyclic reconstruction and NS half-cover are now preserved byte-identically with two checkers and an existing result file. Historical scopes and later corrections are explicitly mapped. Active task reuses the completed complex module bridge instead of requesting it again; prior wording is retained.",
      "scopeEN": "Coverage and source audit of available investigation documentation,not fresh independent validation of every proof.388 entries belong to the entire shared Atlas,not solely this conversation. Presentations and old save packets are not new scientific results. Original one-copy inverse point-norm selection,integral lattice origin and physical field/state/time map remain open. No ledger or physical proof status changes.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3821500cbf4d2b536cd0b311",
        "source:6a8af2f4db128d7184725d00",
        "source:65fd8874f75ddeeff1f74812",
        "source:17ceddae36d9bb5a9b6c0a19",
        "source:18386ba797ed1860f48619f2",
        "source:bac9494230e904d9d3e583ff",
        "source:5fc8ea16ef23762cf363dfa0",
        "source:062f99ff60c8e6d57f15978d",
        "source:2d802ad8e43c38b09f287463",
        "source:6c3f87b792afc1dd48d34ea6",
        "source:6a7492bb87f5496156c8ba89",
        "source:76b13e951d1cc7fafcc5a28d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-clock-norm-power-class-and-canonical-eighth-period",
      "titleEN": "Norm powers form one finite class with canonical period eight",
      "statementEN": "Full finite relations for Wq,k require k=1 mod4. Adding four flips precisely the unresolved alpha sign; adding eight is canonically trivialized by the marked cotangent product and S0²=K. Fixed signed alpha distinguishes k1 and k5; existing projective spin-lift scope has one class. Finite relations do not determine integer winding.",
      "scopeEN": "Complete complex N64/clock scope with retained markings; no inference of unique physical action from residue classes.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c275d34cfd16a7d4f578496f",
        "source:f01a07e354e44070faea8822",
        "source:29be41b24677fd1e3fedc544",
        "source:351a9b39e8bcefa1725ff195"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-unit-winding-selects-one-inverse-norm-in-three-cabled-hardy-pair",
      "titleEN": "Original unit seam winding gives exactly one inverse norm in relative three-cable",
      "statementEN": "Original z=eta/(1−w³) has divisor Dq−Dp, cz=z,Qz=iz. Its open disk preimage is three unramified disks. M_z on S0 tensor L has index−3 and three evaluation fibers as quotient. Relative to the same shift on L, its Fredholm line is exactly Nq(S0)^(-1), with familywise coefficient and permutation cancellation. Jets of z^n give Nq^(-n); original oriented base index−1 selects n1. Half-form e²=dz supplies natural Hardy norm. Full inverse three-cable ratio has beta+i; inverse invariant rank-one defect has beta−i.",
      "scopeEN": "Closes mathematical one-copy origin under the stated Hardy comparison. Actual D_rel/D_ref,state,reflection and Calderon space are not yet identified with this pair. Does not derive integral E8 lattice or physical action normalization.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f696b5b06720afe869a01aef",
        "source:1b2985560d444b6064d7fddf",
        "source:e0e26ea117bbe8058492ae1c",
        "source:db23ec77261621c5d6407102",
        "source:b6837330d130f1e0bb6e5697",
        "source:759ed94dc4dc35697d4f9654",
        "source:f4903c7217a2798989c443e4",
        "source:9315b36e353bd5ca483fc505",
        "source:043cf08381d9d30c2a541042"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-boundary-audit-and-h1-point-restriction-limit",
      "titleEN": "Originals link seam function and three-cover; naive H1 point restriction fails",
      "statementEN": "Targeted fullv21,v31/v42,TFPT45 and September originals supply scalar seam winding, periodic reference and actual three-cover. They do not establish the physical relative spin/scalar Hardy operator pair. Algebraic E(-Dq)→E→E|Dq is not a point-restricted closure of the unchanged H1 Dirac domain: logarithmic cutoffs have energy 2pi/log(1/epsilon)→0, so closure is full domain. The proved Hardy quotient avoids this confusion.",
      "scopeEN": "Source claim limited to read passages, not universal absence. H1 exclusion concerns ordinary first-order operators on smooth closed real two-dimensional curves, not Hardy spaces or additional singular domains.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c2117321fa32d99260964b8b",
        "source:34786874300afb37c5b9c138",
        "source:e5d47ade174510d9a3d0de48"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:eta-phase-conventions-do-not-identify-relative-spin-reference-pair",
      "titleEN": "Eta phase alone does not identify needed spin/reference pair",
      "statementEN": "With lambda=detH0 tensor inverse detH1, positive theta determinant is inverse lambda; inverse Dai-Freed determinant is lambda in this convention. TFPT action factor exp(−i pi Delta eta/2) obeys a²=tau_rel^(-1) for vanishing kernels, not a=tau_rel. A Pfaffian application needs actual operator,real structure,kernel and orientation; generic gluing does not identify coefficients.",
      "scopeEN": "Convention/type check, not exclusion of a properly derived relative anomaly theory. No unchecked detailed erratum signs used.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:cb947172514d7d1dd341fcff"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:same-spin-unit-shift-gives-native-module-class-with-odd-determinant-line",
      "titleEN": "Same-spin shift gives native module class retaining odd defect line",
      "statementEN": "Delta(E,M_z) tensor inverse Delta(E,M_1)=B(E)^(-1)=Nq^(-1) tensor B_O^(-1), using equivariantly trivial spin-relative Poincare norm. B_O has c=beta=1,Q=−1, changing only allowed alpha sign after forgetting grading. Full complex N64/clock class needs no separate unspun physical reference. Superline stays odd, index−3 versus0; two shifted cables give even relative parity. Original index−1 and three-cover index−3 are both odd.",
      "scopeEN": "Equality of classified ungraded complex module class; not equality with fixed signed alpha or of super/Pfaffian sewing functors. Actual physical Cauchy space,action,state,reflection,local insertions remain to be identified. Two-cable ratio remains sufficient normalization, not necessary physical premise.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:same-spin-hardy-shift-against-identity-with-grading-retained"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:7ac63ae4aa67a1f471894281",
        "source:a0033640d135c41489de134a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-even-odd-operator-split-is-compatible-with-same-spin-seam-reference",
      "titleEN": "Original even/odd operator split is compatible with same-spin reference",
      "statementEN": "Original v31/v42 construct D_ref/D_rel from same D and spin carrier, diagonal/offdiagonal in tau blocks, not a change S0→O. This does not exclude seam connection: fullv21 interpolates unshifted and unit-shifted operators on same field space. Leading candidate is M_z versus M_1 on same S0 Hardy space. Source definitions alone do not supply equivariant map from actual positive Cauchy data to this three-sheet Hardy space.",
      "scopeEN": "Targeted original source/operator comparison. Same carrier proves neither Hardy identification nor general exclusion. Geometric beta lift remains distinct from central spin minus one.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:426f49aad1f2a0084220cc3d",
        "source:d0ecfdf3c2d66a43d2b78104"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:elliptic-projector-and-weyl-results-retain-their-source-type-at-cubic-spin-bridge",
      "titleEN": "Elliptic projector and Weyl transport retain source type at cubic spin bridge",
      "statementEN": "Original boundary, conformal-trace and projection-state sources concern E=C/(Z+iZ), NS NS spin, L=partial_t-i partial_s and the full orthogonal two-face graph P_A. Weyl transport fixes complex curve, spin, connection and cut; it supplies no map to genus-two(C,S0). Projection rigidity starts with actual positive full CAR covariance, not a geometric projector alone. Longitudinal old-circle/C2 generator and winding already match but imply no C3 time normalization. A local/reducing isometric source embedding on its cyclic image suffices; global onto identification is unnecessary.",
      "scopeEN": "Targeted original-source comparison of the four supplied summaries. No general impossibility of a P1/C3 map; existing positive conditional sources remain valid.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:same-marked-elliptic-annulus-massless-conformal-metric-family",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bcfeca3820b55fc7533b33ac",
        "source:626979868651edbd43ad208f",
        "source:7ea4d956a24d67907ab88cf7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:cubic-spin-cauchy-range-is-three-hardy-with-strong-domain-distinction",
      "titleEN": "Cubic spin Cauchy range has three Hardy channels; strong domain remains separate",
      "statementEN": "On three normalized disks the closed massless half-form Cauchy range is H²(D)^3. At cubic boundary points z-zj~u³ the coefficient is f~u^-1~|s|^-1/3 and |f|²ds~|s|^-2/3 is integrable. A flat outer factor gives dense compatible smooth boundary germs. Intrinsic H1 retains common vertex values, higher norms retain further jets; the constant derivative sends permitted singular ambient traces out ofL2. Equal L2 ranges therefore do not identify strong domains. Tangential B intertwiners alone do not fix global Calderon projections; bulk Dirac/harmonic data must also be transported. Moreover pi_*S0=O(-1)^3 follows from rank3,chi0,H0=0, so direct pushforward differs from old O(-2)+O(-1)^2 anchor.",
      "scopeEN": "Exact analytic result for explicitly conditional massless spin operator and named ambient core. No smooth Calderon theorem for arbitrary graph domains, freely inserted elementary modification, or physical P1 source/time closure. Scalar Hardy coordinates depend on half-form signs; norm and projection are intrinsic.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:standard-chiral-spin-trace-on-original-cubic-disk-pullback"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5882958830c486560d86ff7d",
        "source:fb5f61a228957878e0909a70",
        "source:c50b88cb59fb18ee296d224e",
        "source:11d81ec6225b69931fee7d20"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-negative-sea-three-mode-ket-is-dual-to-required-hardy-line",
      "titleEN": "Original negative-sea three-mode ket is dual to required Hardy line",
      "statementEN": "Retaining source orientation C=I-PH gives UCU*=C+PiV and PH-U PH U*=PiV. Positivity and full projection determine shifted Xi=a*(v1)a*(v2)a*(v3)Omega and every CAR word without an extra Gaussian premise. Relative ket line detV has beta=-i; Hardy Fredholm line delta(Mz)=detV^-1 has beta=+i and is its dual vacuum line. Both are odd. Spin-relative family gives detV=Nq tensor B_O and delta=Nq^-1 tensor B_O^-1. All state expectations are phase blind and do not choose a directed boundary amplitude. Exact full8D exterior-algebra test checks every creation action,Q²=beta,beta²=(-1)^F,QcQ^-1=c^-1; normal and optimized outputs match bytewise.",
      "scopeEN": "Conditional full CAR connection on the given three-sheet half-form carrier. Actual P1 source and its dual boundary/Pfaffian amplitude remain to be derived. No switch to occupied positive Hardy polarization, particle-hole reversal to fit the phase, or inference from state expectations to charged transition phases.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:same-spin-hardy-shift-against-identity-with-grading-retained",
        "premise:conditional-three-sheet-negative-sea-car-source"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:45889d3dd0ff6c61286fe91c",
        "source:3e4bac79ef465d5e090e92dd",
        "source:407da55653e9e25a4bd0cbf2",
        "source:39005a3b3866fc1c03eeb0d3",
        "source:675cb2edc864d6ed1af9022b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:auxiliary-theta-route-needs-no-physical-cubic-bulk-or-eta-selected-dual",
      "titleEN": "Auxiliary curve and CAR duality require no additional physical C3 or eta selection",
      "statementEN": "The dual of detV already exists by CAR adjunction; for antilinear-first inner product xi-><Xi,xi> is the complex-linear covector. Retain old negative sea,beta signs and odd grading. Original closed eta/Pfaffian phase is scalar and does not select a directed boundary amplitude. Auxiliary C3 need not be a physical bulk source for the inner spin/theta module. Full P1/C3 Calderon identification is needed only for the stronger equality of those sources. The existing local-extension theorem supplies a shorter sufficient source route through actual marked (16,4) sector with the same conformal vector.",
      "scopeEN": "Correction of an overstrong active source task,not a proof of actual P1 field map or physical boundary amplitude. Reuse local-extension theorem and exclusion of ordinary NS vector products as spinor creators. Do not require new eta selection merely for existence of dual representation.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:same-spin-hardy-shift-against-identity-with-grading-retained",
        "premise:conditional-three-sheet-negative-sea-car-source"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8e60f9e4f3164f339310666f",
        "source:9e80afe8d3eaffbbedf4f0a7",
        "source:4cba19267312479f930b6852",
        "source:5e8ac63d4135c81d93040167",
        "source:9a7bd930a79bf01515e5cc84",
        "source:e5fc51516e283018028f45c2",
        "source:5ab7bf7de5768f0991896e1a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:primitive-gaussian-theta-frame-constructs-e8-pair-with-retained-spin-action",
      "titleEN": "Primitive Gaussian theta construction yields E8 lattice pair with actual spin action",
      "statementEN": "Affine phase recipe yields16+96+128=240 roots on60 complex rays. Integer basis B has detB=16 and even integral Gram B^tB/2 with determinant1; an explicit orthogonal map identifies the complete standard E8 root shell. Compensated Clifford generators preserve Lambda. Retained alpha=zeta8 V obeys alpha²=i and swaps Lambda with zeta8 Lambda,while beta=i and sigma preserve both and c=i sigma has order12. Lattices intersect only at0 and their sum in this space is nondiscrete. The extra coset gives a two-element orbit; an actual monodromy cover still needs its supplied representation. Bare theta without inverse norm is not the module used.",
      "scopeEN": "Exact arithmetic construction in completed theta frame with named integral normalization; no P1 selection of that normalization,universal lattice uniqueness or new discovery of known Clifford/Barnes-Wall connection. Reuses v783 and primary literature. Composes actual spin action with completed source module. No G31 VOA splitting or automatically physical double cover.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:marked-theta-frame-with-explicit-primitive-gaussian-root-normalization"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a3e50bfe2ff0ac393b93c947",
        "source:c5c36c7cecc8e086f752b00a",
        "source:668bca99936df4d3b0984448",
        "source:93cc525fe57edc5f1b1bf694",
        "source:48d46a5427dc8c543a6db528",
        "source:dc9127cc34d17a8237ca9762",
        "source:d33a54ae887ed207de1fa014"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:existing-c12-lift-induces-coherent-two-object-e8-vertex-groupoid",
      "titleEN": "Existing C12 lift induces coherent E8 field action between two lattice objects",
      "statementEN": "For every given geometric faithful c0 and every unitary isometry lift T:V0->V1 set beta1=T beta0 T^-1,sigma1=T sigma0^-1 T^-1,alpha01=T,alpha10=beta0 T^-1. Then alpha²=diag(beta0,beta1),alpha^8=1 and alpha sigma alpha^-1=sigma^-1 hold on all lattice charges and finite-energy vertex fields. Both objects carry faithful C12 clocks. Standard cocycle depends only on Lambda/2Lambda; all256 classes and65536 pairs exhaust cocycle checks,while matrix relations separately hold exactly over Z. Character-gauge changes of T give equivalent groupoids. Optional strict C4×S3 census yields256 raw sign sections,but none with the zero-character J lift.",
      "scopeEN": "Two-object mathematical field closure preserves every given c0 linearization. Executable strict witness does not replace original J marking. No full G31 extension splitting,256 physical theories,single common local VOA or P1 source/time identification. Test deliberately uses T² different from1 and [T,beta0] different from1.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:marked-theta-frame-with-explicit-primitive-gaussian-root-normalization",
        "premise:two-theta-lattice-voas-with-given-geometric-faithful-c12-lift"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f09315566fea7f1e767e0145",
        "source:4f82f05a12a5f324b7b447a8",
        "source:e993e563689636aef4993b0f",
        "source:1b46c77eb1b20327b63ca96f",
        "source:3d81fb1ca33b19e89aa57243",
        "source:27b8c74c8fbda198736b98bf",
        "source:d01e50b90f3003cbb4c5a1ef"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-winding-functional-calculus-preserves-ns-ramond-split",
      "titleEN": "Winding functional calculus preserves NS and Ramond and does not create a spinor field",
      "statementEN": "Actual W_ext acts as (0 v)(s c) and commutes with P_R, hence every bounded Borel f(W_ext), including every spectral square root, commutes with P_R. P_s f(W_ext) P_0=0; an s-charge intertwiner requires P_s X_s P_0 nonzero. Existing global E_s has the right sector action but is not a derived local P1 field. Half powers in the field transport refer to coordinate x. The ambiguous later summary sentence was corrected preserving source line counts. D8-relative locality of s is not membership in unchanged NS CAR algebra. Equation32 for the affine winding endpoint is not the same test as constructing M_h.",
      "scopeEN": "No general exclusion of Ramond fields, localized DHR/solitonic sectors, additional nonfunctional roots or geometric reconstruction functors. Fully marked s already contains both64 components; common Ramond lift sign remains basis gauge. Two actual The reviewed consultations were source-reviewed and partly rejected; execution or agreement is not proof. Mathematical parent remains distinct from physical P1 source. Quarter/Pin andtheta two-object audit confirms old narrow exclusion. ConstructedDHR half-kink is different operator on given even quotient net and is not excluded.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:standard-four-d8-module-parent-with-retained-subtheories"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:b695b2a0fb108c46ca2a9fd0",
        "source:cb70029f78c28177487a007b",
        "source:d4974e265f63c6e5ea29c2d7",
        "source:ac1b12bdde6ec1715d98ad7a",
        "source:5353b4167cc44a75beae4e71",
        "source:a1ed35eb77d792312aa3df7e",
        "source:2171fb655182ca87138944b5",
        "source:1d8fd66cb000a7029b31f193",
        "source:806cd1501270b09169b8d746"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:single-chiral-cycle-exchange-selects-e8-in-four-extension-class",
      "titleEN": "Single chiral vacuum line under cycle exchange selects E8 in the complete four-extension class",
      "statementEN": "For all four isotropic supports, exactly S v_H=(|H|/4)v_Hperp. An S-stable chiral vacuum line forces |H|=4 and H=Hperp, hence E8plus or E8minus; fixed source h=(1,1) marking selects plus. S vacuum coefficients are1/4,1/2,1,1. Scalar paired control M=I16 is modular invariant with vacuum multiplicity1 but rank16. CAR purity, unique ordinary vacuum eigenspace or tau=i equality do not imply a single torus-block line. Within this class the test is equivalent to holomorphy and explicitly connects the earlier mu16->4->1 completion to the four-extension classification.",
      "scopeEN": "Conditional exact selection test, not a P1-derived chiral block map or new general CFT classification. Reviewed originals do not define this torus functor there. Actual H=8(L0+delta.p) time and Jacobi background must be transported. M=I is a logical control, not a full P1 countermodel or generic OS output. No forced local-versus-global dichotomy. Not an additional requirement for other possible origin proofs.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:connected-local-same-conformal-compiler-extension-unselected-support"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:718985d0a99f5e5a0ae10b96",
        "source:dbaf401f17c088ec211b2182",
        "source:ceeb9e54d3341d295bfdba2f",
        "source:25fcf2fc169e833adf1277ea",
        "source:9769a7db5853da97cb62e857",
        "source:ac1b12bdde6ec1715d98ad7a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:affine-source-involution-pairs-full-d8-sector-spectra",
      "titleEN": "Affine source involution identifies complete H,Q spectra but not local fields",
      "statementEN": "A=R4 and p*=(++++----)/2 give A delta=delta+p*,A p*=−p*,T(p)=Ap+p*,T²=1. T also permutes oscillator channels,preserves H,Q and exchanges0↔s,v↔c. For beta>0 exactly Z_s(beta,u)=exp(u.p*)Z_0(beta,Au),Z_c=exp(u.p*)Z_v(beta,Au). At u=lambda q,Z_s=Z_0,Z_c=Z_v,hence complete thermal H,Q equality of E8_c0+c and NS CAR0+v. Individual Cartan charges,L0 and field statistics are not preserved. Prior ground-doublet/Ward selection result is reused; second H-zero state has L0=1.",
      "scopeEN": "Full mathematical charge/Fock space with fixed H; no local CAR/E8 dictionary,new P1 source or conformal modular character comparison. Old zero line is not claimed new. Selection of ground density remains distinct from simplicity of kerH.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:four-d8-sectors-with-fixed-affine-source-time",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5f14347055cb4f140bd5e558",
        "source:3c4c9b15f7526ae331acd085",
        "source:18b8cb2c2d66891ff0d589ac",
        "source:f248622235ed2e299b365edb",
        "source:3c2beb6ba4b5cb11d2dfd5ae",
        "source:08918eb55c1d2c1e8a9edd5a",
        "source:6bdd326f1695e5c2d48df3e3",
        "source:ea058d0ff3eb09f42523d5e0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:marked-local-e8-with-unchanged-source-time-fails-euclidean-clustering",
      "titleEN": "Fully marked local E8 completion with unchanged source time violates Euclidean clustering",
      "statementEN": "Twice-root charge q forces Ls. Its H kernel is exactly Omega and psi=|p*>. Hermitian locally smeared root current F has <psi,F Omega> nonzero; bounded local X=exp(i lambda F) retains the transition for suitable small lambda. Connected Euclidean limit is exactly |<psi,X Omega>|²>0. Lc clusters with the same H but lacks q/2 as a lattice root; both exhaust C1. Ward selection of Omega does not remove the transition. H+epsilon P_s is not a continuous local repair with fixed local Z2 net,D8 action and interval motion,since Aut(B|D8)=dual Z2 and lambda_s²=1.",
      "scopeEN": "Exclusion only of joint C1 to C4. P1 requires clustering on A_adm,but identifies neither its transfer with8K on the E8 completion nor every spinor field with an admissible observable. Given D8 subnet has <psi,X Omega>=0. No spatial clustering violation from H alone and no general E8/P1 no-go. Different time/observable map must be derived from original data; it is not an automatic repair.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-local-e8-completion-with-original-source-time-and-euclidean-clustering",
        "premise:four-d8-sectors-with-fixed-affine-source-time",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e43f0a9bd46ee65e62f19a80",
        "source:bf0cf11ea2ad5ff664b82ac0",
        "source:c0cab16d61967409a7b65d7f",
        "source:e09ddc680a53f810695ea8ce",
        "source:cb4aac14cf04fefeb9b4f392",
        "source:f248622235ed2e299b365edb",
        "source:ea058d0ff3eb09f42523d5e0",
        "source:ee72ee9239a1684c97e246d5",
        "source:748b7940e88d21a0f908d8c7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-parity-audit-does-not-supply-local-spinor-gauging",
      "titleEN": "Original parity audit does not provide local spinor gauging completion",
      "statementEN": "Source audit v522: unique reflection-compatible two-torsion of tested NS clock tower is{1,(-1)^F}; stated finite even bondcut algebras pass RP controls,overall contract remains typed UNDECIDED. v490 counts four spin structures with mu_pre4;v469 supplies local holomorphic extension after choosing spinor current,not source selection. Reviewed operational seed,ordinary Haag duality and conditional holomorphic KMS theorem supply no spin-structure sum or Arf weight. Even projection and adding Ramond sectors remain different operations.",
      "scopeEN": "Reuse even source structure and existing extension theorems. No global literature/P1 impossibility theorem and no promotion of finite controls to a derived continuum net. Missing is the actual local charged source operator or equivalent functorial gauging with marking and time. New refinement: old audit concerns full local spinor/GSO extension fromP1. On given even quotient net rho_s and smooth neutral transport now follow from existing current without spin sum. Neutral observable response requires neither individual-field membership nor fullQ-system; raw P1 locality and normalized response still need proof.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9d9d6e54842cff68809d8f77",
        "source:15a896e7f2c0b520dc0a57a8",
        "source:bc2ac32f76c0075a80b694fd",
        "source:ee72ee9239a1684c97e246d5",
        "source:63a389bde9bd8acc46bff118",
        "source:e0d26e429a991b6b9e0a4de0",
        "source:e91abca172999fb5c68aa005",
        "source:6544d002215be4919b8c4793",
        "source:8c083f0ef0bbdd15e64d36b4",
        "source:55ba404e7350afa1c83ea289",
        "source:1eba7623e4e6cb3ece69430c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:hypergraph-local-update-repaired-with-full-family-clock",
      "titleEN": "Actual hypergraph update repaired and full three-mode clock reused",
      "statementEN": "Old _micro_step overwrote T_net@m during family update; old passing test never called it. Integrated fix computes T_net@m@M.T and checks all27 basis inputs through actual function. Existing v486/v487 M replaces incomplete v327 rule:spec M={1,2/3,1/3};O^T M^6 O=diag(1,64/729,1/729). One hand is N C^6=T_net tensor M^6,not (NC)^6. Normal and -OO6/6 with identical output;independently reviewed. McKay Doob transform with existing marks d gives P_ij=(A_ij+2delta_ij)d_j/(4d_i),reversible pi_i=d_i²/120.",
      "scopeEN": "Implementation repair and exact finite recursion identities. v395 matrix comparisons themselves numerical; rational identity derived separately. E8 Cartan,P2 and scheduler remain given inputs;no quantum-field or physical-time origin. Paper sources and local website copy corrected;full publication audit failed on previously retired registry files,no published overall completion.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:specified-petersen-shell-and-full-family-finite-recursions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:61d87a7e7e9e2de024349e7d",
        "source:c34002a86520b189eb44dbc2",
        "source:d2ca7b949711d70108b7070e",
        "source:f076e23b0d384c8af7d717d1",
        "source:e67ad00f28d3ab0e20676e4e",
        "source:f145ea4f94970ba584519033",
        "source:c580edfa760b2518130d9f49",
        "source:20aa0bcfab68bac562e7d3c6",
        "source:5f32ad56f721ebb21c3ada40",
        "source:eabe3d8fc5cf64553636a508",
        "source:9a6e585cf235a3d5d629b49a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:petersen-polar-step-has-exact-double-cover-family-intertwiner",
      "titleEN": "Exact Petersen polar transport on double cover including charge defect",
      "statementEN": "P is selfadjoint on H_pi with eigenvalues1,-2/3,1/3. Marked isometry W identifies |P| with M and sign(P) with K=Z Delta,Z=diag(1,-1,-1). Thus WPW^-1=KM and WP^(2n)W^-1=M^(2n);W_n=K^nW identifies each step in a moving frame. Bipartite double admits fixed six-dimensional intertwiner with transported deck tau tensor K. Simultaneous positive M and literal Delta identification is impossible on simple2/3 eigenspace. Y transports but [Y,P] has rank2:raw Frobenius square125,isometric moving-frame700/9. A physical charged total process needs actual compensating transfer.",
      "scopeEN": "Complete finite operator comparison,stronger than sixth-power or spectral agreement. Z already occurs in v409;identification on the same source with v487 and geometric deck remains open. No fixed electromagnetic charge conservation,physical Hamiltonian or identification of K²=1 with full spin lift alpha²=beta.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:specified-petersen-shell-and-full-family-finite-recursions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:40af664d01eb23108d76a788",
        "source:2bd8d6eb53fafc5754978b7d",
        "source:a6d020ad151dd01f2d94e721",
        "source:00aa43eb96f8b5d54f9c8a0b",
        "source:07102da1dcbcb85e25ff1fa7",
        "source:1bcb6de57e4232cca2a3b6fa",
        "source:eb86ae87ced5edb7efe241cc"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:petersen-source-current-and-hodge-candidates-fail-physical-identification",
      "titleEN": "Original bilocal current and natural Hodge amplitude decide two concrete Petersen candidates",
      "statementEN": "Original bilocal current a_r* a_s changes at most one occupied index and has zero matrix element on all30 directed Petersen edges of disjoint two-words. New natural candidate C_v=*(v wedge .),v=(1,...,1),matches disjointness support exactly,but C_v³=5C_v and chi=lambda^4(lambda²-5)^3. Six of twelve pentagons have negative flux;diagonal phase gauge or orientation does not yield A_Pet. This concerns linear operator equality. Born readout of squared moduli is a distinct specifically tested route and is not excluded merely by this sign result. Existing quartic fields and two-boundary state do not define marked Lambda²C5 compression with weights,compensating charge and time.",
      "scopeEN": "Only direct bilinear candidate and linear Hodge gauge identification excluded. C_v is not defined as physical operator in v474. No general exclusion of quantum probabilities,quartics,original source or E8. Existing Bell Petersen population process retained,not reinterpreted as source dictionary despite incompatible Sym²C4/Lambda²C5 representations.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:specified-petersen-shell-and-full-family-finite-recursions",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:794c03a0274ca5a7dc4ff7a7",
        "source:0de7e0b1523ca4305cc4b90a",
        "source:8328e8b2ac375a0a8ffeae73",
        "source:22509c2d8ec92f61da1cb530"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:a7-clock-direction-identifies-neutral-e7-zero-root",
      "titleEN": "Original eight-clock marks A7 and neutral E7 zero-root mode",
      "statementEN": "With rho_A7=(7,5,3,1,-1,-3,-5,-7)/2 and q=(1,...,1),exactly delta=-rho_A7/8+(2a-1)q/16 and H8=8L0-rho_A7.a0+(2a-1)Q/2. p*=(++++----)/2=omega4(A7) has norm²2,Q0,rho.p*=8 and is unique neutral E8 root of H8 grade0. The126 neutral roots form E7(q/2),exactly56 A7 roots plus70 Lambda^4C8 weights. All240 roots and reflection closure checked exactly.",
      "scopeEN": "New joint interpretation of existing clock shift and already known charge census. No rediscovery of old ground doublet or D8/E8 Coxeter grading claim. Q is source U1,not automatically electromagnetic charge. p* is an E7 root,not E7 singlet. No time generator changed.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:four-d8-sectors-with-fixed-affine-source-time",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6ace4826ef1d7a8401eec5a3",
        "source:377d492305aafb9d227c21bd",
        "source:d14c428d13afcf4e0b8abc6b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:oriented-sewing-cocycle-distinguishes-continuation-and-reversal",
      "titleEN": "Oriented sewing continuation and genuine reversal satisfy distinct exact compositions",
      "statementEN": "alpha01=T,genuine reversal T^-1,continued positive quarter alpha10=beta0 T^-1. Hence alpha10 alpha01=beta0 and alpha01 alpha10=beta1,whereas forward/reverse yields1. Normalized central cocycle omega(1,1)=beta describes nonsplit1->C4->C8->C2 over mu4,with correct adjoint and defect-line dualization. Positive local spin quarter lift squares to+i independently of lift sign,matching marked q norm factor. Literal unextended D4 reflection s²=1 cannot map to alpha²=beta.",
      "scopeEN": "Marked spin transport and existing two-object vertex functor. Full open P1 amplitude functor,its determinant line and identification of U_Gamma with normal spin transport remain to derive. No identification of group orders or two-object set with physical spacetime.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:marked-oriented-quarter-spin-and-two-object-vertex-transport",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ea5062ea6523f85b48ebd224",
        "source:1f4c57be12bf3a4ce5c74095",
        "source:deeeb4e1cf919771c6205b77",
        "source:25b8d775d8a66ddedc8a326f",
        "source:71685c97342e949df19abb07"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:calderon-single-face-compression-is-not-perron-projector",
      "titleEN": "Natural single-face compression of Calderon projector is not Perron projector",
      "statementEN": "For Pi=[[I-C,X],[X,C]],Pi is rank3 orthogonal projector on six-space. Natural single-face compression C has eigenvalues{1/2,4/13,1/10},hence rank3,not a projector and not rank1 Perron projector. I-C also has full rank. Seven rational checks establish counterexample to The reviewed proposed identification in natural finite comparison. Two actual The reviewed Opus4.8 consultations retained with corrections;The reviewed retracted five false time/state/grading claims of first round.",
      "scopeEN": "Exclusion of precisely specified single-face inclusion;not every source-derived invariant shell inclusion. Same formula2P-I or minus sign identifies neither spaces nor actions. The reviewed responses remain external proposals;no automatic proof acceptance or source-time change.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:natural-single-face-inclusion-in-given-family-calderon-graph",
        "premise:specified-petersen-shell-and-full-family-finite-recursions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [
        "Non-scientific attribution omitted from public display."
      ],
      "language": "en",
      "sourceRefIds": [
        "source:878b4f7ae08557e66c1e861e",
        "source:a7b7f546bfea71d9230610e0",
        "source:2c161826e29b19fe92df7a4f",
        "source:68cfb86ff5c85238575b5e75",
        "source:ccaa860fc851f4cb6a9f54b4",
        "source:f5034a020d9a883e37fa9638"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:hodge-born-magnitudes-and-filtered-petersen-jump-match",
      "titleEN": "Hodge Born magnitudes and filtered Petersen jump block agree exactly",
      "statementEN": "Entrywise |C_ef|²=A_Pet[e,f]. For x=cos(sqrt5 t),U(t)=exp(-itC) has exact population values p_diag=(2+3x)²/25,p_edge=(1-x²)/5,p_nonedge=(1-x)²/25. Thus no full U(t) population is pure Petersen transition. At t*=(pi/2+k pi)/sqrt5,added edge filter yields existing subnormalized jump block A_Pet/5 with probability3/5. Reject is4/25 at input plus1/25 at each of six nonneighbors,not old stay block2I/5. Conditioning on change gives A_Pet/3 in short-time limit. C/sqrt3 is not Kraus;C/sqrt5 has rank6 projector effect rather than3I/5 and superoperator rank36 versus actual J20 rank40. Six actual J20 phase matrices gauge to -A_Pet,not C.",
      "scopeEN": "New exact Born-magnitude bridge and conditional population matching. No equality of full instruments or P1 derivation of measurement basis,time,acceptance or reset rule. Linear sign obstruction explicitly does not imply general exclusion of quantum-probability derivation.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:oriented-five-slot-hodge-candidate-with-explicit-basis-readout",
        "premise:specified-petersen-shell-and-full-family-finite-recursions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8328e8b2ac375a0a8ffeae73",
        "source:22509c2d8ec92f61da1cb530",
        "source:794c03a0274ca5a7dc4ff7a7",
        "source:0de7e0b1523ca4305cc4b90a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:five-complement-amplitudes-form-full-petersen-quantum-channel",
      "titleEN": "Five complement amplitudes give full Petersen quantum channel and SU5 response sectors",
      "statementEN": "C_m²=P_m of rank6,sum P_m=3I10. Phi=(1/3)sum Ad(C_m) is CPTP,unital,HS selfadjoint;population exactly A_Pet/3 without time or filter,Choi rank5 with eigenvalue2^5,superoperator rank100. Correct covariance connects10 and10bar. Actual24 is dGamma(sl5),Phi(dGamma A)=-(2/3)dGamma(A)^T. On End10=1+24+75,Phi²=Pi1+4/9 Pi24+1/9 Pi75,so Phi^6 spectrum1^1,(64/729)^24,(1/729)^75. Actual radial restriction on Petersen shells1,3,6 yields previously transported P. As specified channel,Phi has unique stationary density I10/10.",
      "scopeEN": "Previously excluded single coherent sum C_v remains excluded as Kraus normalization;five events change premise. Fermionic reduction channel is known mathematics;new result is concrete TFPT source/record/rate connection. Same three values identify neither all100 quantum directions with3D family space nor physical time or initial state.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:specified-petersen-shell-and-full-family-finite-recursions",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9c43e2fcbcb46fd15fb6c790",
        "source:8706c57116d9e93c4066b9c8",
        "source:99615166b8269b2dae27e470",
        "source:a82ac3f040710c1a79f18af1",
        "source:e88fdbf2afa2924ddccbd202",
        "source:c13e2fcc6bd865298409eec1",
        "source:a7488da20e42d6dce25f0ec8",
        "source:9d81083e92c72edd1232ff12",
        "source:0f739621f7af91440417eb9e",
        "source:c50d0923315ad4c0a9bd8874"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-twenty-events-factor-through-hodge-and-conditional-phase-record",
      "titleEN": "Original twenty events factor into Hodge outputs and conditional four-phase record",
      "statementEN": "For each of6 marks,old20 jump events group into5 blocks of4 with Hodge effectP_m/3 and same basis movement. Exactly R_l=D_l C_m onP_m;relative to baselineD0,H_l=D_lD0* form projective K4 with3 characters each multiplicity2. Psi_m=(1/4)sum Ad(H_lD0) after Phi_m. New/old Choi ranks peroutcome1/3,total5/15;superoperator ranks100/40. All60 ordered intersecting-duad coherences permark distinguish channels. No common10-label diagonal gauge for all5 baselines:complete finite test0 solutions permark.",
      "scopeEN": "Outcome-dependent phase averaging before forgetting m,not one phase channel after coarsening. K4 is actual tested projective four-group,not automatically cyclic C4 clock. Proof in fixed event-label chart,without physical Bell10/Lambda²5 or SU5/native group identification. Classically merging20 outcomes does not restore lost coherences.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:specified-old-j20-instrument-in-fixed-six-mark-duad-chart",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9c43e2fcbcb46fd15fb6c790",
        "source:8706c57116d9e93c4066b9c8",
        "source:99615166b8269b2dae27e470",
        "source:a82ac3f040710c1a79f18af1",
        "source:e88fdbf2afa2924ddccbd202",
        "source:c13e2fcc6bd865298409eec1",
        "source:a7488da20e42d6dce25f0ec8",
        "source:9d81083e92c72edd1232ff12",
        "source:0f739621f7af91440417eb9e",
        "source:743592f989c73e9af018f136"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-e8-mixed-current-response-is-full-clifford-channel",
      "titleEN": "Actual mixed E8 current response is full Clifford channel with retained carry",
      "statementEN": "In D5+A3 frame:60 g2=(10,6) root brackets g1=(16,4)->g3=(16bar,4bar),gain15I64. All112 D8 root actions/3584 sign equations and all960 nonzero g2 columns match CAR in joint cocycle chart. Normalized response factors Q5 tensor Q3 with Q5=(1/5)sum(a rho a*+a* rho a),Q3 analog1/3. Reduced carrier theorem also holds for correlated input. Lambda² sends3/5 toLambda³ (Petersen A/5 after duality) and2/5 toLambda¹ as genuine carry. Full Fock population isQ5 cube,antipodal quotient already known Clebsch16 of v810.",
      "scopeEN": "No raw bitbasis partial trace:product phase gauge absent there;full group action must transport. No unconditional A/3 onLambda² and no old stay2I/5. Internal Clifford action on bosonic weight-one current states does not supply spacetime fermion fields. Actual P1 event/time selection from this reader remains open.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-full-e8-current-source-with-fixed-carrier-su5",
        "premise:specified-inclusive-current-response-with-invariant-metric",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f6459e97f5a0efe4ef080b65",
        "source:1606a1e0412c934e1ccdf54e",
        "source:3ecca5d911f750bc84110143",
        "source:b6c66f60baad54286285e53e",
        "source:14747d961c70bd4c7f4e6537",
        "source:adebdf1d40f06bb0e948078d",
        "source:46a0ba85036c6f833f7a896c",
        "source:732e5aebb092a6ca4d5921b7",
        "source:2765e8b2381f52b35272e50a"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:carrier-su5-centralizer-gives-direct-e8-petersen-response",
      "titleEN": "Centralizer of given carrier SU5 supplies direct E8 Petersen quantum response",
      "statementEN": "Fixed carrier A4 inside D5 has exactly20 centralizer roots in same E8 with derived A4 Cartan matrix. Four50 sectors give (5,10),(10,5bar),(10bar,5),(5bar,10bar). Actual bracket(5,10) tensor(10,5bar)->(10bar,5) has50 rank12 Kraus B_mab=C_m tensor A_ab. One joint cocycle chart satisfies600 bracket edges plus1500 neutral A4+A4 action edges,including fixed dual Hodge signs. Gain12I50,normalized response Phi_Petersen tensor WH5,WH5=(Tr sigma I-sigma^T)/4. For all correlated inputs,reduced carrier response is Phi,without3/5 conditioning. All600 original P2 X charges satisfy qout+qenv=qin with dual target and qenv=-X_m.",
      "scopeEN": "Closes algebraic origin of full Hodge/Petersen channel as mathematical inclusive response of same given E8 source. New50s are not old64s;family5 restricts to oldA3=4+1,not new physical generation count. Joint tensor chart instead of raw coordinate trace. Z5 center not automatically original C5/Galois/Coxeter/physical clock. P1 selection of exactly these50 insertions,their record,state and time iteration is not proved by bracket alone.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:given-full-e8-current-source-with-fixed-carrier-su5",
        "premise:specified-inclusive-current-response-with-invariant-metric",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6b7df759ff21adbfe5bfeb3f",
        "source:b845077ba9d616a9d3db683b",
        "source:cf00af672b88914bae50e2b3",
        "source:f313962da40dfa9c7bb6b007",
        "source:1b99e7cc64084bfc25075ed1",
        "source:f06dc4363ad957a733eef55d",
        "source:00b064d1697690583491771c",
        "source:09663551c6849681267848bc",
        "source:7f6de2174fef00f92edada90",
        "source:2765e8b2381f52b35272e50a",
        "source:2d13205f662381f8cfde42ca"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:su5-covariance-and-petersen-support-fix-complete-quantum-response",
      "titleEN": "Full SU5 covariance and Petersen support fix complete quantum response",
      "statementEN": "Actual dual Choi representation splits multiplicity-free5+45+50 with explicit projectors. All25 gl5 actions,Casimirs24/5,64/5,84/5,and one highest-weight line per sector checked. All covariant CPTP Choi are sum p_d(10/d)P_d. Zero stay forces p50=0,zero intersect p45=0,hence T=Phi including phases. Within exact covariant class,total stay/intersect leaks s,o give p50=5s,p45=3o/2-9s/2 and exact diamond distance3o+s. SM plus actual carrier wedge fivecycle would generate full SU5.",
      "scopeEN": "Conditional complete channel classification at fixed carrier,not proof that P1 supplies full SU5 event covariance. General commutant method is known primary literature;concrete rigidity checked here. No physical time inferred from channel powers.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:specified-conjugate-su5-covariant-petersen-channel"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:14049b521ce4f43cf2d40648",
        "source:756af315b172b178cfc3d7ed",
        "source:dca548b7389604fdbfaa0b2f",
        "source:046aed78f0087bc65c77c993",
        "source:f5b30ea37a3f71be1fc9cb65",
        "source:38c8e355a15c9a58bc5df508",
        "source:b14f0d791fb5bb511ddbfb40"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:neutral-pair-witness-separates-old-events-and-hodge-response",
      "titleEN": "Neutral joint process witness separates old events and Hodge response",
      "statementEN": "P5=sum|C_m>><<C_m|/6 is rank5 and full SU5/SM invariant. Normalized Choi pPhi=1,pPsi=1/5 for all6 actual old marks. All single-leg marginals equalI10/10,joint neutral commutant restrictions differ. Old SU5 twirl weights exactly(1/5,2/5,2/5);twirl creates stay2/25,intersect38/75 rather than pure Petersen support and does not restore Phi.",
      "scopeEN": "In specified duad comparison. Bell10=Sym²C4 is not thereby SU5 module Lambda²C5;no physical P1 Choi preparation or admitted P5 measurement established. Image membership and reference separate.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:specified-old-j20-instrument-in-fixed-six-mark-duad-chart",
        "premise:specified-conjugate-su5-covariant-petersen-channel"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:583275f8c4d7b8660c84f042",
        "source:2467931bbe7aa232b4d30ab8",
        "source:8a468d82a7181d4e43d22fbe",
        "source:91df8cb023a8faf7d131ce82",
        "source:2b9656a5a1f16d1fc6ee35bb",
        "source:a6ddb5ba0823fc9e358b941c",
        "source:38c8e355a15c9a58bc5df508"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-degree-clock-is-not-carrier-slot-cycle-at-fixed-source",
      "titleEN": "Original degree clock is not slot cycle of same source",
      "statementEN": "Original U5=exp(2pi iX/5) equals zeta5^3 I5 onV and zeta5 I10 onLambda²V. Its adjoint action generates no additional SU5 directions. Pure central phase lifts with same projective image do not change this. Actual slot cycle moves3+2 mark;nakedS5 differs from markedC_fin withAutC6. On actual50-root E8 insertion sector,W5 preserves roots/fixes familyA4 but Δh8=+1 on40,-4 on10;witnesses e1-e8→e2-e8 have grades1→2,independent of lift phase. Finite H8 kernel is not invariant under this slotcycle.",
      "scopeEN": "Only these explicit U5,W5 and given H8 insertion;no exclusion of noncentral monodromy,resolved C12/C48 or full TFPT. H8 not identified with physical OS time.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:fixed-three-plus-two-mark-and-typed-original-degree-clock",
        "premise:given-full-e8-current-source-with-fixed-carrier-su5"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:898ce78cc19ad06864cd6888",
        "source:7313bedf96d8cb86f0a1575e",
        "source:1ae415ffa3914016494de5fd",
        "source:abce537c9d0e8e2b32e425f2",
        "source:821015865aa5775aeb07faec",
        "source:d5ab000a9bf6677dd6770d1b",
        "source:960c900a1f63e87eea335f5c",
        "source:e3e8477d5bd750c7235fb5d0",
        "source:8c5d9df934cb9716cda093a8",
        "source:38c8e355a15c9a58bc5df508",
        "source:bd5ad50cd366db506e05cf5f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-mark-transport-and-isospectrality-do-not-select-hodge-channel",
      "titleEN": "Full mark transport and equal spectra do not select Hodge channel",
      "statementEN": "For rank3P,U(P)=-I onCC,+I onCW/WW. T_P=Phi o AdU(P) is full SU5 covariant family overGr(3,5) with dual output,G_P covariant,same population/Choi rank5,but P5 value4/15. S_P=AdbarU(P) o Phi o AdU(P) likewise natural family;in adapted real chart real symmetric Kraus,unital,HS selfadjoint,same5 effects,Petersen population,full spectrum,unique fixedI10/10,but P5 value7/15. Powers similar,not identical. U(P) violates exterior-square phase relation,not carrier torus gauge. Full family covariance plus all listed criteria therefore insufficient.",
      "scopeEN": "Counterexample to selection rules in fixed dictionary;not asserted full E8 bracket automorphism,actual OS reflection,or classification of all merely SM covariant instruments. Does not prove fundamental gap is one-dimensional.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:fixed-three-plus-two-mark-and-typed-original-degree-clock"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:14049b521ce4f43cf2d40648",
        "source:756af315b172b178cfc3d7ed",
        "source:dca548b7389604fdbfaa0b2f",
        "source:046aed78f0087bc65c77c993",
        "source:f5b30ea37a3f71be1fc9cb65",
        "source:219b11f9a29caa64956d04f9",
        "source:b14f0d791fb5bb511ddbfb40",
        "source:38c8e355a15c9a58bc5df508"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-pair-source-fixes-state-but-not-selected-epsilon-process",
      "titleEN": "Given two-boundary state does not determine selected epsilon event law",
      "statementEN": "After typed embedding of dual two-hole legs,P5 on fixed sectors is even eight-field word;total contragredient P2 pair charge neutral,individual matrix units only particle-number neutral. Existing bilocal/vertex/GNS theorems transport word if actual local source map given. FullP_A fixes state/word expectations,not input-reference/Choi preparation or Kraus record. In givenE8_1 module,compact50-current Gram delta canonical(raw cocycle26+/24-),gain12 forces inclusiveTP normalization1/12. Using this reader as P1 event operation does not follow from Gram.",
      "scopeEN": "No new free field choice or reopening resolved source bridges. Specific local,time/reflection-compatible P1 embedding of A4+A4 sector and operational epsilon sewing identity remain required source derivation.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:given-full-e8-current-source-with-fixed-carrier-su5",
        "premise:specified-inclusive-current-response-with-invariant-metric",
        "premise:original-admissibility-and-graded-source-interfaces"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:898ce78cc19ad06864cd6888",
        "source:7313bedf96d8cb86f0a1575e",
        "source:1ae415ffa3914016494de5fd",
        "source:abce537c9d0e8e2b32e425f2",
        "source:821015865aa5775aeb07faec",
        "source:14049b521ce4f43cf2d40648",
        "source:756af315b172b178cfc3d7ed",
        "source:748b7940e88d21a0f908d8c7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:single-positive-process-saturation-selects-full-hodge-channel",
      "titleEN": "Single positive process saturation fixes full Hodge channel without SU5 premise",
      "statementEN": "For arbitrary CPTP T:End10→End10bar,T=Phi iffTr(P5 J_T/10)=1. Positivity forces Choi support inP5,henceJ=VKV*,K≥0. Actual25 identities C_m*C_n=delta_mnI-dGamma(E_nm) giveTP Choi partialtrace A(K)=trK I-dGamma(K^T)=I. Coefficientrank25,unique rational solutionK=I5/3,henceJ=2P5. Full100directions/phases/Petersen population follow without assumed group or population rule. Shorter concrete source target isTr((I-P5)J_source)=0 with actualTP insertion.",
      "scopeEN": "Complete mathematical selector for unread channel,not derivation of process saturation fromP1. Actual source amplitude/input-reference required;P_A state purity no substitute. No unique observed instrument/pointer register or full physicalTFPT established.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:specified-cptp-source-process-with-p5-saturation"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:1f3ea202fe5b37aa0a7f279f",
        "source:f4d5923273bef7d0d71fbb81",
        "source:ae739d4b08a1f1f187634525",
        "source:6eb7b3162ed11ffb087e32db",
        "source:691ad4434cc69b266c3caac1",
        "source:6ad5e91724e456b3c7a936bd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-five-slot-wedge-is-exact-e8-hodge-coefficient",
      "titleEN": "Old five-slot wedge table is the exact E8 Hodge coefficient",
      "statementEN": "Old architecture and v880/v888 already contain Lambda²E×Lambda²E→Lambda4E with all15 doily lines. Canonical volume character chi(m)=(-1)^m exactly gives epsilon(m,i,j,k,l)=chi(m)epsilon(i,j,k,l). All30 directed coefficients and sum C_m* C_m=3I match the checked A4×A4 E8 current bracket. Carrier tensor was not invented by later SU5 covariance.",
      "scopeEN": "Algebraic provenance closed. Original text explicitly leaves physical quadratic one-step exhaustion open. Read P1 net does not specify a concrete charged E8 insertion or inclusive50-current contraction; reflection and abstract Z4 Q-system do not automatically supply them.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e5b69c702131e72d940427d8",
        "source:5b2f9200b5e28c1202c13fb3",
        "source:16c2b129b5b3209590e3af39",
        "source:736cb842b69f2d979766a290",
        "source:90c96117f0a6531c04ea5ecc",
        "source:bf4a701d9d26770402cde298"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-pauli-f20-metric-and-quarter-bridge",
      "titleEN": "Native Pauli F20 and cyclotomic four match metrically with quarter lift",
      "statementEN": "Actual v783 words yield C_p=-i(I⊗H)CNOT(S⊗I)(H⊗I),G_p=(Y⊗Z)CNOT(I⊗S)(S⊗I),C_p^5=G_p^4=I and G_p C_p G_p^-1=C_p². Complete Pauli16×mu8 search at fixed C_p yields exactly four mu4-equivalent G corrections. Explicit four-intertwiner T to v419 satisfies both generator equations and T†T=2(5I-J),with dimension-one intertwiner space. G_p has conformal symplectic multiplier i; existing mu8 lift zeta8^-1G_p is symplectic order8. Quarter character makes Sym²4 and Lambda²Perm5 isomorphic F20 modules. Merely imposing F20 leaves ten-dimensional commutant M2(C)+C+C,dimension6.",
      "scopeEN": "Earlier reasoning was too narrow in conflating old noncentral v419 clock with separate scalar hypercharge U5. Available carrier subgroup and metric representation are now explicit. Original physical subgroup selection,full field dictionary and channel equality do not follow. Choi ranks15 and5 remain different.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9c3847a70174e9fd131aa703",
        "source:6e24ff5d3dd3691eafd6f922",
        "source:cd28d8a197ab4a292ef3be30",
        "source:87cfc9dffc0289ad88a13099",
        "source:7851dc89d482330ec3bc37f8",
        "source:62dc602bcabca3d8dae1f982",
        "source:66077aa87139fa32169d995f",
        "source:4ba312f84f1af91c3fa3fd67"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:two-actual-coherent-events-herald-hodge-at-one-over-twenty-five",
      "titleEN": "Two actual coherent events herald Hodge at optimal1/25",
      "statementEN": "In each fixed source-derived duad chart,the Hodge5 Kraus space intersects marked20 jump span in2D (15+5−18) and unmarked60 span in2D (55+5−58);hence no pPhi CP subchannel for p>0 after one step. Two-step products A=[vec(U2U1)] have rank100. Exactly V†(AA†)^-1V has three1/48 and two1/64 diagonal entries in these charts. CP order S/3600≥pVV†/3 gives exact pmax=1/25. Minimal coherent record contraction has three1 and two3/4 row-Gram eigenvalues and input-independent success map(1/25)Phi.",
      "scopeEN": "Changed premise grants coherent history access and active selection. Filter and Hodge target are chosen after a duad chart,not derived fromP1.1/25 is proved for these charts,not automatically for any subsequent metric F20/Spin5 transport. Classically read event labels are insufficient;no physical event-rate or vacuum proof.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:two-actual-source-events-with-coherent-record-access",
        "premise:given-five-slot-exterior-source-with-retained-complement-index"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6b89706a25fc792a05814132",
        "source:0021deead966c46069931705",
        "source:67553ec90270798c028de4bb",
        "source:2ed4a5b4e9544f0460bca987",
        "source:1a8e18a264e18aadca53fd24",
        "source:231d27083660c30d449a69a0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-color-center-removes-only-extra-h8-ground-state",
      "titleEN": "Original color center removes the only extra H8 ground state",
      "statementEN": "Former second zero charge p*=(+,+,+,+,−,−,−,−)/2 maps under fixed Weyl M to e1+e4 in actual(3,2)_(1/6) carrier frame. It is neutral only under transported sourceU1,has colortriality1. Original P_sing=(1+Zc+Zc²)/3 kills it and retainsOmega;[H8,P_sing]=0 as Cartan actions. Full lattice classification gives full kernel{Omega,p*},center-neutral kernel C Omega. Exact H8 gaps3/2 foralpha1/4 and2 for3/4. Global nonroot bound from||delta||²85/128 proves completeness of240-root census for these gaps.",
      "scopeEN": "Precise scope correction to former double-ground obstruction:it remains on full gradedE8 field net but disappears on later center-neutral observable sector. P_sing is center-neutrality,not fullSU3 Haar projection. No established P1/OS identification or4D massgap.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:stipulated-e8-h8-with-original-color-center-selector"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d3a28b77dd7a517d66470997",
        "source:31173cd240dbc226eda17574",
        "source:f349a15a8a58ba4f57d9c5da",
        "source:c8bb85087e9a08f486ef4f65",
        "source:2a70388b714fcaeb14b98acb",
        "source:6864f68f69cb6c243942579d"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:marked-symplectic-functor-fixes-native-hodge-kraus-space",
      "titleEN": "Marked symplectic functor fixes native Hodge Kraus space",
      "statementEN": "At fixed actual nativeF20 word pair and +i quarter orientation,the compatible alternating formOmega is unique up toscalar. W5=(Lambda²V/<Omega^-1>)⊗chi^-1 has positive metric,orthogonalq and compact real structureq conjugation. Canonical Spin5 map S→SOmega→L_S→L_Sq^-1 hasdet8,F†F=inducedSym²metric andHom_sp4 dimension1. It replaces merelyF20 U2×U1² ten-freedom by one phase line. OnW_R,K={x→*(w∧x)} is basis-independent5D,HS Gram6I andsumC†C=3I. ThusF defines a specific native Hodge candidate.",
      "scopeEN": "Full continuousSp4 naturality is mathematical property of category generated by markedOmega;v783 proves no such physical source symmetry. Original source must still select nativeF20 wordpair and quarter orientation. Source-conjugate wordpairs yield conjugateKraus spaces,distinct candidates in fixedBellchart. F20-labelled five-slot chart still has dimension-two Hom. No physical channel execution theorem.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:66dce1c494b4a203d98234ea",
        "source:2e203301085f79cf822408b2",
        "source:ad1ecea7e5ac730b73dfcdca",
        "source:4c1274b753c0f237370f5546",
        "source:9a57a5d47551b9b19e653d32",
        "source:1b143be1940fd477965716ef"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:f20-record-repair-removes-chart-induced-three-plus-two",
      "titleEN": "F20 record repair removes chart-induced three-plus-two split",
      "statementEN": "Raw old duad chart failsF20 generator intertwining. At uniqueF20 fixed outermark5,slot permutation(4,1,3,2,0) and explicit diagonalMu4 gauges repair both actualgenerators for bothquartertwists. Repaired two-record hasV†(AA†)^-1V=I5/48 andRR†=I5 atpmax1/25. Raw3+2Gram failscommutation withnativefivecycle;its splitting is target/chart selected,notF20 structure.",
      "scopeEN": "pmax1/25 verified for two repaired monomial transports. FullF20 freedom is not classified by this test. Do not infer physical3+2 fromrawGram or equate thesecharts withSpin5 transport without testing.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:two-actual-source-events-with-coherent-record-access"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3f2003493337d79abff6089c",
        "source:202e2f3b80869c29955cff50",
        "source:e01399fcf12c725c0ea3e183",
        "source:eeb40477bc43758ff6864c47"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:theta-scalar-square-lift-is-distinct-from-symplectic-f20-lift",
      "titleEN": "Scalar-square theta lift differs from symplectic F20 lift",
      "statementEN": "Existing markedtheta four hasalpha²=iI4. New symplecticF20 liftGhat=zeta8^-1G hasGhat²=−iG²,nonscalar withtrace0;G² is nonscalar. Thusalpha andGhat are not conjugate evenup tocentralphase:projective orders2 and4. Sharedorder8 andfourthpower−I do not identify operations. SharedMu8 scalar resource remains correct.",
      "scopeEN": "Smallest actual operatorcountertest prevents equating differentclocktypes. No contradiction of separateclock constructions or metricF20 carrier bridge;no universalfield orTFPT no-go.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bf1d8fe09a04ca574d009686",
        "source:feab01b069fdeeb74979da9b",
        "source:97f3f254ec041dd689854075"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-admissibility-vacuum-test-needs-source-image-and-transfer-reduction",
      "titleEN": "Full admissibility needs vacuum image and actual transfer reduction",
      "statementEN": "Original P_prim includes positive high-spectrum projector1_[eps²/4,∞)(D_prim†D_prim). An H8 vacuum mapped to a primitive Dirac zero mode would be removed. No original H8→H_prim/OS intertwinerW was found;neither retention nor exclusionOmega is established. QTheta Omega is also undefined onE8 module. OriginalD_adm commutators do not proveH8 commutation. If sourceW exists,Pprim WΩ=PTheta WΩ=WΩ andPadm reduces transportedH8,unique vacuum with gap at least3/2 or2 and exponential temporal semigroup clustering follow. OS reconstruction cannot prove this backwards because its theorem assumes clustering.",
      "scopeEN": "Reuses established image-membership test and refines it at actual original projectors. Dirac gap,transfer ground energy and internal E8 weight are distinct operator quantities. Projector product names or commutation alone do not suffice. No general TFPT no-go.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:stipulated-e8-h8-with-original-color-center-selector"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:172c321ee291cd9b41121b3f",
        "source:90f91221ca6d672fffc954a7",
        "source:d3a28b77dd7a517d66470997",
        "source:31173cd240dbc226eda17574"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:canonical-native-spin5-hodge-is-already-one-source-record-subchannel",
      "titleEN": "Canonical native Spin5 Hodge is already a one-source-record subchannel",
      "statementEN": "Actual symmetricPauliBellbasis P_b/2,inducedSym²metric and explicit compactrealframeR give exactly unitary U=Lambda²(R)†FN intertwining both actualF20 generators withchi^-1. NativeK_m=U†C_mU are fixed withoutduadlabels after fixingOmega. Their entire5D Kraus space already lies in actual60 one-record span ofrank55. Minimum solutionW1X1=V hasX1†X1=3/4I5. Exact CP optimum isp1=1/15. Actualtwo-record rank100 hasV†S2^-1V=I5/64 andp2=4/75. Both optimal contractions haveRowGramI5. One-step exclusion andp2=1/25 applied to different label/monomial target channels and must not be transferred toPhi_native. Source carriesK5 in frameeigenvalue8 space ofdimension45;frame alone does not select5.",
      "scopeEN": "Prior chart-dependent provenance gap is closed at markedOmega. One coherentrecord suffices;recursion is unnecessary for this target and requiredsecondsystemstep lowersoptimum. Mathematically specifiedCP subchannel is not an alreadyexecuted sourcemeasurement. PhysicalF20/Omega marking,recordaccess andcoupling remain originconditions. No completeTFPT solution.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:two-actual-source-events-with-coherent-record-access",
        "premise:actual-single-source-event-coherent-stinespring-record"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e2aa5a9e8330238d999a612c",
        "source:9a0b56a8c846ed65deced1fb",
        "source:9bfbc289faf5074e2154e480",
        "source:0a6bca350726800dca26cda2",
        "source:3527e94d50b7d4b1046ced83",
        "source:bf1d8fe09a04ca574d009686"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-hodge-record-selector-is-image-projector-not-kraus-kernel",
      "titleEN": "Native Hodge record selector is image projector not Kraus kernel",
      "statementEN": "X1†X1=3/4I5 determines orthogonalcoefficientprojectorPi_coeff=(4/3)X1X1†. In standardStinespringconvention sum_l|l>⊗U_l/sqrt60 actualrecordeffectisE=Pi_coeff^T sinceJ_E=W1E^TW1†/60;successbranchPhi_native/15. Same-dimension5DkernelW1 isorthogonaltoimageX1 andgiveszerosystemamplitude. OriginalPprim/Calderon/Qprim/Pfaffian actonotherimages. ExistingRECORDS.md givesconditionalcoherentrotation andexplicitlyassumesrecordcarrier/readoutbasis;stablerecordalgebra/Bornrule donotselectE.",
      "scopeEN": "Coherent C60 access and physical coupling/measurement{E,I−E} remain open for the conditional record implementation. This is not necessary for every Hodge realization: actual current intertwiner and charged OPE coevaluation bypass record measurement. Original image projector, transpose and exclusion of a Kraus-kernel replacement remain correct. See new current and sewing findings.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:actual-single-source-event-coherent-stinespring-record"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a5f15748968bc464af6f7664",
        "source:687c6780e15721e571b1bd9f",
        "source:9a0b56a8c846ed65deced1fb",
        "source:9bfbc289faf5074e2154e480",
        "source:0a6bca350726800dca26cda2",
        "source:3527e94d50b7d4b1046ced83",
        "source:e834c61dedcba1332be8a94e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:irreducible-f20-four-cannot-host-original-independent-native-family-clock",
      "titleEN": "Irreducible F20 four cannot host independent native family clock",
      "statementEN": "ActualnativeC5,G versus frozenv634sigma givecommutatorrank4 andbothranksGsigmaG^-1−sigma^±1 equal4. InanyirreducibleF20four,C5 hasfourdistincteigenvalues cyclicallypermutedbyG. Given[C5,sigma]=0 andorder3,G-fixingpermitsonlyscalartraces4,4omega,4omega²;G-inversiononlytraces4 or−2. Nativesigma hastrace1,hencebothimpossible. Originalcyclotomicplusrelationalreadyexists onrationalrank8Q(zeta30),withfamilymultiplicationtrace−4. Thisisnotnativecomplexsigmatrace1. Thetaalpha inversionisyetanotherclocktype.",
      "scopeEN": "Smallestnecessaryjointclocktestbeforephysicallyequatingseparatelyvalidfour-bridges. NoexclusionofnativeHodge subchannel,separateE8/thetaresults orlargersourcerepresentations. Oldrank8modulefixesarithmeticcommutationbutisnotphysicalsigma realizationwithoutdictionary.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:9371e900d70fa16814031a2b",
        "source:400a22485cf7e86912077d82",
        "source:1e0ce5535d6f89eaef983844",
        "source:80197d9b9a91fe31caae9fb8",
        "source:fb883484d01100dd1087f4ba"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:native-hodge-is-exact-collective-five-current-action",
      "titleEN": "Native Hodge five is the actual collective five-current action",
      "statementEN": "In pinned Bell10=Sym²C4 chart the five anticommuting Hermitian Gamma={XI,YX,YY,YZ,ZI} satisfy GammaᵀOmega=OmegaGamma. Collective D_Gamma(P)=(GammaP+PGammaᵀ)/2 equals a signed permutation of canonical native K_m, with D_YX=-K1 and the other stated correspondences. Sum D†D=3I. The old NS current intertwiner, verified on all16 matrix units, gives J0(Gamma/2)E=ED_Gamma; normalized contraction is exactly Phi_native.",
      "scopeEN": "Exact old A3 descendant operator identity under its given current-net premises. Omega and inclusive five-current contraction are not derived P1 selections. A physical C60 record measurement is unnecessary for this algebraic theorem. No charge-preserving P2 carrier identification.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:local-e8-current-response-realization"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e834c61dedcba1332be8a94e",
        "source:ccfd4a21b2c0cd60058127df",
        "source:876f5c5a9f239797de99d58f",
        "source:a0456c67748c9dc8707db776"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
      "titleEN": "Six ovoid fibers carry the clocks without a common fixed form",
      "statementEN": "The six alternating Pauli forms define six actual Clifford fives. C,G fix IY and induce F20; sigma acts in two 3-cycles and alpha inverts sigma with alpha²=iI. C,G,sigma generate transitive PGL(2,5)≅S5 of order120, certified by explicit conjugacy to its projective-line action; adding alpha gives S6 of order720. Full five-current fibers, not only labels, transport covariantly. J is projectively trivial on fibers.",
      "scopeEN": "Closes the finite common clock family on the existing Pauli object, without new tensor carrier or sigma-fixed symplectic form. Earlier four-dimensional no-go retains its added commutation premise. Original P1 must still select the marked F20 inclusion. Do not equate ovoids with six q/p divisor points, raw spread labels or sixty event records without maps.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:native-pauli-clock-family-with-marked-f20-inclusion"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6ca2a4cb09a9d6fd8a0c9fc8",
        "source:32b8d181b47efe2632e577de",
        "source:4226d1029621c76f3932ecda",
        "source:c74174d7b69ec6e5819bd138",
        "source:f9614622c690d614e4eff36d",
        "source:cf1d7600fa319596e7525135"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:six-hodge-responses-have-exact-full-current-barycenter",
      "titleEN": "Six Hodge responses have an exact common current barycenter",
      "statementEN": "Each of15 nontrivial Pauli current directions occurs in two of6 ovoids. Thus Psi_current=(1/6)sumPhi_Omega=(1/9)sum15 Ad(D_Gamma), gain9I10 and spectrum1[1],(5/9)[15],(-1/9)[84]. All15 current vectors occupy source-frame eigenvalue8. Rank15 E15_coeff=(4/3)XX† obeys sum E_Omega_coeff=2E15_coeff. Physical effects E_Omega_coeffᵀ/2 plus failure give Phi_Omega/30 branches, total Psi_current/5. Choi eigenvalues8/60 and2/3 prove sharp p≤1/5.",
      "scopeEN": "Barycenter requires no distinguished Omega. Uniform current contraction, physical record access and execution remain explicit conditional operations. Unique scalar fixed line is not a physical time law. Do not identify this channel with C60, old family transfer or a physical event rate.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:native-pauli-clock-family-with-marked-f20-inclusion",
        "premise:actual-single-source-event-coherent-stinespring-record"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e834c61dedcba1332be8a94e",
        "source:ccfd4a21b2c0cd60058127df",
        "source:876f5c5a9f239797de99d58f",
        "source:a0456c67748c9dc8707db776"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts",
      "titleEN": "Coxeter seventh-power action has exactly thirty E8 lattice lifts",
      "statementEN": "Actual Bourbaki Coxeter W has unimodular Krylov basis (r,Wr,...,W7r), so every lattice lift GWG^-1=W7 is determined by one of240 root images of r. Complete census gives30 lifts:10 order8 with G4=W15=-I,10 order24 with G4=W5 and10 with G4=W25. They square C5=W6 and fix cyclotomic C3=W10. None normalizes native J or sigma to itself or its inverse. Native sigma real trace2 differs from W10 trace-4.",
      "scopeEN": "Common actual E8 root carrier and complete lift classification; no canonical lift selection or field dictionary between clock subalgebras. Scalar-square theta alpha remains distinct. v634 J sign is +i and traces compare the same real dimension8.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6ca2a4cb09a9d6fd8a0c9fc8",
        "source:32b8d181b47efe2632e577de",
        "source:88d637e53bcd076365a96729",
        "source:d8e97ff8607f88673f83cce9",
        "source:4558a88959efbd5beee9e4d3"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:spin5-hodge-five-is-plucker-kernel-not-original-quartic-hessian",
      "titleEN": "Spin5 Hodge five lies in the Pluecker kernel, not original quartic Hessians",
      "statementEN": "Correct congruences D_m=F_RᵀC_mF_R vanish identically as quartics on S=zzᵀ. Multiplication Sym²(Sym²V4)→Sym4V4 has rank35 and kernel20 with independently checked scalar line and Spin5 five, jointly dimension6. Actual process._code_basis quartics and existing2+2 flattenings have image rank5 and zero intersection with Hodge five. Original holomorphic transport AAᵀ=0 prevents unchanged holomorphic point splitting from lifting the null relation.",
      "scopeEN": "Excludes ordinary quartic polarization, existing Hessian family and unchanged purely holomorphic CAR point splitting. Does not exclude mixed-adjoint or asymmetrically differentiated OPE components; new mixed-current representation is unaffected.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c043bf9cd49668ca7a2e5817",
        "source:8b261058aa9b699932565921",
        "source:ded5707fdeaed36f261634be",
        "source:1b1974344396afdf191c4305"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
      "titleEN": "Ising complement currents need a typed normal-field map",
      "statementEN": "In given A3_1=SO6_1 current net marked Omega selects Spin5=SO5. Five complement currents i:chi_a chi6: match actual Gamma/2 zero modes. Central charges3,5/2,1/2 give local even Ising coset; chi6 belongs to fermionic extension. Original P1 Clifford multiplication gamma_n on Cauchy data is not an internal local Majorana field. Read originals supply no state/OPE-preserving map between these types, and Hermiticity alone cannot select5 of15 currents.",
      "scopeEN": "Focused existing-current-net bridge, not a new auxiliary Majorana theory. Need original state-preserving normal/tangential field intertwiner including Omega; even that would not remove the separate physical P2 charge mismatch.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:native-pauli-clock-family-with-marked-f20-inclusion",
        "premise:local-e8-current-response-realization"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:ce1035eded9552fe9964de45",
        "source:1b8922c6079804fcb9c1701d",
        "source:e6367b122146887160b61bf6",
        "source:c2b62d452ea486f606d5a4fb",
        "source:2d4c9d39cd4a1414fec27f02",
        "source:a76d04f6aab261fba15dbd45"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
      "titleEN": "Neutral native A3 Hodge does not identify the physical P2 carrier",
      "statementEN": "Old Bell corner is (10_D5vector,10_A3descendant), weight2 and mu4 class(2,2). P2 Lambda²5 lies in D5 half-spinor paired with A3 fundamental, weight1, classes(1,3)/(3,1). Original Y spectra {±1/3[3],±1/2[2]} and {-2/3[3],1/6[6],1[1]} are disjoint, giving Hom_Y=0. A3 zero modes preserve D5 Y, center and L0, so cannot connect these types. Positive charged A4×A4 bracket remains valid as a different cut of the same E8 algebra.",
      "scopeEN": "Exclusion only for neutral family currents with unchanged original charge dictionary. No universal TFPT no-go or exclusion of charged insertions, explicit field maps or transported geometry. Prevents equating equal-dimensional spaces.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:given-five-slot-exterior-source-with-retained-complement-index"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a76d04f6aab261fba15dbd45",
        "source:a711458bbdc43e69b71f76dc",
        "source:e6bcffdadfcddceee5d613a5",
        "source:a0456c67748c9dc8707db776"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
      "titleEN": "Compact OPE coevaluation normalizes the given charged Hodge line",
      "statementEN": "In the given compact E8_1 net insertion M=(5,10) can be contracted with its compact adjoint in a closed current line. Invariant two-point metric gives basis-independent coevaluation; existing residues B_(m,ab)=C_m⊗A_ab obey sum B†B=12I50. R/12 uniquely normalizes this given line and its reduced carrier response is the existing Hodge channel. No additional fifty-event sampling policy or measured C60 record is needed for that contraction.",
      "scopeEN": "Conditional on actual charged extension, selected M line and matching two-boundary sewing channel; source origin is separately audited. Does not assert P1 physically realizes every OPE contraction, coevaluation is a localized intervention, or physical time/EM readout follows.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:full-existing-local-e8-field-hull-observer-code"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:e6367b122146887160b61bf6",
        "source:c2b62d452ea486f606d5a4fb",
        "source:2d4c9d39cd4a1414fec27f02",
        "source:3b7620318cf4e36b1a6d766a",
        "source:c5253c971a174a679f86f552",
        "source:a76d04f6aab261fba15dbd45"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:old-ward-root-generates-exact-charged-fifty-module",
      "titleEN": "Old Ward root generates the exact charged fifty-module",
      "statementEN": "Existing conditional Ward root lambda_A=e3+e6 belongs to actual A4×A4 insertion(5,10), with carrier weight(-2,-2,8,-2,-2) and family Dynkin(0,1,0,0). Closure under40 neutral roots reaches all50 insertion roots through500 directed edges. Old quarter grades split30 grade2 and20 grade3; P2 X values are-2[30],+3[20]. A single bracket has rank12 and is not TP. Thus given Ward dictionary determines the algebraic module more sharply than previously stated.",
      "scopeEN": "Concrete new cut bridge under still-conditional original E8 Ward dictionary and full charged current closure. Lie-orbit closure alone derives neither source measure nor actual positive normalized process. Old grade2 alone is not the full50-module. The50-module theorem remains correct as larger A4×A4 closure. New Ward/P2 route needs only original D5+A3 creation30 for carrier response.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:full-existing-local-e8-field-hull-observer-code"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:3b7620318cf4e36b1a6d766a",
        "source:c5253c971a174a679f86f552",
        "source:5c7a61e2af1366ff72bcf9be",
        "source:bdc247cb1341b818839ee4c0",
        "source:a773231f422a1acb52e13d34",
        "source:2e9b63acd5d857637bedc9fd",
        "source:b7dcf3eb8118d96c859f026e",
        "source:9dcff09d8ba8f45444f0b219"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:tp-charged-bracket-support-forces-entire-carrier-marginal",
      "titleEN": "Trace-preserving charged bracket support forces the entire carrier marginal",
      "statementEN": "Every CPTP joint map End(H10⊗F5bar)→End(H10bar⊗F5) with all Kraus operators in actual span{C_m⊗A_ab} obeys Tr_Fout E=Phi∘Tr_Fin. For any family density, reduced carrier map is CPTP with Kraus space inC5; existing injective25-coefficient TP theorem forces Phi without SU5 covariance. Product operators span the full input algebra, extending equality to entangled inputs. Arbitrary coherent insertion metric and unknown family state cannot change this marginal if TP and support hold.",
      "scopeEN": "Removes another unnecessary origin condition: full Killing orbit average is sufficient but unnecessary for carrier marginal. P1 must deliver actual normalized closed CP bracket process on the correct charged carrier. A single Ward current, non-TP postselected branch, extra Kraus directions or mere field availability do not automatically meet these conditions. No complete physical TFPT solution. Whole-CPTP theorem remains correct. Actual sector-resolved source branch only needs same carrier Kraus support and effect pI; its normalized carrier marginal is alreadyPhi. Do not demand an exclusively Hodge unread total process as general necessary physical premise.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:cb5d34b51d73a9471ecf9790",
        "source:3b7620318cf4e36b1a6d766a",
        "source:c5253c971a174a679f86f552",
        "source:e834c61dedcba1332be8a94e",
        "source:2e9b63acd5d857637bedc9fd",
        "source:b7dcf3eb8118d96c859f026e",
        "source:9dcff09d8ba8f45444f0b219"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:original-ward-and-p2-grading-select-smaller-creation-thirty",
      "titleEN": "Original Ward source and P2 grading determine the smaller creation thirty",
      "statementEN": "Original D5+A3 target g2=(10,6) splits into Creation30=(5,6) of U5 residue3 and Annihilation30 of residue2. Neutral SU5_C times D3_F orbit of stipulated lambda_A=e3+e6 is exactly Creation30. Full E8 residue3 instead has50=30g2+20g3; joint internal quarter grade2 and U5 residue3 selects30. Actual Chevalley amplitudes Lambda2 C5 tensor4 to Lambda3 C5 tensorbar4 have360 signed columns and gain9I40 on both sides. With pinned joint CAR phases, normalization1/9,Hodge and family trace, full carrier Hodge channel follows for arbitrary inputs. Color18 and weak12 separately have nonscalar effects; marked union has scalar gain.",
      "scopeEN": "Closes smaller algebraic bridge under given local E8 representation and oriented Ward comparison. No added physical SU5 gauge, mandatory family A4 closure or hardware measurement. Original U5 is scalar on fixed carrier degree; theorem uses uniquely extended adjoint current action. E_lambda is old-source bosonic current of Qsource4, not raw P1 single fermion. Algebraic selection alone derives neither local Xi nor actual response policy.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:given-e8-fold-matrix-with-retained-source-charge-and-p2-grading"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:5305dada83c658d9f56e2031",
        "source:421a16c95c8cf8c38f1a4d2d",
        "source:6126dfbf7fb42d900c3ef3c4",
        "source:c053524ac92b36ecf7183f4b",
        "source:8feb55d553265ddee41989aa",
        "source:403ba90d0ea01b3223680a70",
        "source:47211662f0775d42bf6570a3",
        "source:133887b303c944026320b513",
        "source:bd5ad50cd366db506e05cf5f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:charged-source-quarter-recovers-inverse-internal-glue",
      "titleEN": "Charged source quarter recovers inverse internal glue character",
      "statementEN": "For actual given fold holonomy g_alpha=exp(2pi i Mmu_alpha.H), entire E8 lattice module satisfies g_alpha²=exp(2pi i alpha Qsource/4) Cint^-1. With c0=M(j/4)=(-1,0,2,-1,0,3/2,-1/2,-1/2) and v=(0^5,1/2^3), c0+v=(-1,0,2,-1,0,2,0,0) belongs toD8 subsetE8=E8*. Inverse is essential: C0 differs from Cint on all128 halfroots. For either quarter, U5 residue3 plus eigenvalue-1 of g_alpha² exp(-2pi i alpha Qsource/4) selects exactly creation30. Omitting charge factor leaves raw Ward-phase spaces of1 or11 directions, each with only one creation root.",
      "scopeEN": "Exact joint character identity on same marked source, no fitted extra clock or discarded charged phase. Lattice proof extends beyond complete240-root check. Closes this internal clock comparison; identifies neither affine winding, NS/R transition nor OS time. Actual local P1 use of filter remains part of Xi.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:given-e8-fold-matrix-with-retained-source-charge-and-p2-grading"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:425b0018f36891a572bf8c9c",
        "source:e106aabbd233877b47468149",
        "source:2835362f2317b7f867119f07",
        "source:1aa49ba12764c98eb1a27fee",
        "source:73272635e0d39156ac5d11eb",
        "source:b40485dfe685b4e3312c016f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:state-independent-creation-branch-removes-whole-process-hodge-demand",
      "titleEN": "State-independent creation branch removes stronger whole-process demand",
      "statementEN": "Previously verified full60 current process has canonical CP outputs E+ from carrier degree2 to3 and E- to1. Creationgain3 times familygain3 and annihilationgain2 times3 with totalgain15 give E+*(I)=3I40/5 and E-*(I)=2I40/5. Thus Q+=(5/3)E+ is CPTP and equals direct30 normalization1/9. Tr_F Q+=Phi Tr_F holds for entangled inputs. More generally L_r=sum_m C_m tensorF_rm with effect pI and independence of25 C_m†C_n forces operator-valued sum_r F_rm†F_rn=(p/3)delta_mn I, hence Tr_F E=pPhi Tr_F without uniform weights.",
      "scopeEN": "Sector-resolved response needs actual designated branch with scalar effect. Exclusive C5 support of unread entire process is required only for unconditional purePhi total response. Orthogonal output grades already define mathematical instrument components; added hardware record is unnecessary. Full process retains actual2/5 Lambda1 carry. No physical event-time law,reset or raw P1 use follows. Process and state remain distinct.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:given-e8-fold-matrix-with-retained-source-charge-and-p2-grading"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:06213bbbda0e6c35f2993fc2",
        "source:abb77e4482575bf401651744",
        "source:2e9b63acd5d857637bedc9fd",
        "source:6126dfbf7fb42d900c3ef3c4",
        "source:c053524ac92b36ecf7183f4b",
        "source:af51c369cafee1e84ea4977a",
        "source:541555dd56aa1b205fe17ff9",
        "source:f6459e97f5a0efe4ef080b65",
        "source:1f3ea202fe5b37aa0a7f279f"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:given-source-current-constructs-half-kink-spinor-transport",
      "titleEN": "Existing source current constructs smooth half-kink spinor transport",
      "statementEN": "On given even quotient CAR net g_I=exp(i a_I/2),with exterior values a_I=0,2pi,defines localized automorphism. Branch signs are trivial parity on even words. Fixed q chart labels s=q/2,Q=4,h=1; odd pseudolocality alone does not distinguish s/c. For two localizations b_IJ=(a_I-a_J)/2 is smooth periodic and existing W(-b_IJ oF) implements transport. Exact fold gives J_tot,n=J_cover,8n,level8 and8(1/2)^2=2=s². Original CCR,adjoint and Hall/Wick functionals determine smooth transport histories. K_alpha time gives exp(-itn); unscaled cover time exp(-i8tn). Retain Q zero modes and charged-field action.",
      "scopeEN": "Closes algebraic DHR existence/smooth neutral line on given quotient net. Proven bounded implementers,localized Ad action,and local vN transporters in Haag-dual vacuum-net representation; do not infer norm-C* membership from kernel. Sharp step violatesH1/2; exponent2 and renormalized matrix elements are determined,general closability/UV operator normalization require energy bounds/domains. Quotient interval has eight cover arcs. No raw P1 single-interval,OS-time,field-channel or executed-CP proof.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-eightfold-even-car-quotient-with-marked-charge-and-source-time",
        "premise:given-e8-fold-matrix-with-retained-source-charge-and-p2-grading"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:6544d002215be4919b8c4793",
        "source:8c083f0ef0bbdd15e64d36b4",
        "source:55ba404e7350afa1c83ea289",
        "source:1eba7623e4e6cb3ece69430c",
        "source:fcc131dc4afc26d544ddaf7d",
        "source:4007b19ad73ec76654542699",
        "source:0bb820bf43e81eaebfc66dfe"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:neutral-ward-response-needs-no-spinor-observable-membership",
      "titleEN": "Neutral Ward response needs no spinor field as observable",
      "statementEN": "Pure observable response can be written T(a)=sum L_beta†aL_beta+sum L_gamma†rho_s(a)L_gamma for given localized star automorphism and bounded local observable coefficients. Unitality fixes normalization; each term is CP. Individual charged spinor need not belong toA. Full local E8/Q-system extension is stronger realization for charged individual fields and0<->s field coherences. Spinor endomorphism and smooth transport now constructed on given quotient net are not another missing choice there.",
      "scopeEN": "Conditional normalized-source criterion,not proof P1 suppliesL_gamma or executes a chosen intervention. Priority is original local iota_I preserving support,state,reflection,true time and marked Ward response. For claimed correlation kernel do not require added measurement instrument. Full field/spacetime claims retain stronger conditions.",
      "status": "conditional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-eightfold-even-car-quotient-with-marked-charge-and-source-time",
        "premise:given-e8-fold-matrix-with-retained-source-charge-and-p2-grading"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:f20076ed56174f0acb8386d8",
        "source:25c09e3f5c20a08b230d2d83",
        "source:7573efcb802c4f541c3cb5f7",
        "source:6544d002215be4919b8c4793",
        "source:8c083f0ef0bbdd15e64d36b4",
        "source:55ba404e7350afa1c83ea289",
        "source:1eba7623e4e6cb3ece69430c",
        "source:fcc131dc4afc26d544ddaf7d",
        "source:4007b19ad73ec76654542699"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-source-sector-transport-distinguishes-identical-hodge-marginals",
      "titleEN": "Actual source-sector transport distinguishes identical Hodge marginals",
      "statementEN": "Same FoldM splits Ward input40/output40 asNS20+spinor20 andcreation30 asNS14+spinor16. All360 signed columns are168 sector-preserving and192 sector-changing. UniformNS14 has effects3,4,5 and no scalar TP normalization. Positive weights1/6 on8 actualNS roots and1/3 on6 give exactTP onH40 and family gainI4/3 for everyC_m,hence identical fullPhi marginal even for entanglement. This different process preserves source sector. Physical color e3-e2 takesNS e2+e6 tospinor e3+e6;NS14 support lacks full color covariance. Source gradingw=Me1=(e1+e2+e6+e7)/2 factorsPC tensorPF withcarrier dimensions4+6;pureNS20 inputs have only52 of100 carrier matrix directions.",
      "scopeEN": "Exact comparison within given actual current representation,not new physics or P1-selected weights. ProvesPhi alone cannot identify source andspinor Kraus operators are not necessary for everyPhi realization. NS14 does not embed allH40 states inrawNS vacuum.4+6 is internal grading of ten pair labels,not new physical3+2 or spacetime dimension. No exclusion of neutral DHR route or allP1 sources.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-eightfold-even-car-quotient-with-marked-charge-and-source-time",
        "premise:given-e8-fold-matrix-with-retained-source-charge-and-p2-grading"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c362856027e2d459cd991776",
        "source:1190a2307e6c18ea1be34798",
        "source:a4e0ef5ed7aa625b08cf4e82",
        "source:9719ffda4cdfcf5dc9bbff90",
        "source:07c1952bdfbdbbefaad612c7"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:ordinary-weyl-type-obstruction-to-single-chiral-os-anti-anti-reflection",
      "titleEN": "Ordinary Weyl type excludes single-chiral OS anti-anti reflection formula",
      "statementEN": "For Theta(W(f))=W(Lf), scalar sign c and product-order sign o, the ordinary Weyl relation forces sigma(Lf,Lg)=c o sigma(f,g). A conjugate-linear order-reversing map requires symplectic L. The previously conditional Theta(Wf)=W(-r f) is antisymplectic on the same single chiral current and is excluded under these type premises. A compactly supported local witness g=f-prime has integral f g-prime=-integral(f-prime)^2 nonzero. A common field minus or Weyl characters do not fix the central phase. Conjugate-linear multiplicative and linear order-reversing reconstructed types pass the single-current test. Oppositely oriented faces with swap and r pass the anti/anti algebraic test conditionally.64 declared variants are checked exactly by matrix forms and directly multiplied rationally scaled Weyl words, with independent normal/-OO review.",
      "scopeEN": "Exact necessary algebra identity and complete declared finite menu, not a classification of all profile maps or sources. The excluded candidate was expressly conditional, not an established OS bridge. No exclusion of OS Grassmann symbol products or existing positive Green/null relations. The opposite-face pair is an algebraic target candidate; actual P1 field map, state/RP, physical time/locality/EM and complete TFPT remain open.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-eightfold-even-car-quotient-with-marked-charge-and-source-time",
        "premise:ordinary-weyl-product-and-explicit-reflection-type-comparison"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:55d2dc59d9f0e6e5a943e948",
        "source:e17787720b697a2e0f376a6c",
        "source:394a0fdde3c67506c3eb8353",
        "source:5f0194981540944ec12dcf94",
        "source:40e7f72160f5ce88dc15b0b1",
        "source:df5772d7a112043d8b666f14",
        "source:a1cc9443239ad008986a633c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:given-two-face-source-derives-opposite-neutral-weyls-and-bounded-time-reflection",
      "titleEN": "Given two-face source yields opposite neutral Weyls and bounded time reflection",
      "statementEN": "The old Schottky reflection rho(t,s)=(-t,s) does not reverse spatial profiles; its neutral Weyl profile map is -I and is not excluded by the previous -r_s result. In the existing HS source space, W_R(f)=L_Wf and W_L(f)=R_Wf* have opposite Weyl phases directly from right multiplication. J_HS W_R J_HS=W_L is conjugate-linear multiplicative; centered finite bilinears obey j_L(A)=-R_j(A) and J n_R J=I-n_L. The joint functional Tr(sqrt(rho)Wi*sqrt(rho)Wj) is the positive HS Gram of rho^1/4 Wi rho^1/4 without a Gaussian premise. For the given thermal source, fully ordered heat products K_F handle bounded even insertions: ||K_F||2<=sqrt(Z_beta)product||Aj|| and S(ThetaF,G)=Tr K_F* K_G/Z_beta. Strong approximation extends the existing polynomial free functional to existing bounded neutral Weyls. The old Green midpoint X and all four graph blocks are reused, not chosen anew. Exact NS modes pi,3pi test the same original implementation path, including null relations, particle-hole contribution and reflected noncommuting histories.",
      "scopeEN": "Analytic all-mode theorem in the explicitly existing normal source representation, supplemented by exact finite path controls, not an all-mode inference from finite samples. W(f) must already be bounded in the source von Neumann algebra; no norm CAR membership, bounded imaginary-time conjugates or arbitrary odd OS words asserted. The GNS partner is not identified with a physical P1 second boundary. Older papers32 and45 assume the positive field kernel or its reflection positivity. Actual local physical P1 source map, original measure/coupling, physical time, EM and complete TFPT remain open. The old spatial type exclusion retains its stated scope.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:normal-even-sea-car-source-and-canonical-graded-hs-double",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:existing-normal-thermal-source-with-bounded-neutral-insertions"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4692b9591c52924e32508590",
        "source:b68427c3d00bb9bc6f3c3bed",
        "source:927414636ac816e41d78d7fa",
        "source:dc5228d1cca510cfd82da487",
        "source:84cd993d7533e596444dd5be",
        "source:73ee19623fa909fea78ac7bc",
        "source:e824212d52da9093d601a78c",
        "source:cbe752ee18491411ebd03c90",
        "source:e825505d56a04218d72ae44e",
        "source:b54c34c09388e6044a7dd009",
        "source:a9e0479abeec3c6a6739d295",
        "source:d13661c4b19519c545998528"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:verification-recovery-preserves-local-source-chain-and-eight-gate-completeness",
      "titleEN": "Verification recovery preserves the local source chain and full eight-gate completeness criterion",
      "statementEN": "Inventoried current registry with all707 present modules,788 ledger rows and3108 project Python/Lean/Wolfram sources; closely inspected24 strong Python closure candidates and11 formal interfaces for actual source premises. Reuse the existing QWZ to CAR field/time map,v746/v779 net blocks,v745 analytic sector bound and neutral octic composition. v1015 is a finite QWZ times deck response block; its ZERO wording assumes external source identification. Inspected Lean compositions assume realization implications as axioms,while Calderon/Yukawa interfaces explicitly retain upstream provenance. Two targeted current runs reproduce v622 at10/10 and v1030 at27/27; the latter retains microscopic FEGEN/ALG2 as open. Original master TFPT.TOE.COMPLETE.01 requires AND(T1..T8),all eight remain open in current ledger. Joint two-face source is a current provenance bridge,not sufficient total closure.",
      "scopeEN": "Source-reviewed inventory and reuse audit with explicit coverage: automated inventory is not manual full proof/archive review,not a full current suite run,and not a universal absence claim. Existing model arguments are not upgraded to formal or complete physical proofs. Original sources and ledger unchanged. Earlier local-source criticism is recovered knowledge,not a new scientific gap. Full-CAR ground-state reduction requires the same gapped Bogoliubov action,H>=0,H Omega=0 in the same representation; neutral route directly transports full functional. No unnecessary full E8 observable extension for neutral response.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:declared-p1-p2",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:86518f296b8db03215080499",
        "source:2de6936e95a9ddbb9ff7b9ce",
        "source:445dc81542b1e533b3023cce",
        "source:7061009d69d59426020335a2",
        "source:4e610552625f58aee7cf0073",
        "source:67c445442a0432ba7c2a43f0",
        "source:a9b2c9c970ee80eda934fe3a",
        "source:64233a31ada8280fb3ee5a95",
        "source:5f5c64f397ba554a5b677662",
        "source:ce3a3203db844e1de1ba7796",
        "source:e25fb19c2490e4c8c7257b91",
        "source:98aa5ce5e23fa279752f0182",
        "source:49296a992f8b6dc88b0260f6"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:positive-spectral-reweighting-does-not-establish-original-source-rp",
      "titleEN": "Positive spectral weight alone does not establish original-source reflection positivity",
      "statementEN": "The generic RP preservation inference in the old constructive-measure proof is false. A strictly positive RP base with eigenvalues19,1 becomes non-RP under w=exp(-Tr exp(-D²)),despite positive weights,reflection covariance and gap>=1. Exact Delta=e^-1(1-e^-4)²>75/256>1/9>log(10/9);normalized reflected sign response changes from1/19 to-0.12394264612509166625. General nonconstant positive Laplace profiles haveDelta>0;generic failure uses r in(exp(-Delta),1),while fixed9/10 base requires the stated threshold. Finite W>=0 is the universal Schur-multiplier preservation criterion;for a fixed base K0 elementwise-times W>=0 is exact. A suitable reflected factorization is sufficient for repair. Source-independent positive reference denominator cancels in normalized responses and repairs neither false RP nor missing cross coherence.",
      "scopeEN": "Counterproof only to the generic positive-weight preservation inference in cited original passages,not the entire geometric/BRST measure theorem under all additional conditions. Finite test is no full P1/P2 countermodel,no TFPT prediction,and no newly chosen physical source. Source Bernstein cone means completely monotone profile,not a general Bernstein function. No actual original field map or completeT1-T8 goal closed. Preserve existing given-source paths,positive transfer constructionv330,Schur/projector/Weyl results. Do not introduce full ambient geometric measure construction as a prerequisite for every neutral local response;direct local OS embedding remains possible. P1 already assumesRP;only a proposed derivation shortcut is excluded.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:finite-reflected-spectral-weight-preservation-test"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:8cda86aa53653ad5dde4751f",
        "source:2ac86dfe2b3baa62656e3da9",
        "source:d8d277cf9abcccbe9b2e0281",
        "source:fd7756964a19f472f7efae45",
        "source:e6ecfd38910548c51e399fc4",
        "source:613c46738789a4603d1c5a8a",
        "source:b11863c86078cbc25d33c9ae",
        "source:54de8b1fbfd0927a4933784b",
        "source:e825505d56a04218d72ae44e",
        "source:574d3f21bd2b578cf95cdd8f",
        "source:981a5a3d55035a22800da05a",
        "source:6e712a71a2fb68462ed31a33"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:gapped-quarter-energy-cannot-be-same-borchers-translation",
      "titleEN": "The given quarter energy is not a Borchers translation",
      "statementEN": "Using this same gapped quarter energy as a modularly scaled translation fails already at the full spectral gap: the group law and Stone uniqueness imply unitary equivalence of H and H/2. The least positive spectral point would have to be both1/4 and1/8. Lean grind proves the elementary spectral-set lemma with only the three standard axioms. Independent review confirms the analytic connection and scope. The source remains a conditionally supplied model; neither original-P1 source derivation nor its universal refutation follows.",
      "scopeEN": "Only identification of this same source energy with the Borchers translation generator. Other gapless generators, correctly constructed local standard pairs and HSMI remain possible. Lean formalizes the elementary spectral-set statement, not Stone, spectral theory or the actual P1 source. Other KMS/spectral-profile identifications still require their actual operator dictionaries.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:same-gapped-quarter-source-as-borchers-translation"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d7c04d4fe96d8c51be86a15c",
        "source:18c2cf9c0010200549abfbf7",
        "source:013d8f978b2eb8bf139dde07",
        "source:47405e3d4e0503e9d469482b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:finite-ko6-pairing-does-not-supply-standalone-pfaffian-source",
      "titleEN": "Finite KO6 block alone does not supply a selfdual Pfaffian source",
      "statementEN": "For antiunitary J and selfadjoint D, B(x,y)=<Jx,Dy> has transpose sign epsilon epsilon_prime. The actual v252 KO6 block therefore gives a symmetric form; its standalone Grassmann quadratic term vanishes. Gamma_F J_F changes both signs and does not repair it. An actual Majorana constructor output moreover has four simple eigenvalues in the full96 space; Kramers excludes EVERY square-minus antiunitary commuting with that same D there. The Majorana-off control permits an explicit internal alternative. The ordinary local KO4 times KO6 product instead supplies the correct KO2 Pfaffian type if its original spinor source and common domain are actually derived.",
      "scopeEN": "Only the direct selfdual finite Pfaffian ansatz and universal internal J repair at fixed D. The Kramers countercase belongs to the existing constructor class and does not assert selected physical masses. Independent complex barpsi/psi, other correctly derived local sources and the4D product action remain possible. KO4 modulo8 does not derive metric dimension4, Lorentz signature or P1 quantization. Exact18 control checks and independent analytic review; no full suite or ledger promotion.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-v252-real-finite-block-and-selfdual-field-test"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:dd640e584ecfea0f9f2555d5",
        "source:bfe3bd23a74818d001dc2f44",
        "source:a239e54c122c3b7761619ca0",
        "source:100aa3d9b3a51b30bf9433aa",
        "source:db5673324f5778c098dec302",
        "source:0be6cd466c4540bef6038a10",
        "source:8dcd1cde6b4e09c17fa6fd14",
        "source:786442cef13e11defac007ef",
        "source:53d524c4e83384e7ac767a66"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:full-free-projector-forces-joint-commuting-source-factorization",
      "titleEN": "Full free projector forces factorization with a commuting source",
      "statementEN": "The existing full CAR projection-covariance theorem gives a pure restriction omega_P. For b>=0 from a commuting algebra, phi_b(a)=omega(ab) is positive and dominated by ||b||omega_P; purity forces omega(ab)=omega_P(a)omega(b). All equal-time connected mixed responses of those algebras vanish. A positive mixture of conditional CAR states with full mean projector P consists almost everywhere of the same state. An actual original coupled source with nonzero mixed response therefore cannot have that full free reference projector; it needs its own joint response or a proved independent source sector. The correct conditional complex source identity retains K(phi), or its J derivatives.",
      "scopeEN": "Necessary theorem about the same joint state and specified algebras. Does not exclude every interaction or future entanglement. Full projection and commutation are not inferred from a thermal face or incomplete neutral data. In a finite full Slater block, commutation with its entire even part already suffices via rank1 support. Positive conditional mixtures need actual positive disintegration; complex eta weights are not one. The source identity presupposes an actual bilinear action/integration and is not a derivation from P1. Physical joint response remains open.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:full-projector-car-marginal-and-commuting-joint-algebra"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:dd640e584ecfea0f9f2555d5",
        "source:bfe3bd23a74818d001dc2f44",
        "source:d8cdf210465eadc80591e139"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-neutral-current-source-has-constructive-moebius-standard-pair",
      "titleEN": "Actual neutral source has a constructive Moebius standard pair",
      "statementEN": "Existing currents give L_n^0=Lcal_n^alpha-bJ_n-b²delta_n0/2 with the same Omega and L0^0=H_alpha onQ0. P=L0^0-(L1^0+L-1^0)/2 is dGamma of an operator exactly diagonalized to x/2 by the complete Laguerre basis: P>=0, spectrum[0,infinity), kernelC Omega. With D=(L1^0-L-1^0)/(2i), explicit weighted dilation supplies the full affine group law. The actual local vacuum current net has a standard half-line inclusion with Delta_M^(it)=exp(i2pi tD) and the full Borchers relation. The original t_v quarter onQ0 is precisely R=exp(-i pi L0^0/2); its four positive gapless parabolic generators have opposite-pair averageH_alpha. Local algebras and modular groups are transported together.",
      "scopeEN": "Constructive all-mode theorem in the already given original neutral vacuum source, using primary current-net theorems and independent analytic/executable review. Not an unverified continuum extrapolation of the finite v438 ladder. SAME gapped H remains excluded as Borchers P; P is a different derived generator. The elliptic Gibbs state is not invariant under this P and must not be replaced. No full charged-sector theorem, equality with original P1 Theta/time, automatic eight-arc word transport or3+1D closure. Unbounded-generator sum equalities are on the common core with the corresponding closure.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-quarter-neutral-vacuum-current-core",
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:09f123d8a14174c6a5960c2c",
        "source:c87d9115e7644c1d82dc57d0",
        "source:0122e3b0aab89dadb4473f10",
        "source:a47fe485aa825b8b77318f2c",
        "source:dee9317dffa25c5c183326d6",
        "source:7de3b6cc375bc9332cb32c35"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:continuous-local-current-weyls-cannot-live-in-finite-coordinate-fibers",
      "titleEN": "Continuous local current Weyls do not fit finite coordinate fibers",
      "statementEN": "No unital complexlinear star image of the actual full local Weyl system exists in A_sp with finite matrix fiber rankN. Fiber evaluation of U_sV_t=exp(2ist)V_tU_s and ordinary determinants force exp(2istN)=1 for all s,t; s1,tpi/(2N) already contradict it. Direct identification of spectral coordinate operators with these local quantum-current operators therefore fails before any state matching. The actual sufficient source route remains an embedding into the full operational Seedop A_loc with its actual complete word functional.",
      "scopeEN": "Only the full continuous Weyl system and the chosen finite matrix-fiber class. Does not exclude discrete Pauli/clock algebras, an isolated W8 subalgebra, correct field quantization or a source image in actual A_loc. A smooth center alone does not imply this finite-fiber class. This does not prove the general C_seed functor unfaithful or universally noninvertible.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-local-weyls-and-finite-fiber-coordinate-target"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:2f50b88a704f6ee09fb6f5eb",
        "source:c87d9115e7644c1d82dc57d0",
        "source:11d80374281a55777d215e66",
        "source:4f78cb29641d41a29bb0dcb3",
        "source:352d35529f4fe61bec952d68",
        "source:6ea92be1fe1c8f07ff0a16ab"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-folded-current-ward-and-state-determine-all-neutral-words",
      "titleEN": "Actual current action and state determine all neutral words",
      "statementEN": "Under the explicit sufficient eight-current contract, positivity of actual H forces all positive modes to annihilate the vacuum. CCR and adjoints yield every ordered moment recursively and the full PBW Gram, hence a unitary intertwiner on exactly the cyclic current space with the energy closure. Fock/Gaussian and complete CAR/E8 embedding are not additional prerequisites. Original quarter R=exp(-i pi H/2) is identity on this H=8N cycle; the larger c1 Moebius cycle is distinct. In the actual KMS case the denominator1-exp(-8 beta n) recursion determines oscillator moments, not the joint zero-mode law, delta or second-face representation. Truly compatible reflection yields all reflected word values, while separate face moments do not replace it. Actual CAR controls3897words,9216CCR vectors,464energy transitions in both quarters and189 exact infinite Gibbs trace comparisons agree; the all-mode conclusion comes from the analytic proof.",
      "scopeEN": "Standard Heisenberg uniqueness as a concrete reduction of the original neutral source comparison, not new general physics. Actual local P1 current image, actual time/state type and for joint OS claims reflection/two-face representation are not derived. W8 means exactly native F8^(d) in the old eight-arc/point-splitting dictionary, not automatically its separate E8-invariant primary completion. No c1/c8 point-net identification, no forced free subtheory for all P1 models and no complete T1-T8 closure. Known minimality limit is reused, not counted as a new finding.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:neutral-current-recognition-with-actual-time-state-and-local-image"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:4a057c9cfb3f440ede8d237a",
        "source:8df4d65cb06eef8a3f3337c6",
        "source:a5cf2e117b507c3c39d957d8",
        "source:899e27f2d7ebc92643e8ff24",
        "source:6ed2b06d6c6a49838325490b"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:mixed-vector-axial-current-is-existing-full-car-subalgebra",
      "titleEN": "Mixed vector axial current is a subalgebra of the existing full CAR source",
      "statementEN": "In the supplied complete Dirac CAR collar, J_R=(J_V+J_A)/2=:Psi* fP_R Psi: is an explicit local subcurrent. The old opposite component cocycles c,-c give c_VV=c_AA=0,c_VA=c_AV=2c,c_RR=c; at the original profiles mixed=-4i and right=-2i. The old normal-commuting vector exclusion explicitly did not cover this generator. Existing free B0 time satisfies [B0,P_R X_n]=-nP_R X_n on the actual one-particle path, with n->8n after folding. Restricting this existing subalgebra needs no separate chiral determinant. The second face remains thermal, so no positive vacuum generator has been derived.",
      "scopeEN": "Applies known two-dimensional current algebra to the statistically supplied full source, with no general novelty claim. Does not prove physical P1 intervention admissibility, original full source map, OS time/reflection or a free current subtheory in every coupled P1 source. The old vector exclusion remains valid in its original scope.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:charged-car-pure-two-face-cauchy-graph-state",
        "premise:constant-finite-dirac-product-mixed-current-test"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b848f377045634c3326fcad0",
        "source:4eadbbe5eae5bb99d82fc3f5",
        "source:849fa79c5dbb170c063fdcfd",
        "source:1acbe7a98b84225d3dc025eb",
        "source:5ae9f882056c4f8c05987597",
        "source:c09d9b7f95783fb967aa180d",
        "source:1395ee1fa9aeb4b369c39732",
        "source:20ba7d005ffba64df6121ea0",
        "source:9a0778c486ca2fbfd87e42c4",
        "source:2cd013e431762d93dcd0dc00",
        "source:fab79d87c34193ae37fe0ddd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:constant-product-time-stable-current-level-is-kernel-index",
      "titleEN": "Time-stable constant product channels carry current level only in their kernel",
      "statementEN": "All constant reducing orthoprojections of B_Phi=Gamma A-S tensorPhi are E=diag(E_R,E_L) satisfying E_R Phi=Phi E_L and E_L Phi=Phi E_R. On ker(Phi²-mu²),mu>0,E_L=(Phi/mu)E_R(Phi/mu); on kerPhi the projections are independent. On the actual full two-face Cauchy graph,N_face=diag(-Jn signPhi,Jn signPhi) and the old HS Lagrange lemma prove massive cocycle cancellation. Hence kappa=rankE_R^0-rankE_L^0. A bare right channel reduces iff Phi E=0; total grading Gamma tensor gamma_F still reduces. Its full finite v252 channel has netlevel0 even for singular Phi by48/48 and oddness. Explicitly reuse the old normal spin index source: its already reducing finite kernel has level equal to index. Its L2 case r+=1,r-=0 also preserves the same circle time. The full E2 twist r+=k,r-=k-1 has netlevel1 but no single right time Ward for k>1. Equal index level therefore does not yield an all-word/time intertwiner.",
      "scopeEN": "Complete narrow classification for constant Phi and constant local reducers, not all P1 sources, variable normal profiles or momentum-dependent/dressed images. Normal elliptic D_N and finite Yukawa D_F remain different operators. The old spin product pushforward and horizontal connection remain conditional, not selected from P1. Reflection lift S tensor gamma_F is tested only at symbol level, not domain/reference/RP. Actual v252 integer controls are not physical Yukawa values. Source correction and independent reviews precede persistence; normal and -OO identical. No T1-T8 closure.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:charged-car-pure-two-face-cauchy-graph-state",
        "premise:constant-finite-dirac-product-mixed-current-test",
        "premise:given-finite-sm-triple-yukawa-inputs",
        "premise:given-normal-spin-line-and-genuine-circle-product"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:b848f377045634c3326fcad0",
        "source:4eadbbe5eae5bb99d82fc3f5",
        "source:849fa79c5dbb170c063fdcfd",
        "source:1acbe7a98b84225d3dc025eb",
        "source:5ae9f882056c4f8c05987597",
        "source:c09d9b7f95783fb967aa180d",
        "source:1395ee1fa9aeb4b369c39732",
        "source:20ba7d005ffba64df6121ea0",
        "source:9a0778c486ca2fbfd87e42c4",
        "source:2cd013e431762d93dcd0dc00",
        "source:fab79d87c34193ae37fe0ddd"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:paired-quarter-source-candidate-needs-original-filter-and-oriented-conjugation",
      "titleEN": "Quarter pairing is valid; lowest carrier block does not follow from original filter",
      "statementEN": "The original Pprim=P_(Sigma,+)1_[epsilon_adm²/4,infinity)(P_(Sigma,+)Dprim*DprimP_(Sigma,+)) is a highpass of the compressed operator,not ker(|B_Sigma|-lambda1). Even granting the additional operator identification,lambda1<epsilon_adm/2<=lambda2 removes the proposed lowest block. For the explicit paired quarter source,j²=1 and jBj=-B hold on full H1. The full Cauchy graph has the standard Araki conjugation C=j directsum(-j),CGC=1-G. Equal-sign doubling has exact cross defect [[0,2c],[2c,0]]. A single thermal face covariance is not a projection. Balanced F eigenspaces follow only for a j-invariant full selfdual one-particle block,not for a separate internal 3+2 marking on E.",
      "scopeEN": "Source correction of the new external candidate,reuse of known positive compression and standard purification by Araki1970/71. No new general quantum theory or P1 no-go. Specified selfdual dynamics on a single quarter fails; complex charged CAR remains possible. Hcar selection,local field map,original real structure and physical time remain to be identified. No T1-T8 closure.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:paired-quarter-external-lowest-block-candidate"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:080d7d25a3634501a35c239b",
        "source:87236d65e4142fc9e1b3ae45",
        "source:a4d504ae460aee727f4f9d38",
        "source:0b44dda4f2886e985d6d048f",
        "source:c1565366722f99a531f2beb6",
        "source:cf7337f72906cd78af4ce6e4"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:graded-boundary-clifford-typing-transports-full-scalar-and-finite-coupled-source",
      "titleEN": "Geometric Clifford boundary identifies full scalar and finite coupled source",
      "statementEN": "In the existing free collar,T(v,bar w)=(v,i_old w) is a local domain-preserving unitary for Ical=i_old Gamma. C0=i_old gamma_n supplies the appropriate new real structure without freely choosing J gamma_n. The oriented two-face chart with +i_old and -i_old sends the ENTIRE G(B) to G(A) directsum(I-barG(A)),including crossing correlations. Ical B=i_old A preserves old scalar circle evolution; the free geometric reflection matrix preserves graph and real structure. For the actual v252 coefficient,E v=(P_F+v,i_old P_F-v) is unitary onto the entire positive total grading and B_Phi E=E h_Phi with h_Phi=A gamma_F-i_old gamma_F Phi,selfadjoint on H1 and h_Phi²=A²+Phi² on H2 in the constant scalar case. The same full map holds for smooth tangential backgrounds with even a(theta) and odd Phi(theta); then h_Phi²=A²+Phi²-i[A,Phi] on H2. The full chart gives G(h_Phi) directsum(I-barG(h_Phi)). When the graph is the actual quantum covariance,the old pure-projector theorem transports all CAR words. No independent right field source or additional chiral determinant is required within this functor type.",
      "scopeEN": "Constructive application of standard Clifford boundary quantization,no new general functor theorem. Original physical choice of this type,actual charge J_F/Pfaffian,quantized bosons,original markings and OS time remain to be proved. The old complex-CAR vector exclusion retains its different premise. For nonzero Phi,h_Phi is not scalar A time;96 antiparticle labels do not newly derive physical species. No P2 3+2,E8 charged extension or T1-T8 closure. Exact controls and two independent source reviews. The smooth extension remains normal-independent; no single exp(-ell B) graph formula for arbitrary B(r).",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:given-finite-sm-triple-yukawa-inputs",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
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        "source:251a551b4d69f1b19f606881",
        "source:b488c30196579677d6b4bf73",
        "source:e5ac5dd24a510e809f86f91e",
        "source:9776fac87e9b9707b0a76396",
        "source:662452a55693790e1517beb9",
        "source:690d534419ad3bc433ee571b",
        "source:0e9d865ddad87298348bed51",
        "source:9f5c29eb6d1b8f702df03dc7",
        "source:0062466fd3d3dd1872e4116e",
        "source:b848f377045634c3326fcad0"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-charge-j-transport-retains-full-dirac-and-distinct-pairings",
      "titleEN": "Actual charge J and entire Dirac pairing in geometric chart",
      "statementEN": "In the existing chart,Jhat=I tensor J_F is new-complex-linear and T^-1 Jhat T(v,bar w)=(-k w,overline(k v)),with k=-gamma_F J_F,k²=-I. Jloc=S Jhat is new-antilinear and induces c=-i_old J_F,c²=I. Fully,c h_A c^-1=h_{-A^J},difference -(a+a^J)gamma_F,and Jloc D_A Jloc^-1=-D_{-A^J}. For a^J=-a,[c,h_A]=0 and an actual old full-space skew form <Jloc x,D_A y> result; its restriction to E times E vanishes. The reduced boundary pairing <c v,h_A w> is symmetric and is a different form. Full D is new-complex-antilinear; its pullback retains normal derivative,A and Phi. The old finite mass pairing <J_F v,Phi w> is recovered exactly. For scalar holonomy,c sends alpha to -alpha; explicit W=exp(-i theta) gives 1-alpha and index -k-1.",
      "scopeEN": "Analytic full operator transport for general complex Yukawas and complex symmetric Majorana block,on the smooth interior core; global selfadjoint J-stable domains need separate checks. No [Q,Phi]=0 is needed for this J/B test,and no electric-charge selection follows. Neither a universal Pfaffian exclusion nor a physical chiral Pfaffian rule follows. C0 is not J_F. No new physical halving,species count,bosonic quantization or OS time. Original audit preserves the already complete chosen QWZ CAR source and complete operational Seed; no extra free quantization demand for these given sources.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:original-v252-real-finite-block-and-selfdual-field-test"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:18928f465d4e52c4ad9a12ec",
        "source:ba64c374b539397826ca96d1",
        "source:5d68ed03f7dec5ab5c95bbfe",
        "source:db5673324f5778c098dec302",
        "source:099d63070a41b632282adbd6",
        "source:c150c059c5f6a90f4d086c61",
        "source:a9e0479abeec3c6a6739d295"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:fixed-graded-chart-transports-normal-dependent-source-and-given-mixed-moments",
      "titleEN": "Fixed graded chart transports normal-dependent source and given mixed moments",
      "statementEN": "For B(r)=Z tensor A(r)-S tensor Phi(r),with fixed even connection,odd selfadjoint coefficient and fixed normals/grades,E remains background-independent and B(r)E=E h(r). In a compatible finite regulator,K'= -B(r)K gives exactly C0 K C0=(K*)^-1,without commutation at different r. Thus Cfaces sends the entire graph to its orthogonal complement and the oriented two-face chart gives P_K -> P_Kplus directsum(I-bar P_Kplus),including all crossing blocks. The same fixed algebra map transports all existing integrable joint bosonic insertions and conditional CAR words under an already given common measure. An exact smooth ordering countercase disproves the wrong unadjointed K^-1 formula.",
      "scopeEN": "This replaces the prior normal-independence restriction by a broader explicitly fixed product type without redefining the old premise. No arbitrary unbounded Cauchy problem: continuum claims concern actual elliptic Cauchy data,Green form and compatible domains. No moving grading/normal without connection terms. Positive conditional-state integration generally gives a mixed,nonquasifree state; no Wick rule for averaged covariance or projector purity is required. A complex eta/Pfaffian density gives only the integrable algebraic identity. No derivation of measure,physical quantization,original reflection positivity or physical time.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:fixed-frame-graded-normal-dependent-source-family"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c2bd7a836277b86f9d32cd58",
        "source:c8b7bffa44f4e6c77d859465",
        "source:251a551b4d69f1b19f606881",
        "source:ba64c374b539397826ca96d1"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:neutral-many-body-source-time-is-not-finite-summable-geometric-dirac",
      "titleEN": "Full neutral source time has different spectral growth from finite-rank geometric Dirac",
      "statementEN": "Actual neutral even pairs b*_{-r}d*_{r+1}=a*_{-r}a_{r+1} have energy2r+1. Each subset of the first m disjoint pairs yields a distinct orthonormal Q=0 state of energy at most m². Thus N_H,Q0(m²)>=2^m and Tr_Q0(1+H)^(-p)>=2^m/(1+m²)^p diverges for every finite p>0. This entire many-body time generator therefore cannot be time-intertwining unitarily identified with |D| in the tested finite p-summable geometric type,even after neutral/even selection or positive affine energy rescaling.",
      "scopeEN": "Exact occupation-count proof in the already existing infinite limiting source,no new model or numerical asymptotics. No divergence claim for a fixed finite microscopic lattice. No exclusion of abstract Hilbert unitaries,compact resolvent,finite thermal heat traces,separately defined D_coll or correct one-particle extraction. Primitive P1 definition does not require the excluded equality or explicitly all comparison summability assumptions. No general P1 no-go or rejection of the already complete chosen source. This test only prevents unproved identification of full OS/GNS time generator with geometric one-particle operator.",
      "status": "excluded_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-quarter-many-body-source-and-compact-dirac-comparison"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:0ad5a056b67350f0184bf076",
        "source:5a8f298f1e056e902a7b7bb5",
        "source:2d9795c98e7a7f5dd7712c68",
        "source:6ea92be1fe1c8f07ff0a16ab",
        "source:a9e0479abeec3c6a6739d295"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-product-reflection-and-same-time-have-full-positive-clifford-source-intertwiner",
      "titleEN": "Product reflection and same time support the entire positive Clifford source",
      "statementEN": "For the existing normal-independent B=Z A-S Phi,F=S tensor gamma_F is the already present product-reflection factor. With Cfaces=(C0,-C0) and R=faceswap tensor F,Ical F=-C0,R G R=G,and the exact real crossing kernel is -i M with positive M. Actual face-Wick ordering is an invertible basis; its Gram blocks are (-1)^{n(n-1)/2}(-i)^n Lambda^n M. Every even n has factor+1,so RP holds on the ENTIRE bounded even CAR algebra. The natural full creation map iota c=a_R*(v0)-a_L*(v1)+a_R(w0)-a_L(w1),with annihilators antilinear in w,has exactly G(h)=[[1-C,X],[X,C]] at beta=2ell. In the corresponding normal thermal HS representation,J_R=(P_even+iP_odd)J_HS implements both geometric field phases. The same entire chart obeys iota(c(exp(t Ical B)u))=U_t iota(c(u))U_t* with THE SAME t,including cyclic GNS closure. No spectral conjugation or inverse time is needed. The even reflection form is ||rho^(1/4) A rho^(1/4)||_HS². Source H=sum |lambda_j| n_exc is positive with finite thermal heat traces; full HS time is the two-sided Liouvillian L_H-R_H. The normalized sech midpoint kernel does not obstruct positive heat evolution at finite ell.",
      "scopeEN": "The common mathematical field/covariance/reflection/time diagram is closed within the already assumed canonical Clifford graph type. R acts antilinearly and MULTIPLICATIVELY on CAR; an antihomomorphism is a different type and already fails an even occupation word. Odd words require fixed parity twist; untwisted odd RP is not claimed. Normal HS representation needs the stated free thermal class; separate Wick proof needs no trace-class presentation. rho(h_Phi) is not identified with old scalar NS/QWZ density;already h0=A gamma_F is not A tensor I. The inverse-time gap from annihilator labelling is repaired in the preferred creation chart and is not an open problem of this graph type. Original P1 selection,physical insertions/references/domains,quantized bosons and old-source identification remain separate. No RP for arbitrary normal-dependent bosonic families from the constant proof,no 4D/species-count/physical total closure.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:given-finite-sm-triple-yukawa-inputs",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:57927044c7f09c98f673f19d",
        "source:9d74943738bc66a036eb3f4f",
        "source:812fc6fd29c10606c6b11e73",
        "source:82490bb33da3736629d0fef1",
        "source:e3eed5d635ec56c337f45625",
        "source:251a551b4d69f1b19f606881",
        "source:e824212d52da9093d601a78c",
        "source:4907fe7387b7629b6e8f4385"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:actual-v252-positive-grade-has-global-p2-wedge-dictionary",
      "titleEN": "Positive v252 sector has actual global P2 wedge dictionary",
      "statementEN": "On the full real gauge lift,det(pi(u))=(lambda det(m))^4 per generation. On the connected unimodular branch,gamma_F=+ is exactly Q_L,L_L,u_R^c,d_R^c,e_R^c,nu_R^c with original SM charges. An explicit unitary map to 1,c_c wedge w_a,epsilon_cjk c_j wedge c_k,w1 wedge w2,epsilon_cjk c_j wedge c_k wedge w1 wedge w2,vol_c wedge w_a intertwines the ENTIRE S(U3xU2) action with Lambda_even(E3+E2),including global Z6 form and opposite action. Three generations use W tensor I3. With an additionally supplied sigma=(123),eigenvalue1,the unique SM-neutral fixed line is e=nu_R^c tensor s,s=(1,1,1)/sqrt3. Actual coefficient gives Phi e=nu_R(MR s)+nu_L^c(barYnu s); preservation iff MR s=barYnu s=0. Reuse existing level4 result concretely for actual Y: tr16Y²=10/3 versus D5_1 basic norm5/6,three-family ratio12. Rescaling to match levels changes Ward charges.",
      "scopeEN": "New content is the concrete global v252/P2 dictionary and actual Phi test. Basic spinor-CAR level4 was already finding:joint-spinor-not-source-coefficient and is not rediscovered. Full Spin10 can be transported to v252,but is neither implemented there nor derived as physical source symmetry. A charged invariant ray is not a neutral fixed vector;sigma eigenvalue1 is stronger than ray invariance. Sterile neutral line carries source-clock charge but Y0,not automatically physical EM readout. No derivation of Ynu,MR,physical family clock,E8_1 source identity,4D or full solution.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:oriented-p2-exterior-carrier",
        "premise:actual-full-v252-unimodular-p2-gauge-lift"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:a6c008124c2f24a9d53061da",
        "source:807a343978b0c4b333986fba",
        "source:aadcb4da1e764a25d13798e6",
        "source:2900573bbeeefa807e0f1a4b",
        "source:55e1a01319dc1feaa105883e"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:old-quarter-full-source-embeds-locally-exactly-on-decoupled-channel",
      "titleEN": "Entire old quarter source embeds locally precisely on a decoupled channel",
      "statementEN": "For fixed local V_e f=f tensor e in the given Clifford graph,Phi e0 gives full H1/Borel/CAR/graph/product-reflection/time intertwining with the SAME QUARTER time. Actual original maps obey B_Sigma W_alpha=4pi W_alpha A_alpha and B_cov W_alpha=2 W_alpha A_alpha; W1/2 gives the entire graph at ell2pi,beta4pi without fit. Unchanged eightfold gives8 directsum A_mu,mu_a=(a+alpha)/8,beta_fold32pi and already existing full theta charge law. Delta_a=mu_a-1/2 is transported old reference correction. New exact result for all constant oddPhi: for p=k+alpha nonzero,n_e(p)=1/2[1-p<e,tanh(beta sqrt(p²+Phi²)/2)/sqrt(p²+Phi²)e>]. Strict monotonicity of tanh(cx)/x proves n_e(p)>=n_beta(p) for p>0,reversed for p<0,equality IFF Phi e0. A single occupation is thus equivalent to the entire fixed scalar source/time map. Positive classical averaging reproduces it only for Phi e0 almost surely.",
      "scopeEN": "Conditional actual embedding into supplied graph quantization,not original P1 selection. Reuse earlier theta law; neutral KMS alone remains weaker. Delta is not thermal mean charge. CAR direct decomposition gives graded tensor-product state,not direct sum of densities. Entire NS-cover identity does NOT follow from Spec(-A_alpha)=Z+1-alpha:its map reverses support;original u_cov=[[0,u_base],[I,0]] exchanges quarters whereas u_base I_F preserves grades. Already [B_cov,u_cov]=u_cov versus[2h0,u_baseI]=2u_baseg. Abstractly transported winding is not thereby the actual original local multiplier/deck operation. Iff and averaging theorem assume constant Phi,fixed e,p,beta;not complex eta/Pfaffian measures,variable profiles or quantum bosons. Full interacting TFPT is NOT required to preserve old free source exactly. No complete physics,EM or4D derivation.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:fixed-local-quarter-channel-in-constant-odd-source"
      ],
      "attemptIds": [
        "contract:tfpt-unified-source-derivation-20261029"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:31086671382beb32ea5395dd",
        "source:35fa42dcda3c0d95a6ef3f3a",
        "source:e8c60aa7f089cda54f1b5de7",
        "source:eddc42621e1d49b5621569ad",
        "source:a6e3b33420fdeb283f29f9ab",
        "source:9abbdd1d97ecab558a6beb99"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:petersen-population-full-cptp-p5-range-zero-to-ten",
      "titleEN": "Full Petersen populations allow the entire P5 range",
      "statementEN": "Among all CPTP channels in the fixed given 10 to 10 dictionary with all 100 Petersen transition probabilities, Tr(P5 J) ranges exactly over [0,10]. The original Hodge channel attains 10. Dm obtained from Cm by flipping three signs is HS orthogonal to all five Cn, preserves each Kraus effect and all 100 populations; J0=(1/3)sum |Dm>><<Dm| is CPTP and unital and attains 0. Since 0<=P5<=I and Tr J=10 and mixtures preserve populations, all intermediate values occur. The concrete J0 is not SM covariant by an exactly checked SU3 commutator.",
      "scopeEN": "Entire class of fixed finite one-step CPTP channels with the specified full populations, without SM covariance, derived P1 Choi identification, or multitime process. No physical no-go.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:012a0567cde5a0d536ba6d33",
        "source:57575df0f36aa435514d0176",
        "source:f09ccafcb50ca6a3f1525719"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:marked-sm-phase-p5-exact-range-and-response-collision",
      "titleEN": "Complete P5 range for marked SM phase family and witness collision",
      "statementEN": "For the previously defined SM covariant family Phi o Ad(aP_CC+bP_CW+cP_WW) with unit phases, Tr(P5J)=|a+4b+c|²/6+|a+b|² and covers exactly [2/3,10]. This is not the global range of all SM covariant channels. The choice a=-1,b=1,c=(1+2i sqrt2)/3 has the same P5 value 2 as the old Psi channel, but P45 values 16/3 versus 4. Both preserve original populations; one Choi response does not identify the entire process under these conditions.",
      "scopeEN": "Only the stated internal phase family and particular comparison with the given old channel. Not P1 sewing, complete SM channel classification, original measurement, or a universal process.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:fixed-three-plus-two-mark-and-typed-original-degree-clock"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:012a0567cde5a0d536ba6d33",
        "source:57575df0f36aa435514d0176",
        "source:f09ccafcb50ca6a3f1525719"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:shared-epsilon-tp-process-fixes-hodge-marginal-even-for-correlated-inputs",
      "titleEN": "Joint trace-preserving epsilon process fixes Hodge marginal even for correlated inputs",
      "statementEN": "For every joint finite-dimensional CPTP operation with Kraus operators L_s=sum_m C_m tensor A_sm on the given H=Lambda²C5 and arbitrary finite family spaces, global trace preservation and the 25 linearly independent C_m* C_n force sum_s A_sm* A_sn=delta_mn I/3. Thus Tr_F' E(rho_HF)=Phi(Tr_F rho_HF) for all joint states, including correlated and entangled ones. No preselected family state or pre-imposed isotropic Gram is needed. For one trace-decreasing event this fails: two exactly constructed joint states with the same H marginal produce probabilities 1 and 0. This is a corollary of the already recorded 25-product selection theorem.",
      "scopeEN": "Finite joint process on the given epsilon carrier assuming every Kraus operator in the stated tensor amplitude span and global trace preservation. Does not derive the original P1 source, carrier, local embedding, full trace preservation, event register, general multitime process or full TFPT physics.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index"
      ],
      "attemptIds": [
        "contract:elliptic-moebius-source-bridge-20261026"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:bb2729223c46365a95a0aad1",
        "source:30105ea37aca6faa8845e721"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:puncture-meridians-have-one-glue-class-and-residue-duality-does-not-select-metric",
      "titleEN": "Puncture meridians carry one glue class and residue duality does not select a metric",
      "statementEN": "H1=Z4/Z1 and H^1=ker sum have a canonical index-four quotient Z4 through the marked counting construction. In the normalized realization meridians mi=ei−1/4·1 are A3* weights and their differences are A3 roots. m0 literally equals original v983 OMEGA_F and with the supplied D5 spinor gives its actual LAM. All four mi have the same discriminant class. Corner C4 acts trivially on A3*/A3, so its mark permutation is not glue-class translation. The four-by-four delta residue pairing on puncture loops in Architecture section011:32–45 conflicts with their zero sum; correct readers use zero-sum residues or I−J/4. This dual pairing alone selects no positive metric.",
      "scopeEN": "Integral marked topology and supplied original charge dictionary; no new selection of four punctures, physical clock or blanket exclusion of a different sector-changing field map. Metric normalization follows only under the separate joint-completion theorem. Original paper and ledger unchanged.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-puncture-spinor-extension-with-integral-selfdual-pairing"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c17ab8197b9853a3dc4ae542"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:joint-integral-unimodular-charge-closure-uniquely-selects-complete-invariant-metric",
      "titleEN": "Joint integral selfdual charge closure selects the entire invariant metric",
      "statementEN": "On the fixed original additive spinor-meridian glue lattice the entire positive real W(D5)×C4 invariant metric has three parameters x,a,b: carrier xI5 and family a(P−vvT)+bvvT, P=I−J/4,v=(1,−1,1,−1)/2. W(D5) removes mixed blocks without assumed orthogonality. Integral root pairings force x,b,a+b and hence x,a,b to be positive integers. The original index four gives detL=x^5 a^2 b. Unimodularity forces exactly x=a=b=1. Carrier scale, orthogonality, root lengths and evenness are no longer extra premises in this class. An explicit A3→D3 map identifies the completed lattice with D8 union D8+(1/2)^8; evenness follows. The theorem covers the entire class analytically rather than by sampling. Thirty exact checks pass normally and with −OO; two independent analytic and full invariant-space reviews.",
      "scopeEN": "Conditional rigidity of charge completion. Fixed additive glue lattice, actual product symmetries, real charge metric and integral unimodular total pairing remain joint inputs. Does not derive their physical origin from P1, select a quarter source/state/time, or close3+1D or F1. Derived in this session with no claim of global mathematical novelty. E8 is not an additional premise of metric selection.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-puncture-spinor-extension-with-integral-selfdual-pairing"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:c17ab8197b9853a3dc4ae542"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:meridian-spinor-joint-source-product-has-actual-family-root-simple-pole",
      "titleEN": "Joint spinor-meridian source word produces the actual family root",
      "statementEN": "For original v983 spinor and four meridian weights vi=(s,mi), the common metric gives vi²=2, vi·vj=1 for different marks and vi−vj=(0,ei−ej). The actual existing current constructor with v498 Affine.act, ordered cocycle and compact adjoint was then executed: all16 spinor signs times12 ordered distinct marks give192 simple poles exactly on their original family roots,96 with coefficient+1 and96 with−1. No phase fit. All64 diagonal cases have double-pole coefficient+1 and the original Cartan simple pole; mixed double poles vanish. Leading twisted terms transport the remaining family root and the known diagonal Cartan shift. This response was not an input of metric selection.",
      "scopeEN": "Given local E8 current realization with its actual cocycles, adjoints and meridional coordinate map; known general E8 root-product rules are not claimed as globally new mathematics. Does not derive the P1→Z_adm field map, physical state, measure, time generator or full regional Higgs/metric gluing. No F1 or ledger closure.",
      "status": "established_scoped",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "topicIds": [
        "topic:e8",
        "topic:clocks",
        "topic:quantum",
        "topic:origin"
      ],
      "goalIds": [],
      "premiseIds": [
        "premise:fixed-puncture-spinor-extension-with-integral-selfdual-pairing",
        "premise:local-e8-current-response-realization"
      ],
      "attemptIds": [],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:d5a231ebc428888c245cb1bb"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r098-withheld-response-search-has-exact-conditional-affine-certificates",
      "titleEN": "Existing search separates withheld response, rational identity and numerical approximation",
      "statementEN": "An executed withheld-response path now exists in run_search. Queries contain no target and are not imposed as source constraints. Min/max use the same declared moment class. Sparse rational elimination and solver-free replay check conditional affine identities. Full2D controls give [0,1] without added relation and exactly1/3 with a different supplied response. Contradiction, positivity emptiness, complex coefficients, rounding and tampering are checked.66 existing tests passed. CLI control explicitly retains inconclusive rational completion.",
      "scopeEN": "Software and conditional equality identities. Exact rational contract coefficients differ from rounded solver coefficients. Numerical endpoints are not certified bounds or full processes. Affine identity proves neither existence, original P1 identification, Z0 nor physical uniqueness. Replay shares row generation and is not independently coded semantics.",
      "status": "established_scoped",
      "problemId": "problem:automatic-origin-response-decision",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:finite-positive-kernel-search-class",
        "premise:typed-source-structures"
      ],
      "attemptIds": [
        "contract:seam-positive-kernel-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:417e93adf107c107ab2cb23c"
      ],
      "reviewState": "reviewed-authored"
    },
    {
      "id": "finding:r098-whole-finite-process-segment-preserves-2245-moments",
      "titleEN": "An entire exact process segment retains2245 responses and a free composite response",
      "statementEN": "Stored full32D source-clustering endpoints share Omega,all ten Majoranas and quarter. T(s)=(1-s)Tmin+sTmax,0<=s<=1,keeps all2245 supplied moment polynomials constant. The difference annihilates Omega and all ten single-field vectors. The shared positive lower bound and clustering cone persist by convexity. All ten existing separating two-field responses are q(s)=1/4+s/2; this family attains the entire interval[1/4,3/4].",
      "scopeEN": "Entire constructed finite family, not all processes or full P1 sources. Floor/gap1/4 are search assumptions. Interval contains attained values, not global extrema. Ten responses are correlated, not independent selectors. Real s analytically covered;rational s additionally serializable. Genuine original q would select only this segment; source map and other freedom remain separate.",
      "status": "established_scoped",
      "problemId": "problem:automatic-origin-response-decision",
      "topicIds": [
        "topic:origin",
        "topic:quantum",
        "topic:process"
      ],
      "goalIds": [
        "goal:T1",
        "goal:T2",
        "goal:T8"
      ],
      "premiseIds": [
        "premise:finite-positive-kernel-search-class"
      ],
      "attemptIds": [
        "contract:seam-positive-kernel-search-20261015"
      ],
      "historical": false,
      "publicationNotes": [],
      "language": "en",
      "sourceRefIds": [
        "source:417e93adf107c107ab2cb23c",
        "source:9f8bd3cec0d8a03be4b3e5bc"
      ],
      "reviewState": "reviewed-authored"
    }
  ],
  "premises": [
    {
      "id": "premise:declared-p1-p2",
      "titleEN": "P1/P2 remain declared starting axioms",
      "statementEN": "This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2."
    },
    {
      "id": "premise:quarter-phase-retained",
      "titleEN": "Quarter phase is retained",
      "statementEN": "Comparisons retain the original charged quarter phase; switching to another phase branch is not an admissible solution to the selection problem."
    },
    {
      "id": "premise:typed-source-structures",
      "titleEN": "Do not identify source types",
      "statementEN": "Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them."
    },
    {
      "id": "premise:fixed-input-models-scoped",
      "titleEN": "Model results remain conditional",
      "statementEN": "Calculations in a fixed E8 net, quotient, family packet, or readout apply only under their stated inputs and do not select those inputs."
    },
    {
      "id": "premise:future-answer-functional",
      "titleEN": "Declared complete answer functional",
      "statementEN": "A fixed set of allowed experiments and the answer functional r for every finite experiment sequence are additional operational inputs; they define the future quotient only relative to that experiment alphabet."
    },
    {
      "id": "premise:positive-word-kernel-null-stability",
      "titleEN": "Positive word kernel with null stability",
      "statementEN": "The GNS/Gram reconstruction requires a Hermitian positive kernel K, normalized reference, declared composition and adjunction, and stability of null relations under every allowed continuation; these are conditions on a supplied K source, not TFPT axioms proved from bare future answers."
    },
    {
      "id": "premise:parallel-irreducible-family-connection",
      "titleEN": "Common parallelity to irreducible family connection",
      "statementEN": "Only for the commutant conclusion, assume additionally that the marked SU(3) family connection is irreducible and beta preserves it in the same marked frame. This is not an accepted P1/P2 axiom and must be derived from the source."
    },
    {
      "id": "premise:sign-covariance-only",
      "titleEN": "Only sign covariance is given",
      "statementEN": "The conditional counterexample assumes C=(I+sgn H)/2 and [rho,C]=0, without knowing positive magnitude |H| or a complete transfer."
    },
    {
      "id": "premise:known-faithful-kms-or-full-transfer",
      "titleEN": "Known KMS scale or full transfer",
      "statementEN": "Positive dynamics reconstruction assumes either known nonzero beta and faithful finite covariance 0<C_beta<I, or the same full transfer operator T=exp(-tau |H|), known tau, and commutation with the sign; a spectrum alone or physical identification of the TFPT channel is insufficient."
    },
    {
      "id": "premise:fixed-em-seam-function",
      "titleEN": "Specified EM function with positive seam response",
      "statementEN": "F(x)=x³−2c³x²+(4/5)c⁶M log(p+q(1−q)^(−5/4)), c=1/(8π), p=1/(6π), q=48c⁴exp(−2x), M>0; original budget M=41. The function and inputs are premises here."
    },
    {
      "id": "premise:native-current-clock-ope-access",
      "titleEN": "Native clock fields and mixed OPE access",
      "statementEN": "Fixed free eight-current vacuum, original C/J/P5 in the same E8 index basis and real-symmetric quadratic fields; access to mixed two-point responses of iterated weight-two double-pole OPE coefficients is assumed. Four individual measurements or a physical detector from P1/P2 are not thereby supplied."
    },
    {
      "id": "premise:declared-native-round20-source",
      "titleEN": "Declared native charge/scalar source",
      "statementEN": "Fixed finite periodic spatial lattice source of rounds20–26 with original G, cocycle, neutral Z8 charges, scalar field and H=Hdiag+Hhop; a,m,beta>0 and original couplings are supplied. Nontrivial memory requires J>0. The original grade k is additionally retained, without presuming its selection from P1/P2."
    },
    {
      "id": "premise:stipulated-even-e8-seam-lift",
      "titleEN": "Stipulated even E8 completion with actual Klein signs",
      "statementEN": "Assume the E8 extension of the even D8 CAR sector constructed in seam-joint-ward-state, with original ordered cocycle, retained quarter transition and explicit P-lift convention. An ordinary-local inclusion of odd CAR fields is not assumed."
    },
    {
      "id": "premise:stipulated-e8-clock-tuple",
      "titleEN": "Stipulated E8 Fock space with marked clock tuple",
      "statementEN": "Given the original ordered CAR/E8 cocycle, E8 Fock representation, Kδ(p,N)=|p|²/2+δ·p+N, original q and full uncompensated quarter transition. J is the actual Gaussian lattice operator, not the cyclotomic Galois operator. A covariant comparison transports δ,q,τ together; a fixed marked source holds them fixed."
    },
    {
      "id": "premise:neutral-current-vacuum-insertions",
      "titleEN": "Every insertion preserves all eight Cartan charges",
      "statementEN": "In the same given E8 Fock space every word starts in the vacuum. Each individual insertion belongs to the fixed Heisenberg/quadratic Jordan OPE algebra and commutes with all eight Cartan zero modes; normal ordering, operator labels and initial state do not change with δ. Overall neutrality or Qq neutrality alone is insufficient."
    },
    {
      "id": "premise:normalized-charged-primary-time-access",
      "titleEN": "Normalized charged primary responses with known time scale",
      "statementEN": "For the given Kδ, normalized primary charge states ±bi for eight independent original E8 basis charges and their positive e^(−tKδ) return amplitudes at known common t>0 are supplied. Global charge shifts are not thereby derived local physical instruments."
    },
    {
      "id": "premise:fixed-nonzero-quarter-twist-comparison",
      "titleEN": "Fixed nonzero chiral quarter twist",
      "statementEN": "The comparison target is the stipulated Kδ Fock space with original nonzero quarter twist, normalized ±Bp primary states, fixed charge marking and the same positive time. Equality of all these responses is required."
    },
    {
      "id": "premise:native-full-charge-field-source",
      "titleEN": "Full original charge-field source",
      "statementEN": "Finite Round20 lattice/scalar space with the original bilinear E8 cocycle, complete integer charges, onsite T and balanced W, coercive quadratic Hdiag and supplied hopping. No P1/P2 selection or local chiral field identification is presumed."
    },
    {
      "id": "premise:native-c-invariant-start",
      "titleEN": "Charge-conjugation-invariant start",
      "statementEN": "The initial density is invariant under linear C:n→−n, including full and C0 Gibbs starts of unchanged H. Compare actual adjoint-paired, opposite marked T responses at the same time."
    },
    {
      "id": "premise:native-zero-sector-chemical-comparison",
      "titleEN": "Chemical comparison with charged intermediate sectors",
      "statementEN": "Additionally supplied Hη=H+η·Qtot, C-invariant initial density in C0 and full propagation after onsite T moves C0 into Cp. η is comparison input, not a derived seam parameter."
    },
    {
      "id": "premise:native-fixed-link-phase-a-invariance",
      "titleEN": "Fixed link phases and A-invariant start",
      "statementEN": "Arbitrary fixed unitary link phases in the same hopping, real original Hdiag/cocycle and initial density invariant under A=C times complex conjugation. Positive Euclidean T return responses are considered; no general real-time equality is assumed."
    },
    {
      "id": "premise:fixed-car-crossed-half-charge-search",
      "titleEN": "Fixed CAR source and adjoined half sector",
      "statementEN": "Ordered eight-channel cocycle, s=(1/2)^8, Q, quarter phase and K_alpha=N+|p|²/2+delta_alpha.p are supplied; alpha=1/4,3/4. Parity equivalence is in the global operator envelope without a separately marked physical X. Neither source nor extension is derived from P1/P2."
    },
    {
      "id": "premise:fixed-positive-crossed-state",
      "titleEN": "Positive base functional and explicit observable algebra",
      "statementEN": "For finite crossed words omega0 is positive; dual Z2 invariance is additionally required for unique algebraic extension. Comparing physical densities must retain the actual Cartan observables and the common normal ground space of supplied K."
    },
    {
      "id": "premise:unchanged-quarter-car-qwz-source-comparison",
      "titleEN": "Unchanged specified CAR/QWZ source",
      "statementEN": "Compare the known quarter-CAR source or full mass=1, ny=8 QWZ operator with the identical Hilbert representation, Cartan action and physical time. Preserve its previously proved unique ground state and spectral gap. This does not compare all P1/P2 realizations."
    },
    {
      "id": "premise:oriented-p2-exterior-carrier",
      "titleEN": "Original oriented exterior carrier",
      "statementEN": "Given E=C5=E3⊕E2, a Hermitian metric, volume orientation, S± and Y=(-1/3)^3⊕(1/2)^2. Internal carrier labels are not physical vacua; geometric seam reflection is not identified with carrier conjugation."
    },
    {
      "id": "premise:fixed-e8-fold-quarter-dictionary",
      "titleEN": "Stipulated E8 quarter-fold dictionary",
      "statementEN": "The existing Weyl lift M, affine E8 module, Q'=2(H3+H6) and K_alpha=L0+delta_alpha.H0 with alpha=1/4,3/4 are held fixed for comparison. This representation is not derived from P1/P2; an unbroken SM time action is not assumed."
    },
    {
      "id": "premise:actual-chiral-opposite-quarter-domains",
      "titleEN": "Given chiral source in both quarter domains",
      "statementEN": "D_alpha=-i∂theta on f(theta+2pi)=exp(2pi i alpha)f(theta), filled negative spectrum and relative particle/hole excitation time; alpha=1/4,3/4. This compares two conjugate domains, not opposite charges in one fixed domain or all P1 sources."
    },
    {
      "id": "premise:given-first-marked-quarter-character",
      "titleEN": "First 5+3 marking and Z4 character supplied",
      "statementEN": "In the supplied E8 dictionary, D5 on the first five coordinates, D3 on the last three and k=2sum(p1..p5) mod4 are given for the first quarter domain. The other domain may transport these data covariantly; their original physical selection is not presumed."
    },
    {
      "id": "premise:given-d5-a3-free-fermion-realization",
      "titleEN": "Supplied free D5+A3 realization",
      "statementEN": "Compare the documented free D5_1+A3_1 realization with five plus three complex fermions and spin-field sectors; realization by the raw P1 source is not presumed."
    },
    {
      "id": "premise:full-normalized-charge-time-character-family",
      "titleEN": "Fully normalized time/charge family in the given E8 completion",
      "statementEN": "The given chiral quarter source, its eightfold pushforward and stipulated even E8 completion supply K_alpha and the full additive U1 generator Q. Only characters in the real span of their torus vectors modulo E8 are searched; no P5 is supplied as a search variable or target projector. Physical identification of this completion and of a composed marking is not assumed."
    },
    {
      "id": "premise:actual-wold-source-operator-hypotheses",
      "titleEN": "Hypotheses of joint operator reconstruction",
      "statementEN": "For this conditional theorem: orthogonal projection C, unitary U, (1−C)UC=0, index(CUC)=−1, pure isometry and minimal unitary dilation. Actual selfadjoint B satisfies U*BU=B+1 and Bw=alpha w on a common invariant core, alpha=1/4 or 3/4. These conditions are not presumed derived from P1/P2."
    },
    {
      "id": "premise:charged-car-negative-sea-source",
      "titleEN": "Charged CAR algebra and original negative sea",
      "statementEN": "Assume the actual field algebra is charged CAR(H) and its reference state is the pure quasifree sea with occupation 1−C. Relative charge and positive excitation time are normal ordered against this sea. This physical identification is an additional premise."
    },
    {
      "id": "premise:fixed-scalar-quarter-hardy-source",
      "titleEN": "Fixed scalar Hardy model with quarter time",
      "statementEN": "H=L²(S¹), C projects onto n≥0, B_alpha=−i∂theta+alpha with alpha=1/4 or 3/4. C and B remain fixed for every candidate. Consider scalar unimodular multiplication operators: continuous symbols for isometry classification and H1 symbols for finite excitation energy. This source class is not derived from P1/P2."
    },
    {
      "id": "premise:actual-product-collar-two-face-data",
      "titleEN": "Complete data of both product-collar faces",
      "statementEN": "A selfadjoint B occurs in an exact normal-independent product equation. The full orthogonal L2 Cauchy graph projection of both labeled faces, their actual fiber identification and independently known positive normal length ell are supplied. Selection of these data from P1/P2 is not presumed."
    },
    {
      "id": "premise:charged-car-two-face-graph-state",
      "titleEN": "Charged quasifree state for the complete graph covariance",
      "statementEN": "Additionally identify the actual field algebra with charged CAR(H direct_sum H) and the state with the gauge-invariant quasifree state whose occupation covariance is G_ell. This is an extra physical premise, not a consequence of the geometric projection calculation."
    },
    {
      "id": "premise:local-geometric-dirac-deck-lift",
      "titleEN": "Local geometric lift on a Dirac boundary",
      "statementEN": "The claimed geometric deck reflection acts at the fixed boundary through a local bundle lift over the same base reflection. Compare an ordinary positive-dimensional Dirac boundary with orthogonal Calderon projection; a nonlocal operator subsequently defined as 2P_C−I is not a pre-established geometric action."
    },
    {
      "id": "premise:literal-carrier-after-positive-compression",
      "titleEN": "Literal carrier embedding after positive compression",
      "statementEN": "Read the archived phrase H_car after primitive admissibility compression literally as a subspace of Ran(Pprim)⊂Ran(C), then define internal polarization as (2C−I)|H_car. A different coefficient-factor interpretation instead requires its own embedding and internal involution."
    },
    {
      "id": "premise:declared-finite-operator-synthesis-inputs",
      "titleEN": "Explicit finite operator-synthesis inputs",
      "statementEN": "The recovery control assumes the given five-mode CAR representation. The inverse solver assumes explicitly supplied finite operator pairs and adjoints. The map is unknown; physical source selection is not assumed derived."
    },
    {
      "id": "premise:finite-positive-kernel-search-class",
      "titleEN": "Declared finite positive kernel search class",
      "statementEN": "Given up to five CAR modes, an extra selfadjoint transfer operation, 0<=T<=I, T Omega=Omega and internal CAR quarter invariance. Five-mode completions additionally use a minimal irreducible Fock representation with pure occupations inferred from searched moments. Objectives, positive floor and cluster gap are declared search choices; neither these nor the representation are presumed consequences of P1/P2."
    },
    {
      "id": "premise:actual-car-graph-and-oriented-boundary-pairing",
      "titleEN": "Actual CAR boundary covariance and oriented amplitude pairing",
      "statementEN": "The full geometric two-face graph G is additionally identified as the actual CAR state covariance. The first labeled fiber is input/dual, the second output; the source realizes the specified fermionic boundary-state/operator pairing. These are physical identification premises, not consequences of matrix sizes or classical Cauchy projection. Normalized data determine only the operator ray and not the absolute partition factor."
    },
    {
      "id": "premise:given-complex-fermion-source-quantization",
      "titleEN": "Explicit complex-fermion source quantization",
      "statementEN": "Given the actual invertible free kinetic operator K, its reference, Grassmann source couplings and oriented Berezin measure with integral exp(-barpsi psi)=1. A mode partition is not a spatial boundary decomposition without geometric identification. Neither comparison part D_rel nor a general spectral profile is automatically identified with this K or -log det K; this quantization is not presumed derived from P1/P2."
    },
    {
      "id": "premise:given-angular-quarter-zeta-cut",
      "titleEN": "Given angular quarter operator and zeta cut",
      "statementEN": "Given a single circle operator D_alpha=-i partial_theta with f(2pi)=exp(2pi i alpha)f(0), 0<alpha<1, complex-fermion zeta quantization and negative eigenvalue argument +pi. The quarter source has alpha=1/4; alpha_ref=3/4 is a diagnostic comparison, not archival D_ref. Its angular Green propagation is not positive occupation covariance or already physical time evolution."
    },
    {
      "id": "premise:given-thermal-sea-abel-subtraction",
      "titleEN": "Explicit Abel subtraction of chiral sea",
      "statementEN": "For the already given single chiral particle/hole source, use the exponential Abel sum of negative sea energies and subtract only its -1/epsilon² term. This is a declared absolute regularization; its selection and compensation of the central loop phase by an original eta/bulk contribution are not presumed consequences of P1/P2."
    },
    {
      "id": "premise:carrier-covariant-invariant-ring",
      "titleEN": "Covariant invariant-ring primitiveness at variable carrier rank",
      "statementEN": "For the local inference test: V=C^b, W=C², G=S(U(V)×U(W)), both fermion legs in Λeven(V⊕W). Primitiveness excludes invariant factors of smaller positive carrier degree in the covariant polynomial invariant ring. No global minimum over different sources/ranks or independently selected special tensor support is assumed."
    },
    {
      "id": "premise:fixed-background-quarter-fermion-source",
      "titleEN": "Given free quarter-source background without a selected Higgs derivative",
      "statementEN": "The existing two-mode source path has K0=diag(17/16,4097/4096) and a fixed Berezin measure. Compare only completely coincident fermionic source polynomials at Φ=0 and explicitly supplied extensions K0 or K0+Φσx. These are diagnostic extensions, not two claimed P1/P2-admissible worlds or a comparison of complete Φ-dependent functionals."
    },
    {
      "id": "premise:first-order-perturbation-graph-estimate",
      "titleEN": "Audit of the general perturbation argument",
      "statementEN": "Given: a selfadjoint first-order anchor with H1 graph norm and a symmetric first-order perturbation with bounded coefficients on the same domain. The quarter/reflection control uses the explicit compact torus operator in section11.2, not a claimed original P1/P2 source."
    },
    {
      "id": "premise:fixed-field-four-mode-inverse-data-control",
      "titleEN": "Fixed fields in the four-mode diagnostic",
      "statementEN": "Given: the first two particle/hole pairs of one chiral CAR source, energies (alpha,1+alpha,1-alpha,2-alpha), the same Hurwitz sea energy and fixed field labels. U rotates only neutral pairs p0h0/p1h1 by 3/5,4/5. Spatial locality or P1/P2 selection of U is not assumed; this is not the internal P2 V16 carrier."
    },
    {
      "id": "premise:quarter-circle-coordinate-local-algebra",
      "titleEN": "Local coordinate algebra of the conditional quarter source",
      "statementEN": "Given the conditional scalar circle realization H=L²(S¹), Dom B=H¹_per, Bα=−i∂θ+α with α=1/4 or3/4. The local algebra investigated here is explicitly smooth multiplication C∞(S¹) on this line, not a complete physical field-insertion algebra already derived from P1/P2."
    },
    {
      "id": "premise:quarter-circle-nonlocal-cauchy-enlargement",
      "titleEN": "Explicitly additional nonlocal Cauchy enlargement",
      "statementEN": "On the Fourier basis en,n∈Z, U is the bilateral shift and C projects onto n≥0. Consider the algebraic or explicitly smooth *-algebra with controlled bounded commutators generated by U,U*,C. No identification with B(l²), automatic domain statement for its norm completion or original local field algebra is assumed."
    },
    {
      "id": "premise:given-finite-sm-triple-yukawa-inputs",
      "titleEN": "Given finite SM representation with symbolic Yukawa inputs",
      "statementEN": "Use only the existing v252/v254 representation with C⊕H⊕M3, already supplied color/weak modules and four symbolic complex3×3 Yukawa blocks. No physical values are chosen or fitted. Classify the particle LR one-form block; no proof of the full real96-dimensional fluctuation with antiparticles, JAJ and Majorana sector is claimed."
    },
    {
      "id": "premise:complete-labeled-even-car-kernel",
      "titleEN": "Complete kernel in a fixed CAR dictionary",
      "statementEN": "Given: full even T in a fixed labeled finite CAR Fock basis and explicit boundary/trace condition. Link logarithm needs T00≠0; finite selfadjoint matrix logarithm needs T>0. Physical identification, length and original Φ-dependence are not presumed derived from P1/P2."
    },
    {
      "id": "premise:local-domain-product-dirac-skeleton",
      "titleEN": "Declared product skeleton for algebra identifiability",
      "statementEN": "Given a compact spin collar with a local selfadjoint elliptic geometric boundary problem stable under smooth multipliers, or closed double with H1 domain. On H=L²(M,S)⊗HS(Mn(C)),n≥2: D=D0⊗I, B=B0⊗I, J=J0⊗(X→X*), Γ=Γ0⊗I, R=R0⊗I, with zero finite Dirac term. Compare scalar and left matrix insertions on the same H. No arbitrary APS-domain invariance, complete OS source, unit winding or minimal P1/P2 branch is claimed."
    },
    {
      "id": "premise:unmarked-hermitian-rank-five-exterior-carrier",
      "titleEN": "Given unmarked Hermitian rank-five carrier with volume",
      "statementEN": "Given E=C5 with Hermitian metric and unit complex volume, F=ΛE, Γ=(-1)^degree and conjugate-linear Hodge J_H. Neither3+2, named particle/gauge modules nor Yukawas are inserted. Internal Clifford operators are not identified with physical local fermion fields; rank5 and volume are not newly source-derived."
    },
    {
      "id": "premise:minimum-rank-holomorphic-even-even-fundamental-class",
      "titleEN": "Minimum rank in the covariant even-even-fundamental tensor test",
      "statementEN": "Given E=V⊕W with b,s≥1, Hermitian metric and unit complex volume; G=S(U(V)×U(W)); two nontrivial positive even exterior fermion legs and one fundamental boson leg in W. Rank and split vary. Primitivity is in the holomorphic covariant invariant ring without independent conjugate/dual field variables. At rank5 restrict the same volume tensor vol(α∧β∧h) to all splits. No actual source vertex, equal complete S1 minimum defect or physical P1/P2 countermodel is assumed."
    },
    {
      "id": "premise:reverse-bootstrap-e8-closure-framework",
      "titleEN": "Reverse selection in the discrete closure framework",
      "statementEN": "The origin paper discrete E8 closure framework with rank, family, spinor and simple-current conditions is given. Its numerical fixed-point identities are not identified with a physical operator realization."
    },
    {
      "id": "premise:local-e8-current-response-realization",
      "titleEN": "Given local E8_1 vacuum representation and explicit cocycle",
      "statementEN": "Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation."
    },
    {
      "id": "premise:faithful-differentiable-covariance-chart",
      "titleEN": "Given differentiable faithful covariance chart with explicit sector embedding",
      "statementEN": "Finite or explicitly regulated CAR one-particle chart with 0<C<I; h(C)=log(I-C)-log C. The individual sector-block statement requires fixed sector projectors commuting with the background covariance; moving embedding, grading, scale and source must be differentiated separately. Interpretation as a complete state uses the quasi-free hypothesis. No physical P1 source or Phi insertion is selected."
    },
    {
      "id": "premise:differentiable-isometric-source-frame",
      "titleEN": "Given differentiable isometric embedding in fixed source charts",
      "statementEN": "Q(Phi) is a differentiable isometry from finite/regulated carrier coordinates into a fixed source Hilbert chart, with differentiable covariance C_Sigma. a=Q*partial Q and N=(I-QQ*)partial Q are its induced frame/normal components. This premise does not select Q or Phi from P1; moving source charts and unbounded operators require additional connection/domain conditions."
    },
    {
      "id": "premise:fermionized-ns-vector-algebra-fixed-d5",
      "titleEN": "Unchanged local NS fermionization with fixed D5 group action",
      "statementEN": "The existing conditional D8->Z^8 fermionization of the selected E8_1 theory and its nonanomalous Z2 with spin/twist data is supplied. Its16 real local NS generators carry (10,1)+(1,6) under the fixed Spin10 x Spin6 cut. Consider their generated algebra in the same NS representation, without adjoining Ramond/twist intertwiners, field/crossed-product extensions or changed group action. No physical3+1D identification is presumed."
    },
    {
      "id": "premise:process-composition-finite-controls",
      "titleEN": "Explicit finite process and cyclicity controls",
      "statementEN": "The controls compare finite classical and complex-quantum processes and C4 versus L(M2) on HS(M2), J(X)=X*, Omega=I/sqrt2. Both cyclic/separating, faithful and order zero; the C4/M2 centers differ. No complete P1/P2, OS, seam or minimality countermodel is asserted."
    },
    {
      "id": "premise:unmarked-five-traceless-hermitian-quartic",
      "titleEN": "Unmarked traceless Hermitian five-dimensional endomorphism",
      "statementEN": "The diagnostic grants X=X* on an unmarked complex rank-five carrier, trX=0 and trX²=1 for shape classification. It studies trX⁴ or -t+t²±trX⁴, t=trX². Field, trace constraint, contraction, sign, even symmetry and dynamics are not derived here from P1."
    },
    {
      "id": "premise:geometric-two-face-response-and-kernel-quotient",
      "titleEN": "Geometric two-face compression and explicit projection kernel",
      "statementEN": "Given selfadjoint B, labeled identified fibers and ell>0, G is the orthogonal graph projection of T=e^-ellB, A=(I+T²)^-1, V=(A^1/2,T A^1/2). The geometric scalar F_f=diag(M_f,0), L_f=V*F_fV and K_G(x,y)=<x,Gy> are studied without identifying a physical covariance, instrument, Born rule or reprojection law."
    },
    {
      "id": "premise:boundary-kernel-frame-sewing-interpretation",
      "titleEN": "Explicit boundary-kernel interpretation with identity kernel A",
      "statementEN": "For positive injective dense-range F=A^1/2, K_O=F O F are interpreted as bilinear kernels in a nonorthogonal frame with identity kernel A. In finite regulators A W A=A forces inverse-Gram sewing; in infinite dimension it is defined as a bounded form using F^-1 K. This is an explicitly conditional representation reading, not a physical intervention, projection or measurement law selected by the original action. The alternative reading of F_1 as an actual face filter is not excluded."
    },
    {
      "id": "premise:foundational-reset-no-target-input",
      "titleEN": "TFPT for later comparison only",
      "statementEN": "The explicit research reset studies independent starting classes. E8, five,3+2, SM algebra, Yukawa data, Hilbert space, complex amplitudes and TFPT clocks are not inputs. Preserve existing TFPT results. After at most three failed origin attempts on unchanged premises change at least one fundamental premise or direction; coding bugs do not count. State assumptions, necessary consequences and newly explained properties."
    },
    {
      "id": "premise:finite-event-poset",
      "titleEN": "Finite event order as starting data",
      "statementEN": "A finite strict partial order is supplied as event/precedence structure without metric, space, rates or probability. Order is an input in this class."
    },
    {
      "id": "premise:finite-deterministic-joint-replication-control",
      "titleEN": "Finite deterministic processes with full joint replica control",
      "statementEN": "Supply finite nonempty local input/output sets and total w:product O->product I. Every finite number of coordinatewise independent replicas allows every joint deterministic map I_k^M->O_k^M at corresponding interfaces, including constants/erasure. Require at least one global solution for every such experiment; do not assume a global order."
    },
    {
      "id": "premise:finite-update-observation-errors",
      "titleEN": "Supplied finite update, observation and errors",
      "statementEN": "Finite X, deterministic step f and observation o, optionally error support T, are inputs. A record-cell system is a family of disjoint nonempty forward-closed observationally distinguishable sets, not automatically an exhaustive invariant partition."
    },
    {
      "id": "premise:finite-operational-composition-action",
      "titleEN": "Supplied finite operational action and effects",
      "statementEN": "A transformation monoid acts on finite X; effects define operational distinguishability. Composition, action, effects and any selected time generator are separate starting data."
    },
    {
      "id": "premise:repeatable-distinction-benchmark",
      "titleEN": "Explicit repeatable-distinction benchmark",
      "statementEN": "Recognizable reports, reproducibility of a declared context and available serial continuations are separate commitments. The sharp benchmark additionally has an immediately result-repeatable test and two preparations with different certain reports. These conditions are stronger than mere observability; probability, free erasure, re-preparation, replica control or physical time are not assumed to follow."
    },
    {
      "id": "premise:three-explicit-observability-countermodels",
      "titleEN": "Three explicit operational countermodels",
      "statementEN": "R has deterministic preparation/read traces and continued partial-identity branches only, no primitive mixing or internal re-preparation. I is the classical two-bit simplex with probabilities and nondisturbing joint access. D is the square with explicit positive X/Z branches, square symmetries, preparations, mixtures and finite serial/adaptive closure. These selected rules define counterworlds rather than necessary physics."
    },
    {
      "id": "premise:finite-prefix-consistent-sequential-data",
      "titleEN": "Finite prefix-consistent sequential response tables",
      "statementEN": "Supply finite preparation/action/report sets, finite horizon and nonnegative normalized sequential probability tables. Summing out the last report recovers prefixes and earlier marginals do not depend on future choices. Impose no memory, locality, stationarity or preparation-noncontextuality bounds on the representation."
    },
    {
      "id": "premise:native-g31-concrete-event-representation",
      "titleEN": "Actual native G31 event representation",
      "statementEN": "Use the actual original Hamming/E8/J matrices and60 reflections, their four-dimensional action, characteristic P64=O2(G31), and existing S6 quotient. These are accepted mathematical core data, not a physical source derived from P1 in this round."
    },
    {
      "id": "premise:native-symmetric-quartic-and-erasure-constructors",
      "titleEN": "Symmetric quartic and actual erasure intertwiner",
      "statementEN": "Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product."
    },
    {
      "id": "premise:fixed-complete-four-five-primitive-reflection-generators",
      "titleEN": "Complete four/five generators with exactly60 reflection jumps",
      "statementEN": "Consider only Poisson generators sum_j lambda_j(Ad_rj-id) over the actual60 native reflections, with complete continuous-time four- and five-generators fixed. No extra Hamiltonians, coherent algebra events, or generators inferred uniquely from one finite-time channel."
    },
    {
      "id": "premise:complete-logical-nondisturbance-native-covariance",
      "titleEN": "Complete logical nondisturbance and native covariance",
      "statementEN": "A CPTP residual channel Phi on V5 tensor bar(V4) preserves Tr4 Phi(X)=Tr4 X for ALL joint X and is covariant under the native G31 product representation. This is stronger than preservation only of erasure states rho tensor I4/4 and defines an explicit conditional process class."
    },
    {
      "id": "premise:coherent-block-source-algebra-operation-menu",
      "titleEN": "Extended coherent source-algebra operation menu",
      "statementEN": "For realization of the residual channel, unitary elements of the represented group C*-algebra may serve as Kraus events. This mathematical menu does not assert physical permission derived from P1. The block algebra or each sector is considered; extra coherences between inequivalent representations are not automatically accessible observables."
    },
    {
      "id": "premise:existing-logical-clock-and-charge-marking",
      "titleEN": "Existing logical clock and charge marking",
      "statementEN": "Retain the existing logical labels weak0/1, color2/3/4, source point5 and Y5,R5,sigma5. Equivalence under their stabilizer is not automatically an equivalence of lifts commuting with the original native four/P1 clock."
    },
    {
      "id": "premise:original-marked-simplex-positive-polar-rule",
      "titleEN": "Original simplex and positive polar rule",
      "statementEN": "Use the actual W6 simplex and raw metric, unchanged native three-clock and original positive polar prescription at one of its three marked fixed points. The prescription and its physical selection are not derived from P1."
    },
    {
      "id": "premise:actual-clifford-identification-and-finite-overgroup-theorem",
      "titleEN": "Actual Clifford identification and finite-overgroup theorem",
      "statementEN": "Retain the actual concrete identification of <G31,zeta8 I4> with complex Clifford X2. Apply NRS6.5 only to the proved finite determinant slice; a group-order match alone does not suffice."
    },
    {
      "id": "premise:original-erasure-decoder-and-same-native-quarter-polynomial",
      "titleEN": "Original decoder and same native quarter polynomial",
      "statementEN": "Fix original erasure decoder D(A)=W(A tensor I4)W* and its mark P220=P2 tensor I4. Substitute actual sigma20=sigma5 tensor bar(sigma4) and all four native reflection lifts of original tau5 into the existing R polynomial. This tests that continuation, not all coherent lifts."
    },
    {
      "id": "premise:unitary-full-branchwise-erasure-clock-lift",
      "titleEN": "Unitary continuation with full branchwise erasure action",
      "statementEN": "Consider unitaries T on the actual erasure carrier satisfying T(rho tensor I4/4)T*=RrhoR* tensor I4/4 for every logical state rho and a given logical unitary R. This is a declared compatibility class, not a physical instrument rule derived from P1."
    },
    {
      "id": "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark",
      "titleEN": "Original clock/simplex without an imposed polar mark",
      "statementEN": "Retain actual normalized W6 simplex, sigma=(234), tau=(01), q=5. Consider ALL Hermitian rank2 projectors P with RanP inside Fixsigma, [P,tau]=0 and one positive/one negative tau eigenvalue on RanP. The original polar rule is a comparison point, not an imposed condition of this compatibility class."
    },
    {
      "id": "premise:original-native-fourth-moment-parent",
      "titleEN": "Actual original moment parent",
      "statementEN": "Use the actual native fourth root moment with 40M4=Pi5+Psym4 and Hnat=I-(Pi5+Psym4)/2. Add no new marking-dependent Hamiltonian. Physical identification as a time generator is not inferred merely from matrix existence."
    },
    {
      "id": "premise:local-product-code-orbit-geometric-parallel-transport",
      "titleEN": "Geometric parallel transport of local-product code paths",
      "statementEN": "Consider moving code subspaces T(t)RanV, T(t)=tensor_j Uj(t), Uj(0)=I, returning to the original code. Use the Grassmann/Berry connection induced by the actual Hilbert inner product. No general collective code path, additional internal dynamics or physical adiabatic generator is assumed or excluded."
    },
    {
      "id": "premise:original-coupled-determinant-event-cover",
      "titleEN": "Original coupled determinant event lift",
      "statementEN": "Compare all60 original events with h=exp(-i pi/4)r and A5=-rho5(r) on the coupled finite SU4 cover. This is not the unchanged order2 G31 word or a selected physical pulse."
    },
    {
      "id": "premise:literal-charged-current-native-register-dictionary",
      "titleEN": "Literal charged-current/register identification",
      "statementEN": "The tested dictionary identifies the four original charged C_a currents with the unchanged native four-register and requires the actual erasure tensor intertwining under gl5 source operations. This is a tested hypothesis, not a P1-derived fact."
    },
    {
      "id": "premise:literal-native-positive-cartan-quartic-fock-embedding",
      "titleEN": "Actual positive Cartan quartic Fock embedding",
      "statementEN": "Use original Construction-A roots with physical metric dot/2 and u_j=(h_2j-i h_2j+1)/sqrt2 as J=+i basis. Canonically embed the actual five Sym^4 code support sums as neutral grade4 Heisenberg polynomials in the given E8_1 lattice vacuum. No physical preparation follows."
    },
    {
      "id": "premise:compact-inner-e8-zero-mode-operation-class",
      "titleEN": "Compact inner E8 current operation class",
      "statementEN": "Consider exponentials of compact weight1 current zero modes and arbitrary sequences preserving the given code at the endpoint. Optional conformal L0 propagation commutes with them. Nonlinear Hamiltonian polynomials, higher modes and non-automorphisms are not identified with or excluded as this class."
    },
    {
      "id": "premise:original-neutral-root-pair-moment-fields",
      "titleEN": "Original neutral root-pair moment fields",
      "statementEN": "Use existing E8_1 neutral_source_response reader:64 chirally selected roots, original omission of one SU4 family weight line, B48=12T_E8+R_neut, AR=4P_A2-8P_U1. Family omission is an explicit existing input, not derived here from P1; neither it nor the R port or physical coupling is newly selected."
    },
    {
      "id": "premise:solely-neutral-local-weight-two-zero-mode-class",
      "titleEN": "Solely neutral local weight-two zero modes",
      "statementEN": "Consider energy-preserving zero modes o(v)=v_(wt(v)-1) of all Hermitian lattice-charge-zero weight-two fields in given vacuum and temporal sequences solely of these generators. Grant the mathematical class without claiming P1-derived physical intervention permission, time or projections. Alternating root-current operations, individual K48 mode roundtrips, nonneutral fields and higher mode products are different classes."
    },
    {
      "id": "premise:original-displayed-j-equivariant-cartan-root-isometry",
      "titleEN": "Original displayed J-equivariant root isometry",
      "statementEN": "Use existing S=_SIMPLE and T=_TARGET_SIMPLE from cartan_source._glue_deck_character_certificate: O=T S^-1/sqrt2 maps actual Construction-A roots r/sqrt2 to original Chevalley roots r/2, preserving metric and J. This is the existing concrete map, not a newly fitted embedding; physical P1 selection stays separate."
    },
    {
      "id": "premise:original-positive-adjoint-two-insertion-response-profiles",
      "titleEN": "Original positive adjoint two-insertion response",
      "statementEN": "Compute o(W_beta), W_beta=E_beta,0 R_neut, with unchanged original real transverse v_beta. Ordered return is positive Fock Gram o(W)*o(W) between code or original trimer states without intermediate projection. Allow W=sum a_beta W_beta for arbitrary complex input coefficients; distinct lattice charges force nonnegative weights |a_beta|². Nonadjoint returns, other complex transverse fields, longer histories or physical instruments are not thereby selected."
    },
    {
      "id": "premise:common-unnormalized-positive-return-erasure-test",
      "titleEN": "Common unrenormalized positive-return erasure test",
      "statementEN": "The tested hypothesis reads actual positive K5 and K20 of the same source response with common original normalization as complete branchwise erasure continuation: K20(rho tensor I4)K20=K5 rho K5 tensor I4 for all rho, equivalent under positivity to K20=K5 tensor I4. This is a tested candidate identification, not a claim every correlation is a physical instrument. Independent relative20/5 recalibration is outside this fixed map."
    },
    {
      "id": "premise:specified-original-pair-ordered-response-composition",
      "titleEN": "Specified ordered response family of original single pair",
      "statementEN": "Examine mathematically specified moments M_n=Pi L_beta^n Pi,n>=0, L_beta=o(W_beta)*o(W_beta), for same original doubled root(0,0,0,0,0,0,-2,-2). Pi/Q only split full amplitudes; no projection is executed. This tests composition/memory of the already determined source, not P1 selection of physical history, coupling, preparation or time. Full coherent multiroot processes must additionally retain nonneutral final charge sectors."
    },
    {
      "id": "premise:canonical-source-stress-all-mode-history",
      "titleEN": "All modes of original canonical source stress tensor",
      "statementEN": "In given E8_1 lattice vacuum use exactly T_E8=(1/2)sum:h_A h_A:,c=8, without improvement/background charge. Examine all Virasoro modes and well-defined pure stress histories in original neutral Cartan-Fock space. This is a mathematically specified geometric transport class, not P1-selected physical history or time. It differs from prior class of all neutral weight2 ZERO MODES; do not combine exclusions. First erasure Ward action uses existing a_a=bar u_a(1), no extra source, root or family choice."
    },
    {
      "id": "premise:original-cartan-current-local-smearing-and-weyl-class",
      "titleEN": "Full original Cartan-current insertion and specified Weyl class",
      "statementEN": "In existing neutral Cartan-Fock module use full original current field and its actual CCR, all smooth real8-vector profiles with Vhat_-n=conjugate Vhat_n and h0=0. Ordered unitary classification uses only finite exp(iJ(V)) histories of these currents. Explicit mathematical class in given source net, not raw-P1-derived permission, field coupling, physical time or code=H_adm identification. Root currents, general field products and mixed stress histories are outside."
    },
    {
      "id": "premise:full-existing-local-e8-field-hull-observer-code",
      "titleEN": "Full existing local E8 field algebra with observer five-code",
      "statementEN": "Accepted field-algebra scope: In accepted original E8_1 lattice vacuum use all existing Cartan/root currents, normal products, derivatives and local smooth smearings; native five-code is input/observer slice, not assumed dynamically closed. Retain all exterior charges/modes and both actual twenties. P,Q only decompose analytic endpoint/memory formulas, never execute intermediate projection. Global mode products of local fields are not localized instruments. PhysicalP1 pullback, intervention history, state/time stay separate. Intrinsic tensor/real-form/simplex reconstruction is not a postulated physical potential/state rule."
    },
    {
      "id": "premise:original-native-event-difference-fields-and-state-controls",
      "titleEN": "Actual native event fields and distinct state controls",
      "statementEN": "In accepted full E8 field net test actual native reflection automorphisms on reconstructed quartic fields and coherent difference against identity. Original sigma=(234),tau=(01),markedq=5 remain given comparison data; preparation ofq not derived. Vacuum and normalized marked source state are distinct mathematical controls. Difference of automorphism and identity is NOT assumed physically allowed intervention/instrument. Retain all local Wick/Taylor products and complete source states. Positive Gram/relative normalization is examined as computable tensor, never imposed as physical selection rule."
    },
    {
      "id": "premise:intrinsic-native-event-geometry-without-marked-clock",
      "titleEN": "Intrinsic event geometry without marked clock as selector",
      "statementEN": "User159c5316 17Oct replaces automatic instrument/whitening-origin next step with intrinsic structure test. In accepted full unitaryE8_1 fieldnet use actual quarticproducts,eventrelations,*-operation,centralOPEnormalization. No originalpolar/P2,desired3+2,markedq,selectedclock orphysicalrealstate rule as construction criterion. Compare originalgeometry/clocks only afterwards. Transportmetrics withbasis changes; distinguish centralalgebraicOPE data andstate-dependentGNS responses. Only states with definedcommonfieldmoments; positivefiniteenergycontrols not automaticallyRP/clustering/finiterelativeactionP1seeds. Retain full localproducts,composition,correlations; no assumed independenttensorphysics."
    },
    {
      "id": "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
      "titleEN": "Original seam/state data on actual60 flags without fitted selection",
      "statementEN": "User17Oct: test originalseam/statedata onactual60 flags P(q,S); no fittedclock,coupling,newselectionrule. Additional EXISTING data topreviousunmarkedobject: fullchargedinternalv=(0^5,1/2^3),deck square,originalE8vacuum; optionaloriginalR_neut/retained48familyomission explicitgivenpremise,all4cases. SEPARATEactualoriginalfoldphasesalpha1/4,3/4withfixedexistingM,d=M((j+alpha)/8−1/2);disshift/timediagnostic,notautomaticallyfullCARcovarianceorE8vacuumexpectation. Fullroot/fieldaction,nocompressiononly. NopostulatedphysicalTheta,field/state/normalorderingdictionaryorP1selection."
    },
    {
      "id": "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
      "titleEN": "Fixed conformal current reference in original fold-state transport",
      "statementEN": "Continuation17Oct: same givenchiralCARquarterfold,sea,F Cα F*,existingM/literalO; no newcopies/clock/coupling/selectionrule. NativehidentifiedherewithFIXEDconformalNSpointsplitcurrents;countertermagainstsea-normalorderedHfollowskerneldifference. ThisreferenceidentificationisCONDITIONALdictionarypremise,notphysicalP1originfromM/O. OriginalQWZpositivej≥1andnegativeDfoldorientationwithcharge/current/particleholetransportseparate;bothquartersretained. E8DeltatwistedextensionandoriginalglobalW4fromexistingevenCAR/E8cocyclefactorizationremaingivenextension,nooddCAR/E8localityproof. Noreselectedgroundstate;sourcechargesinitiallyZ8. Fullproducts/oppositepolarization/exteriormodes/charges,noperformedcodeprojection;originali0boundaryvalues,nofittedcontactterms."
    },
    {
      "id": "premise:original-single-circle-local-density-and-geometric-stress",
      "titleEN": "Original single-circle density and geometric stress",
      "statementEN": "Same stipulated chiral CAR source, negative-D sea, actual quarter domains, eightfold F and existing M/O. Local density J_m=sum:a_r* a_(r+m): and its half-density geometric stress with alpha ground energy follow from this source. Original scalar phases fold to correlated generally offdiagonal channel profiles, not independently selected E8 root weights. NS/quartic reference remains conditional. Global Fourier modes control existing fields; no P1-selected local profile/detector/coupling. No isolated b->-b invariance for these new responses; transport positive QWZ occupation with charges/currents/V/b together."
    },
    {
      "id": "premise:original-gap-normalized-primitive-relative-action",
      "titleEN": "Original gap-normalized relative P1 action",
      "statementEN": "Original source defines chi_seed=1/lambda_1^+(|B_Sigma|), S_prim=Tr f(D_rel/chi)-Tr f(D_ref/chi)+i pi Deltaeta/2 for declared spectral test profile. D_rel/ref are geometric odd/even parts; varying reflection, boundary domains, reference, state and eta must be retained. This is the given source function, not a new coupling or physical event rule. Scalar quarter CAR realization and NS/native field dictionary remain explicitly conditional."
    },
    {
      "id": "premise:positive-scalar-first-order-source-comparison-class",
      "titleEN": "Whole scalar positive first-order comparison class",
      "statementEN": "Compare all smooth scalar first-order differential operators on already given oriented source circle, fixedL2(dtheta),H1per,positive nowhere-zero principal symbol. Periodic chart contains quarterphase in c/holonomy; do not add domain twist again. Original Balpha is reference point; comparison operators are not all claimed physically admissibleP1 data. Point defects,matrix fibers,nonlocal and general higher-dimensional sources are outside."
    },
    {
      "id": "premise:given-original-fixed-one-particle-time-winding-ward",
      "titleEN": "Actual fixed one-particle time-seam Ward of given source",
      "statementEN": "Already given source Balpha=-i dtheta+alpha,Z=multiplication exp(itheta) satisfies[Balpha,Z]=Z, equivalently exp(-itBalpha)Z exp(itBalpha)=exp(-it)Z. Retaining THIS concrete operator relation is stronger than unit spectral flow. It is given-source datum, not a rule derived here from bareP1. Do not identify one-particle Ward with charge-dependent CAR sea term or physical second. Charged quarterlift Qalpha=exp(i pi alpha/2)Q4,reference sea and integer carry retained separately."
    },
    {
      "id": "premise:four-starts-fixed-state-versus-whole-datum-comparison",
      "titleEN": "Four starts at fixed state versus joint datum transport",
      "statementEN": "Comparison scope: q2,3,4,5 and globalS01. Retain originalFCαF*,M/O,fullE8fields,nativeJ andactualchargedfold,time,adjoint,normalordering,erasure. Separate passive whole-presentation changes, active mathematical field automorphisms and symmetries of FIXED given source state. Marks are actual intrinsic quartic rays/polar planes,not chosen couplings; equivalence retains stated field/coordinate/reference object. Do not postulate physical access orP1selection from comparison."
    },
    {
      "id": "premise:pascal-carrier-exhaustion-equation",
      "titleEN": "Pascal exhaustion condition as input",
      "statementEN": "g is natural; the stipulated equation is 2^g=g^2+g+2. The equation itself is the additional carrier exhaustion rule."
    },
    {
      "id": "premise:specified-finite-carrier-discriminant-form",
      "titleEN": "Specified finite carrier discriminant form",
      "statementEN": "The model is El=Fin4 x Fin4 with componentwise addition modulo4 and qZ(x,y)=(5x^2+3y^2) mod8. Its identification with a concrete physical carrier is not inferred without premises."
    },
    {
      "id": "premise:specified-shared-s3-register-channel-family",
      "titleEN": "Specified shared S3 register family and homogeneous GKLS time",
      "statementEN": "The specified six native words u_g act in each register by the same S3 representation; shared event weights w(q)=(1/2+q/6,q/6,q/6,1/18-q/6,2/9-q/6,2/9-q/6), 0<=q<=1/3. Seek a consistent time-homogeneous GKLS semigroup on the same finite registers with unit time step."
    },
    {
      "id": "premise:specified-marked-m4-clifford-channel",
      "titleEN": "Fixed marked M4 Clifford channel",
      "statementEN": "Five specified Hermitian Gamma_j on M4 satisfy {Gamma_i,Gamma_j}=2delta_ij I. The endpoint is Phi=7id/12+sum_j Ad(Gamma_j)/12 with spectrum 1,1/3,2/3 on orthogonal blocks 1,5,10. Comparison class is any homogeneous GKSL generator on the same M4 with exp(L)=Phi^n for positive integer n."
    },
    {
      "id": "premise:original-stable-pointer-instrument-and-given-context",
      "titleEN": "Original conditional pointer template and supplied context",
      "statementEN": "Original text assumes A_obs subset A_rec and complete orthogonal pointers, then writes M_O(rho)=sum P_i rho P_i tensor |i><i|. Optional context Q supplies rho0, observables, time and readout. No identification with native Pq or physical P1 implementation is assumed."
    },
    {
      "id": "premise:same-full-positive-energy-separating-local-car-source",
      "titleEN": "Same full positive CAR source with locally separating sea",
      "statementEN": "Given negative-D quarter-CAR representation with full H_alpha=sum(n+alpha):a_n* a_n:>=0,H Omega=0 and support-preserving time covariance. Omega separates each larger proper-interval algebra. Test class: bounded proper-local A with A Omega an exact positive-energy eigenvector. NS/quarter chart retains support, reference and time; no physical P1 net identification follows."
    },
    {
      "id": "premise:charged-car-pure-two-face-cauchy-graph-state",
      "titleEN": "Given charged CAR quantization of the full two-face Cauchy graph",
      "statementEN": "As in section4 of the original collar proof, additionally assume charged CAR(H direct_sum H) and the pure gauge-invariant quasifree state with occupation G_ell. The second labeled face has n=(1+exp(2ell B))^-1. This is a field/statistics premise, not a consequence of P1; reduction does not select or physically execute a one-face operation. The long-collar limit is used only within this declared operator/CAR class."
    },
    {
      "id": "premise:complete-lagrangian-dirac-cauchy-car-quantization",
      "titleEN": "Complete Dirac Cauchy source with Lagrangian normal action",
      "statementEN": "Complete orthogonal Dirac Cauchy projection C on the entire boundary module, with actual normal unitary Clifford action N satisfying N C N*=I-C. Explicitly assume charged CAR quantization with pure quasifree covariance C. Bounded current generators X,Y commute with N and have Hilbert-Schmidt commutators with C. The existing compact product collar B=diag(A_alpha,-A_alpha) on both components and both faces is the concrete control; its smooth scalar boundary multipliers are implementable. Statistics and physical measure selection are not derived from P1; no automatic extension of the unrenormalized trace to higher boundary dimensions."
    },
    {
      "id": "premise:unchanged-quarter-qwz-full-excitation-source",
      "titleEN": "Unchanged full quarter-QWZ excitation source",
      "statementEN": "Current v1033 QWZ cylinder at mass1,width8,ONE complex CAR copy,alpha1/4 or3/4,full negative sea and H_N=N/(2pi)[dGamma(h_N)-Tr(P_Nh_N)]. Retain both edges,massive modes,charge sectors and physical energy/vacuum reference; compare actual low eigenmodes. No P1/P2 selection of this realization,changed stress or executed quotient."
    },
    {
      "id": "premise:given-d8-uniform-z4-twist-and-fixed-fold-time",
      "titleEN": "Given D8 target with uniform Z4 twists and fixed fold-time law",
      "statementEN": "Only in the conditional eight-channel target test,D8 currents with roots +/-e_i+/-e_j,twist charges q=(r/4)^8+m,m in Z8,r0..3,h=q²/2+N and existing fold time K=q²/2+delta.q+N,delta_k=(k+alpha)/8-1/2 are given. Keep all D8 currents and Cartan charges fixed,chiralities distinct. This creates neither eight physical source copies nor local defect endpoints from P1."
    },
    {
      "id": "premise:given-eightfold-source-odd-refielding-dictionary",
      "titleEN": "Given eightfold source fold with explicitly changed odd target action",
      "statementEN": "Given existing one-copy CAR source,sea,fold,p in Z8,Heisenberg oscillators,Q=sum p,H=8K,K=N+p²/2+delta.p with delta_k=(k+alpha)/8-1/2,and actual SOURCE windingT1=Rp+e0,alpha1/4or3/4. Test explicit Phi=I on D8,rho=Pp+r on odd v with oscillator-P to odd spinor extension. Odd target Cartan action is explicitly changed by this comparison; inclusion in the original local net is separate. Neither folding,SOURCE/P1-core circle identification nor bosonic statistics is derived from P1."
    },
    {
      "id": "premise:sharp-half-flux-original-net-state-contracts",
      "titleEN": "Sharp half flux in separate original net/state contracts",
      "statementEN": "Check separately under their own premises: v1033 with expressly ADDED M4 flux register,F_A=X² tensor(-1)^N_A,even algebra M4 tensor CAR+,common strip flux and uniform fixed zero-space filling; v746 with full CAR of paired window I union(I+N/2),NS-clockS^(N/2),halfcircle sign; direct chiral free limit as sharp-sign Bogoliubov on standard locally normal NS CAR net. No unproved identification of these nets and no exhaustion of smooth/renormalized outer-field limits. Even-to-full normality argument uses the standard free local factor contract."
    },
    {
      "id": "premise:local-register-retained-in-joint-charged-word-limit",
      "titleEN": "Local register retained in full charged word-limit contract",
      "statementEN": "Comparison class: original v1033 register grade2 under AdZ, Z retained as bounded even local unitary outside field support, full joint positive word limits with nonzero field norm. No boundedness of renormalized field sequence assumed. Separate two-edge test retains original shared flux ZL=ZR. Projection classification only when retaining the FULL original even matter algebra, time and A/A*-admissibility."
    },
    {
      "id": "premise:conditional-local-parity-gauss-completion-with-common-H",
      "titleEN": "Conditional local parity-Gauss completion with common original time",
      "statementEN": "ADDED comparison contract, NOT P1-derived: old four-state register with total-even matter; redundant Z2 link qubits and local Gx=(-1)^nx tau_(x-1)^x tau_x^x=1; gauge-invariant local observable net. Original QWZ hopping coefficients, common microscopic Hamiltonian and energy reference; no new electric energy. Sector-specific f(Z) subtractions must map to f(W) and can be nonlocal. No identification of Gauss space with original Padm."
    },
    {
      "id": "premise:fixed-one-copy-eightfold-connection-charge-dictionary",
      "titleEN": "Fixed charge-preserving connection in original one-copy eightfold",
      "statementEN": "Given one-copy fold has transition C(h), C(h)^8=hI. Available register half flux changes cover holonomy h to -h. Compare uniform spinor-OPE twist -C(h) in same complex U1 charge dictionary and connection, up to charge-preserving fiber conjugacy/periodic gauge transformation. Real SO16 charge conjugation at h=±i, changed connections/domains and eight independent copies lie outside exclusion class. Source circle/P1 core and cover/P1 deck are not identified."
    },
    {
      "id": "premise:original-neutral-eightpreimage-parity-pair",
      "titleEN": "Original neutral eight-preimage parity pair",
      "statementEN": "Actual v1033 menu F_A=X² tensor(-1)^N_A and products F_B F_A*, plus the ALREADY GIVEN one-copy eightfold dictionary eta_j(u)=psi((u+2pi j)/8)/sqrt8. E is union of all8 preimages E_I of a base interval. Register factors cancel; no added Gauss rule or copy. Fold, free chiral source and P1/core-circle interface are not newly derived premises. Finite filled Fourier band is separately declared regulator comparison with a second Fermi edge."
    },
    {
      "id": "premise:complete-vector-phase-word-Ward-comparison",
      "titleEN": "Complete vector phases with unchanged Cartan Ward action",
      "statementEN": "Only original complete Dirac/CAR Lagrangian source with normal-commuting implementable smooth profiles H_i h and fI, common analytic domains and regular Weyl representation. Target comparison retains same8 vector Cartan currents and mixed Ward words. Two grading components C,1-C on ONE face are neither strip edges nor collar faces. Finite complementary determinants are algebraic controls only; no unregulated infinite determinant or automatic QWZ/Dirac source identification."
    },
    {
      "id": "premise:smooth-unitary-pair-return-fixed-compact-source-time",
      "titleEN": "Smooth unitary pair return at fixed compact source time",
      "statementEN": "Given original chiral current/Weyl source, sea and K=Hcover/8 with delta_k=(k+alpha)/8-1/2. Periodic real phi(theta)=f(8theta), normalized UNITARY vector state W(phi)Omega; pi->0 return squeezed into base width eps on fixed source circle, same original energy reference. No assertion about general nonunitary sums, charged covariant representations, sector energy connections or decompactified time. Conditional Sugawara sector energy already fixed once lambda is given."
    },
    {
      "id": "premise:unchanged-full-source-observable-map-and-continuous-time-insertion-limit",
      "titleEN": "Full old observable map and continuous original time for nonunitary insertions",
      "statementEN": "Fixed full quarter-QWZ carrier has compatible entire finite-dimensional low spectral windows. Every retained bounded A_N is uniformly bounded and converges on them to the original operator action,including odd intermediate states. This is an operator premise independent of prepared v_N=T_N Omega_N. Arbitrary T_N,including divergent renormalization,nonunitarity and growing word degree,are required to have finite nonzero norm and a limiting ACTUAL original positive-time or real unitary-time kernel continuous at0 with that norm. No bounded first energy moment,different charged Hamiltonian or new P1 realization assumed. Spinor consequence additionally retains the given unchanged D8/even-CAR dictionary."
    },
    {
      "id": "premise:retained-local-register-with-one-common-original-vacuum-reference",
      "titleEN": "Retained local register with one common original vacuum reference",
      "statementEN": "Original v1033 Z4 register Z remains even local and remote from the proposed localized bosonic field. Initial sea has definite quarter r1or3. Full joint words retain norm of remote commutator[Z,T_N]Omega_N,required to vanish. Register Hamiltonian stays block diagonal in Z with ONE common initial-vacuum subtraction,no independently chosen sector energies. Keep actual mass1width8 Bloch matrix with both edges and all massive modes. No new Gauss support rule."
    },
    {
      "id": "premise:actual-neutral-pair-heat-filter-and-separate-chiral-Weyl-comparison",
      "titleEN": "Actual neutral pair heat filter and separate chiral Weyl comparison",
      "statementEN": "Diagnostic nonunitary attempt v_Ns=e^(-sH_N)P_E Omega_N with actual neutral eight-preimage parity pair and original full QWZ time/sea,s>0. No physical selection of this filter preparation claimed. Retain full Slater covariance,norm and time responses. Separately given chiral Weyl comparison usesK=H_cover/8,phi=f(8theta),Heisenberg oscillators; its sharp kernel is NOT identified with bare lattice parity limit without a separate proof. Joint Bloch-residue charges are not automatically separate chiral D8 Cartans."
    },
    {
      "id": "premise:given-holomorphic-kms-inclusion-and-local-global-modular-domains",
      "titleEN": "Given holomorphic KMS inclusion with distinct local/global domains",
      "statementEN": "Testing the cited abstract theorem assumes already existing holomorphic conformal c8netB,mu_B1,A=B^Z4,irreducible localindex4 andinternalgauge commutingwithrotations. omega_beta is DEFINED as Gibbs(B)restriction. Distinguish globalGNS KMSmodulargroup,L0rotations andlocalmodulargroups ofrestrictedfaithfulstates. These premises do not constructmicroscopicBfromP1; originalH_source=8(L0+delta.p) isnot silentlyidentifiedwithL0orphysicalbeta_angle2pi."
    },
    {
      "id": "premise:canonical-source-gibbs-and-parity-probe-with-retained-winding",
      "titleEN": "Canonical source Gibbs/parity probe with retained Cartans and source winding",
      "statementEN": "In existing conditional one-copy eightfold dictionary retain all8namedCartans,pinZ8,originalsea,H_source=8K,Q,globalPhi:D8+v→D8+c andactual SOURCE W1with[Q,W1]=W1. PrimitiveP1circle identification remains missing. CanonicalGibbs traces forEVERYbeta>0 are mathematicalfaithfulword/operator probes,not selectedphysicaltemperature. Retainbothoriginal limitingedges/parities; distinguishTOTAL-even andLEFT-even. No independent edgefluxregisters or microscopic pairedpumpfactorization asserted. ChangedphysicalCartan/netdictionary still needsderivation."
    },
    {
      "id": "premise:original-p1-seed-boundary-and-local-restriction-definitions",
      "titleEN": "Original P1, boundary, seed and local restriction definitions",
      "statementEN": "Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner."
    },
    {
      "id": "premise:marked-seam-pure-mathematical-program",
      "titleEN": "Active purely mathematical marked-seam program",
      "statementEN": "Within the stated mathematical scope, marked pairs, lattice transport systems, reflections, clocks and cohomology are independent mathematical objects. Earlier origin/completion tasks are historical, not active. Distinguish new definitions, derived theorems and optional markings."
    },
    {
      "id": "premise:native-even-e8-gaussian-clock-and-sign-extension",
      "titleEN": "Existing even E8 lattice, Gaussian J and sign lifts",
      "statementEN": "Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts."
    },
    {
      "id": "premise:ordered-four-punctures-fixed-quarter-projection",
      "titleEN": "Four ordered punctures with fixed quarter-clock projection",
      "statementEN": "X is CP1 minus ordered(1,i,-1,-i), positive meridians product1, fixed rho(gamma_i)=J. Classify all sign lifts into full preimage Gamma of<J>, modulo simultaneous Gamma conjugation with optional prescribed peripheral conjugacy classes. No mapping-class, puncture permutation or additional spatial reflection-equivariance quotient."
    },
    {
      "id": "premise:native-clock-complex-reflection-and-quartic-subspace",
      "titleEN": "Actual clock/complex-reflection subgroup and native quartic space",
      "statementEN": "R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power."
    },
    {
      "id": "premise:original-g31-central-determinant-extension",
      "titleEN": "Original G31reflections and central determinant class",
      "statementEN": "The60original reflections generate G31of order46080. Use exactly E=Z4xG31with determinant cocycle from original holonomy proof§4; distinguish E,effective diagonal quotient and noncentral lattice lifts. Mark z."
    },
    {
      "id": "premise:ordered-original-g31-reflection-and-clock-markings",
      "titleEN": "Ordered G31reflection quadruples and chosen quarterclock",
      "statementEN": "U=P1minusmu4, four ordered positive meridians in the60reflection class with product1. Chosen clocks have exact order4and conjugate meridians cyclically. Equivalence is simultaneous inner conjugation; central relaxations are separately defined relation contracts."
    },
    {
      "id": "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
      "titleEN": "Full original G31action and inherited lattice sign extension",
      "statementEN": "The60actual original complex reflections act on the same original even E8lattice. Study exactly their full preimage in the automorphism group of the lattice group defined by unchanged eps_e8. Kernel A=Hom(E8,Z2), with g.a=a composed g^-1. No scalar replacement, enlarged coefficients or extra square relation for lifted puncture meridians."
    },
    {
      "id": "premise:fixed-native-d5-a3-compiler-split-and-seed",
      "titleEN": "Original D5+A3 compiler split and established seed",
      "statementEN": "Retain the established P1/P2 compiler with cyclic C4 glue to E8, D5 on the first5 and A3=D3 on the last3 standard coordinates, c3=1/(8pi) and phi_base=(4/3)c3=1/(6pi). No replacement by an optional E7 readout. Cut equivalence is the actual W(D5)xW(A3) action in the fixed chart, without conjugating J."
    },
    {
      "id": "premise:existing-marked-cyclic-cover-and-burau-model",
      "titleEN": "Existing marked cyclic covers and Burau lattice model",
      "statementEN": "On B=P1 minus(mu4 union infinity), Cn:un^n=x^4-1 for n=2,3,4 are the existing marked covers with positive finite exponent1. Fix the mu3 deck orientation omega. Use the original J and sigma with c=J sigma, actual reduced Burau matrices at omega and their retained Z[omega]^3 basis and invariant Hermitian form. Do not identify this integral model and trace form with independently constructed geometric cycles or their intersection form."
    },
    {
      "id": "premise:joint-native-compiler-cover-covariance-category",
      "titleEN": "Joint category of original compiler flags and cover actions",
      "statementEN": "Retain original E8 lattice VOA products, J/sigma/c/Y, D5+A3 root factors and quartic/erasure diagram. Transitions transport all marks through actual lifts in the original sign extension; they are not fixed-J stabilizers. The Burau peripheral comparison uses the associated local system induced from the existing marked C3 cover and its retained deck module. No independent geometric Gauss-Manin identification, added line correction or selected E6 vertex."
    },
    {
      "id": "premise:marked-c4-unitary-local-extension-reconstruction-class",
      "titleEN": "Exact local reconstruction class of the marked C4 glue",
      "statementEN": "Mathematical object class Ext_H(U): U=V_D5 tensor V_A3 with fixed embedding and sector chart, H=<(s,f)>=C4. Objects are connected local unitary conformal VOA extensions with the same conformal vector and underlying labelled U module exactly the sum of M_h for h in H, each once. Isomorphisms fix U and sector labels. This is an explicit mathematical reconstruction class; membership of primitive P1 is neither assumed nor derived."
    },
    {
      "id": "premise:literal-boundary-minimality-and-first-order-domain-statements",
      "titleEN": "Literal boundary-minimality and analytic-perturbation statements",
      "statementEN": "Audit objects are the original boundary-source definitions and proofs: C_seed maps an operational seed forward to a spectral boundary tuple; defect order is lexicographic on N4; the self-adjointness statement asserts relative bound0 for every symmetric bounded-coefficient differential perturbation of order at most1. These source assertions are audited rather than assumed true. No special symbol cancellation, domain invariance or absolute scale is silently added."
    },
    {
      "id": "premise:connected-local-same-conformal-compiler-extension-with-generator",
      "titleEN": "Local conformal compiler extension containing one marked generator",
      "statementEN": "U=V_D5 tensor V_A3 has its fixed unitary conformal structure and marked discriminant chart. W is a connected local unitary VOA extension sharing its conformal vector and finite dimensional weight spaces; isomorphisms fix U. The marked module M_h for h=(1,1) occurs. Exact sector support, multiplicities, finite extension index, holomorphicity and an additional minimality rule are not assumed. Membership of primitive P1 in this realization is not claimed."
    },
    {
      "id": "premise:fixed-native-reflection-rotation-character-markings",
      "titleEN": "Fixed native spatial reflection and rotation markings",
      "statementEN": "In the original E8 sign lift stratum M_i=D_ci j, additionally mark T=D_t j^s t0 for s=0,1 and/or R=D_r j. T0 is the existing alternating sign isometry. Impose the stated peripheral equivariances and dihedral relation at s=0. Marked morphisms are simultaneous character conjugations with fixed projected operators. Forgetful images use full Gamma conjugacy. No arbitrary normalizer isometries or physical selection."
    },
    {
      "id": "premise:ordered-quarter-clock-pure-hurwitz-equivalence",
      "titleEN": "Pure Hurwitz quotient of the ordered quarter clock stratum",
      "statementEN": "In addition to original Gamma conjugacy identify ordered four J tuples by pure mapping classes generated by adjacent squared Hurwitz moves b0²,b1², with b_i(x,y)=(xyx^-1,x). No puncture permutations or silently frozen extra reflection marking."
    },
    {
      "id": "premise:standard-e8-root-cut-full-flag-incidence-category",
      "titleEN": "Regular E8 cuts and full compiler flags",
      "statementEN": "Fix the standard E8 roots with their actual Weyl action. E6 objects are complements of regular A2 root systems and E7 objects complements of root lines. A tetrahedron comprises the four A2 faces of a regular A3 normal system with common D5 core; its D8 incidence requires both factors. Relations are literal root inclusions and intersection sizes. Signals are rational, real or complex functions with counting inner product. Equivalence transports all flags by the Weyl action, without a selected corner or physical source."
    },
    {
      "id": "premise:scalar-eight-channel-twist-and-explicit-compiler-charge-chart",
      "titleEN": "Given scalar quarter twist and explicit charge chart",
      "statementEN": "Compare the given eight complex current channels, q=(1/4)^8, standard D5+D3 lattice and F=I5+T with T(x,y,z)=(x+y+z,x-y-z,-x+y-z,-x-y+z)/2. Eight channels and their normalization are not derived here from P1. Distinguish a local charged field, scalar monodromy character, flux register and native clock."
    },
    {
      "id": "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
      "titleEN": "Full unitary E8 field conjugacy with transported marks",
      "statementEN": "Start with the existing unitary E8 lattice VOA, original cocycle and actual chat,Jhat,sigmahat. Full inner unitary E8 automorphisms are allowed for this conjugacy comparison. Cartan, Gaussian V4, Y, P5 and other marks are transported rather than frozen. This category is explicitly larger than original sign lifts and implies neither a G31 splitting nor a preferred microscopic conjugator."
    },
    {
      "id": "premise:literal-microscopic-charged-scaling-and-v988-slater-data",
      "titleEN": "Literal charged scaling contract and original Slater case",
      "statementEN": "Audit actual H_N, Psi_lambda,N and bosonic refinement definitions in the original charged scaling contract and unchanged v988 qwz_cylinder/occ_frame functions at Nx16,Ny6,M1, h0 at twist0 and Slater state at twist1. This audits that source path and finite energy case, without assuming microscopic bosonization or a uniform continuum bound."
    },
    {
      "id": "premise:original-v988-periodic-zero-mode-state-comparison",
      "titleEN": "Actual periodic v988 state and occupied frame",
      "statementEN": "Keep unchanged qwz_cylinder, occ_frame and fermi_cov at Nx16 Ny6 M1 and original twists0,1,2,3. Compare their actual finite CAR covariances. Physical selection of either state or equality with the E8 vacuum is not assumed."
    },
    {
      "id": "premise:original-six-ovoid-covariant-instrument-category",
      "titleEN": "Finite instrument category of the actual six ovoid effects",
      "statementEN": "Fix the rank1 six-effect POVM transported equivariantly from the marked E8/J doily into the original quartic H5. Consider completely positive instruments from End(H5) to itself with exactly these effects and covariance under the actual60 generators. Physical selection of this measurement, an instrument, a preparation or a time unit is not assumed."
    },
    {
      "id": "premise:relational-native-quartic-tensor-sector-without-state-selection",
      "titleEN": "Relational quartic tensor sector without selected physical state",
      "statementEN": "Consider conjugate(H5) tensor H5 with the actual diagonal G31 action as a finite kinematic category. Keep its unique invariant vector ray, its multiple invariant densities and correlations conditional on a chosen singlet separate. Mathematical construction does not derive the microscopic presence or population of this sector."
    },
    {
      "id": "premise:native-tensor-povm-and-coherent-source-category",
      "titleEN": "Native tensor actions and covariant six-outcome observation",
      "statementEN": "Fix the original unitary G31 representation on V4, its ordinary complex tensor powers and the actual six-point action on E8/J ovoids. Consider all positive normalized operator families with this covariance. For the additional response identity x^tensor3 is a specified family of coherent probe inputs, not a physically derived or cloned preparation. Covariance does not select measurement contrast, an instrument, a physical time or a state."
    },
    {
      "id": "premise:original-quarter-car-fold-current-subalgebra",
      "titleEN": "Original quarter CAR source with fixed fold and current dictionary",
      "statementEN": "The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data."
    },
    {
      "id": "premise:original-microscopic-qwz-integer-car-edge-limit",
      "titleEN": "Existing microscopic one-channel CAR theorem",
      "statementEN": "Use the original width8/mass1/r1 QWZ strip, its negative spectral projector and filled state, its positive relative excitation Hamiltonian, actual local top-edge CAR fields and the proved field/adjoint/charge/time limit. Full orientation transport identifies this source with negative sea alpha1/4. Its identification with P1 is not supplied."
    },
    {
      "id": "premise:full-graded-car-with-original-positive-time",
      "titleEN": "Full CAR image and same positive vacuum time as a conditional hypothesis",
      "statementEN": "Conditional reduction: the FULL graded local CAR algebra including odd fields and adjoints belongs to the same OS vacuum representation; original time restricts to a(f)→a(exp(itK)f) for the same selfadjoint gapped one-particle K; H≥0 and HΩ=0. The P1 embedding/time identification is not established. Even CAR alone is insufficient."
    },
    {
      "id": "premise:original-seam-pair-and-full-moment-os-statements",
      "titleEN": "Original seam operators and explicit moment definition in the OS passage",
      "statementEN": "Source basis: the original boundary core supplies selfadjoint tangential B_Sigma; the seam has winding and stated spectral flow one. EM later names an allegedly selected rank-one line. QFT defines S_n^T as log-Z derivatives and uses them as the OS family. These statements and operator identifications are audited at the originals, not assumed proved."
    },
    {
      "id": "premise:strong-seam-covariance-and-same-pair-index",
      "titleEN": "Conditional strong seam covariance, gap and index of the same operator pair",
      "statementEN": "Conditional operator contract only: on the same original complex H, B is selfadjoint and u unitary; exp(itB)u exp(-itB)=exp(it)u for every real t, zero is outside sigma(B), and ind(P_B u P_B)=-1 with P_B=1_(0,infinity)(B). Actual exp(2 pi i B)=i I is an additional condition only for epsilon=1/4. These conditions are not derived from the reviewed original TFPT passages; P_C is not identified with P_B or a CAR covariance."
    },
    {
      "id": "premise:historical-original-circle-and-transfer-source-passages",
      "titleEN": "Historical concrete circle, heat-transfer and source-functional passages",
      "statementEN": "Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters."
    },
    {
      "id": "premise:given-quarter-circle-full-heat-transfer-comparison",
      "titleEN": "Original quarter circle and complete heat transfer as a scoped comparison class",
      "statementEN": "Mathematical comparison using existing original objects: B_a=-i partial_theta on twisted H1 f(2pi)=exp(2pi ia)f(0), a=1/4 or3/4; T_t=exp(-t|B_a|), R_t=exp(t/4)T_t. Ordinary Fredholm determinant, independent argument Q and given b=5/4. Twist is supplied rather than derived from winding. Identification with Ran(P_adm), the EM trace and q_EM=delta_top exp(-2alpha_EM) remains open; |B| heat is not automatically CAR or OS time."
    },
    {
      "id": "premise:historical-sf-sector-action-and-relative-normalization",
      "titleEN": "Historical SF sector action and explicit relative normalization",
      "statementEN": "fullv27/v28 set J1=SF,J=d SF,d2,SF1 in S_def(alpha)=S_def0+alpha J. Review concerns the intended defect-only relative reweighting and its extension to complete measure-compatible sectors Z_s=e^(-alpha d s)Z_s^0(alpha),Z0=Z0^0(alpha). Constancy of R=Z_s^0/Z0^0 is an explicit condition, not assumed from SF."
    },
    {
      "id": "premise:original-admissibility-and-graded-source-interfaces",
      "titleEN": "Original admissibility and graded-source interfaces",
      "statementEN": "v42 defines P_adm through primitive seam/Cauchy,gap,color and determinant conditions; v31 closure assumes an RP CAR kernel without identifying it with the old circle. v42 exp(W_k[J]) is a formal parent integral; spectral action, positive geometric marginal and full graded source are not equated. The separate eta term of the master functional is retained. Seek an original local image, not global Hilbert equivalence."
    },
    {
      "id": "premise:literal-positive-rg-map-on-finite-halfline-measures",
      "titleEN": "Printed positive RG kernel on finite half-line measures",
      "statementEN": "Literal archived theorem contract: nonzero finite positive nu on[0,infty),0<∫psi dnu<infty and Tnu(dt)=(∫K(s,t)dnu/∫psi dnu)dt with0<m<=K(s,t)<=M on the entire infinite Lebesgue target half-line. No extra compact support,finite target reference or integrable envelope is introduced."
    },
    {
      "id": "premise:original-a4-same-moebius-order-four-pin-lift",
      "titleEN": "Original A4 lift of the same Moebius identification",
      "statementEN": "The order-four spin lift explicitly named by fullv21 A4 belongs to the same geometric Moebius Z2 identification. As a Pin lift it has r²=-I; the local spin-reference channel is examined. Extra flat U1 connection holonomy and physical OS time are not inferred."
    },
    {
      "id": "premise:fixed-marked-glue-and-retained-source-d8-frame",
      "titleEN": "Fixed marked glue and actual source D8 frame",
      "statementEN": "Retain marked K=D5+A3 in E8 with E8/K=Z4, original O frame and existing M of the one-channel CAR fold. The actual even source frame is D8_F=M(D8_CAR); no fitted new Weyl rotation. Cartans,time vector d=Mdelta,cocycles and field words transport together."
    },
    {
      "id": "premise:standard-four-d8-module-parent-with-retained-subtheories",
      "titleEN": "Standard four-module parent with supplied CAR and E8 subtheories",
      "statementEN": "For the mathematical bridge use the standard four-module AIA over D8*/D8={0,v,s,c} with its supplied CAR 0+v and E8 0+s cocycle restrictions. NS space,actual R8 source winding and quarter time are the existing data. Ramond completion and global spin-surface/gauging functor are not assumed physically derived from P1. Transport of a complete common intertwiner basis is allowed; an independently marked mixed junction would be stronger input."
    },
    {
      "id": "premise:same-original-circle-trace-class-covariance",
      "titleEN": "Same original circle with trace-class changed polarization",
      "statementEN": "For the mathematical continuation retain H,B_a psi_n=(n+a)psi_n,0<a<1,u psi_n=psi_(n+1),P=1_(B_a<0),uPu*=P+Pi. C is a positive contraction with trace-class C-P; actual functional-calculus C_beta=(I+exp(beta B_a))^-1,beta>0 belongs to this class. Physical KMS/OS/EM source identification is not presumed."
    },
    {
      "id": "premise:existing-finite-orthogonal-carrier-on-same-source",
      "titleEN": "Supplied finite orthogonal carrier on the same source space",
      "statementEN": "In the carrier-transport theorem F is an actually supplied finite-rank orthogonal projection on the same circle H,Q=I-F. Physical application additionally needs the original map into active seam space and carrier isometry. A finite internal index retaining infinitely many spacetime modes is not this finite rank. No freely chosen F establishes origin."
    },
    {
      "id": "premise:trace-class-polarization-pair-with-restricted-unitary",
      "titleEN": "Trace-class polarization pair with actual unitary action",
      "statementEN": "P,Q are orthogonal projections on the same H,Q-P in L1. The covariance theorem additionally assumes Q=UPU*,U unitary,0<=C<=I,C-P in L1. The theorem is on this common space; physical source membership is not inferred from index alone."
    },
    {
      "id": "premise:smooth-matrix-clutch-on-original-negative-fourier-sea",
      "titleEN": "Smooth matrix clutch on original negative Fourier sea",
      "statementEN": "H=L2(S1,C^r),P=1_(n<0) tensor I_r and U=M_g for smooth g:S1→U(r). The existing bosonic branch has c1(det E2)=1,c1(det E3)=0 on the normal S2. A common physical identification of that clutch equator with the tangential source circle,C_Sigma and response is an additional map to prove."
    },
    {
      "id": "premise:actual-finite-ns-kernel-and-sampled-original-winding",
      "titleEN": "Actual finite NS kernel and sampled original winding",
      "statementEN": "Comparison uses the unchanged free NS kernel in v519/v524/v526 and sampling of original u=M_z on N=2M circle sites. Fourier modes n=-M,...,M-1 are cyclic. No UV contribution is removed and no ordinary finite determinant is declared an already renormalized continuum determinant."
    },
    {
      "id": "premise:given-normal-spin-line-and-genuine-circle-product",
      "titleEN": "Given normal spin line and genuine circle product operator",
      "statementEN": "Assume oriented spin S2,L2=det E2=O(1),normal twisted spin operator D_N with grading gamma_N and actual selfadjoint product B_prod=B_a tensor gamma_N+I tensor D_N on H1 product spinors,B_a=-i partial_theta+a,0<a<1. Normal metric,connection and horizontal product rule are given;no derivation from the original bosonic Callias operator or P1 is asserted."
    },
    {
      "id": "premise:given-exact-reducing-indexline-with-horizontal-connection",
      "titleEN": "Given exactly reducing index line with horizontal connection",
      "statementEN": "The normal kernel line exactly reduces the actual full operator and carries B_A=-i partial_theta+A(theta),A real smooth periodic,Dom=H1_per,at fixed circle time unit. Comparison preserves u=M_z using smooth periodic multipliers. Exact reduction is assumed,not inferred from an adiabatic approximation."
    },
    {
      "id": "premise:positive-determinant-response-of-transverse-product-channels",
      "titleEN": "Positive determinant response of given transverse product channels",
      "statementEN": "Compare positive scalar circle operators A_(a,lambda)=(-i partial_theta+a)^2+lambda^2,lambda>0,with common relative zeta normalization. a denotes spectral holonomy,not electromagnetic alpha. Actual two-dimensional block multiplicity is retained;separate infinite zeta factors require their own gluing/anomaly proof."
    },
    {
      "id": "premise:closed-normal-fredholm-with-retained-complex-kernel-representation",
      "titleEN": "Closed normal Fredholm operator with retained complex kernel representation",
      "statementEN": "Given densely defined closed Fredholm A:Dom(A) subset H_+ -> H_-,its true adjoint A*,finite complex kernel M of dimension r,and ker A*=0. Genuine product is B_a tensor gamma+I tensor [[0,A*],[A,0]] on its full Fourier intersection domain. Reduced-circle comparison uses P=1_(B_a<0) tensor I_M,U=M_z tensor I_M,C-P in L1,0<=C<=I,|z|<1. If M is an SU2 doublet retained at fixed operator,r=2;one doublet multiplicity is not substituted as r=1. Provenance,statistics and full physical source role are not assumed."
    },
    {
      "id": "premise:smooth-matrix-circle-source-and-moving-projector-with-fixed-scalar-symbol",
      "titleEN": "Smooth matrix circle source and moving projector at fixed scalar principal symbol",
      "statementEN": "Given comparison class:H=L2(S1,C^r),B_A=-i partial_theta+A(theta),Dom=H1_per,A smooth periodic Hermitian,P(theta) smooth periodic orthogonal of fixed rank. P is a fiber family,not an executed measurement. Neither P nor A is selected from P1. A real normal operator family additionally needs its own common domains and field map."
    },
    {
      "id": "premise:oriented-d3-tetrahedron-in-bloch-chart-versus-original-quarter-marks",
      "titleEN": "Oriented internal D3 tetrahedron in Bloch chart versus original quarter marks",
      "statementEN": "Compare T={(+++),(+--),(-+-),(--+)}/sqrt3 from the existing chiral (16,4) block,p(n)=(I+n.sigma)/2,z(n)=(nx+i ny)/(1+nz),and original ordered quartet(1,i,-1,-i). Equivalence is a biholomorphic Mobius map,even allowing arbitrary relabeling. Internal D3 direction sphere,physical normal S2 and tangential source curve are not identified. Bloch projectors are not the orthogonal E6 root-block projectors."
    },
    {
      "id": "premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images",
      "titleEN": "Existing marked cyclic cover tower and compact elliptic images",
      "statementEN": "Use only existing C_n:u_n^n=x^4-1 with fixed x base,deck Delta_n and already forced compiler clock R12=Q12 Delta12^4=(ix,omega s),Q12=(ix,s). Compare compact algebraic curves over C and pullback function fields. A comparison of punctured local systems must retain its removed points,peripheral loops,spin and field transports."
    },
    {
      "id": "premise:natural-joint-spin-family-lift-with-given-split-connection",
      "titleEN": "Existing natural joint lift with given split connection",
      "statementEN": "Assume a GIVEN unitary E=E3+E2 and GIVEN block U3xU2 connection A_E. Use only the natural iota_m with sum m=-2 completely classified on22September and their derived connection A_Wm=rho_LambdaEven(A_E)+M_m tr A_E. This does not select A_E from P1;an independent nonabelian family connection is not silently assumed."
    },
    {
      "id": "premise:fixed-kappa-toral-third-centralizing-split-carrier",
      "titleEN": "Fixed glue quarter and toral thirds centralizing the carrier split",
      "statementEN": "Fix the standard E8 Cartan,five plus three chart,three color and two weak indices and four family axes. Kappa=exp(2pi i v0),v0=(1/2^5,0^3). Study every sigma=exp(2pi i b/3),b in E8/3E8,centralizing the given U3xU2,and c=kappa sigma. This is a specified toral class of vertical bundle automorphisms,not an assumption about physical time or original base transport."
    },
    {
      "id": "premise:same-angle-evaluation-of-primitive-determinant-clutch-as-native-clock",
      "titleEN": "Additional direct-angle identification of determinant clutch with native clock",
      "statementEN": "Only for the diagnostic comparison evaluate a supplied diagonal integer loop k,sum k=1 and m,sum m=-2 as h=(k,-v_m) at the same angles:Q=exp(pi i ad h/2),C=exp(-2pi i ad h/12),C^9=Q. Pure weak k=(0,0,0,1,0);larger weak toral class k=(0,0,0,a,1-a). A transition is not connection holonomy or derived physical time."
    },
    {
      "id": "premise:native-cartan-four-in-full-clock-conjugate-source",
      "titleEN": "Native Cartan four in whole conjugated source",
      "statementEN": "Given original Cartan h_C,H+=ker(J-i),and whole native clock chat with chat^9=Jhat,chat^4=sigmahat. Existing inner conjugacy transports the entire tuple and Cartan to kappa. H+ is not identified with SU4 family factor. In current W_m orientation,+i64 is its dual branch. No preferred conjugator is selected."
    },
    {
      "id": "premise:primitive-normal-sphere-joint-k-bundle-class-two",
      "titleEN": "Old joint class2 bundle on the same normal sphere",
      "statementEN": "Given natural lift iota_m,sum m=-2,acts over the old common normal S2 with(c1(E3),c1(E2))=(0,1). For every m,its K=(Spin10 x SU4)/Z4 principal bundle has class2 in pi1(K)=Z4. Proposed choice is an everywhere smooth whole Cartan subspace in its fixed kappa sector. No identity with separate punctured flavor base is assumed."
    },
    {
      "id": "premise:given-same-normal-base-degree-pullback",
      "titleEN": "Actual degree pullback to precisely the same normal base",
      "statementEN": "Conditional cover connection assumes an actual degreeq map f:Sigma to S2 from a closed oriented surface,pulling back exactly the joint K bundle. Connection statement assumes a smooth branched cover. Existing C2,C6,C12 qualify only after proving identity of base and bundle map."
    },
    {
      "id": "premise:declared-original-octic-quantum-completion-ansatz",
      "titleEN": "Fixed octic completion in the existing current space",
      "statementEN": "In the supplied positive c8 current space,seek W8 only in the declared17 dimensional space:H8=sum_roots(alpha.h_-1)^8-30Q11^4 and the16 weight8 Q_ab monomials. H8 leading coefficient is1;root zero mode and L1=L2 must vanish. This specifies a mathematical existence ansatz,not an extra physical source or preparation rule. Uniqueness beyond this space is not assumed."
    },
    {
      "id": "premise:existing-elliptic-curve-with-specified-normal-spin-factor",
      "titleEN": "Existing elliptic curve with a specified normal spin factor",
      "statementEN": "On the actually existing E:y²=x⁴-1 with p=x,delta:(x,y)->(x,-y),q:(x,y)->(ix,y),compare normal spin Dirac operators twisted by p*O1. In the q-fixed nontrivial spin alpha=O(T-O),O=(0,i),T=(0,-i),transport the two-dimensional holomorphic kernel with genuine spin lifts. No identity of this curve base with the original normal base or of delta with the Calderon reflector is assumed."
    },
    {
      "id": "premise:existing-cut-cover-car-with-actual-winding-and-sea",
      "titleEN": "Existing full cut-cover CAR source with actual winding and sea",
      "statementEN": "The already constructed NS double-cover source Hcov=W0K⊕W1K is given, with common negative sea m<0 and original winding U=[[0,u_base],[I,0]], u_base e_m=e_(m+1). Quarter stress fields retain their original CAR coefficients and Wick ordering. Base intervals carry two cover preimages. This assumes the mathematical source realization and does not derive its physical P1 field map or descent into a fixed Pin collar domain."
    },
    {
      "id": "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
      "titleEN": "Given flat Moebius Dirac boundary family and its full sea",
      "statementEN": "The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances."
    },
    {
      "id": "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover",
      "titleEN": "Given free Green quantization of the flat Pin Dirac operator on its NS cover",
      "statementEN": "Given is the free charged Gaussian field realization with the Green operator of the concrete flat Dirac boundary family D=−i(sigma1 partial_x+sigma2 partial_w),w in[-1,1],sigma1 psi at boundary=b psi,b=±1. Original Pinminus c=±i forces psi(x+2,w)=−psi(x,w) on the orientation cover. The tested Euclidean kernel belongs to L=i sigma1 D=partial_x+H,H=i sigma3 partial_w. This Green quantization and x as Euclidean time are named premises,not identified with the D spectral sea,the old quarter Hardy state or original P1 kernel."
    },
    {
      "id": "premise:declared-recursive-native-som-update",
      "titleEN": "Explicitly chosen recursive SOM rule on60 native signal cells",
      "statementEN": "Given solely for the authorized model study is the60x35 complex update of RECURSIVE-SOM-AUDIT.txt section1,with native K60,fixed neighbors,row normalization,Euclidean winners,batch means and chosen c,beta,eta. The code basis is readout only. This update and its initial alignment are not primitive TFPT laws."
    },
    {
      "id": "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
      "titleEN": "Existing C2 group with untwisted raw flat spin pullbacks",
      "statementEN": "On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed."
    },
    {
      "id": "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
      "titleEN": "Free chiral Cauchy quantization of the canonical elliptic annulus",
      "statementEN": "Treat the dividing half of the given square curve in its canonical flat conformal representative as a product collar. Compute the Cauchy graph of Dplus=partial_t+B_Sigma,B_Sigma=−i partial_s with NS boundary,then interpret it using the expressly free chiral CAR construction as a quasifree two-boundary state. The labelled second-face compression is the covariance;the other is complementary. This Gaussian interpretation does not derive the original relative spectral-action measure,P1 time or EM/Quillen response."
    },
    {
      "id": "premise:original-eight-arc-additive-density-stress-restriction",
      "titleEN": "Additive scalar density and stress algebra on eight original arcs",
      "statementEN": "The restricted insertion candidate is the additive original scalar density/stress subnet on eight proper arcs with disjoint closures. Full neutral interarc CAR products are not automatically included."
    },
    {
      "id": "premise:given-pin-source-conformal-normal-geometry-probes",
      "titleEN": "Controlled conformal normal geometry of the given Pin Dirac source",
      "statementEN": "For the authorized source study,the same given Dirac comparison D0 on its fixed(c,b)Pin/boundary domain is varied by smooth real even profiles h:g_e=exp(2e h)g0,D_e=exp(-e h/2)D0 exp(-e h/2)after unitary density transport. Profiles/amplitude are explicitly chosen diagnostic interventions,not a P1-selected history. Original pure D0 sea remains initial state;thermal Green quantization stays separate."
    },
    {
      "id": "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
      "titleEN": "Original full four-mark inversion and distinct equatorial Real slots",
      "statementEN": "The supplied marked base has x->ix and the inversion x->1/x already present in v512. Compare their actual lift to E:y²=x⁴−1,retaining the original four-marked base circle Gamma=|x|1. v510/v519 distinguish pointwise equatorial x->1/bar x from the OS family x->mu bar x acting along Gamma. These operations must not be identified in a source comparison. The old free carrier is named;no general physical P1 equality is presumed."
    },
    {
      "id": "premise:original-p2-order-three-cusp-and-stable-anchor-target",
      "titleEN": "Original P2 order-three cusp class and stable bundle anchor",
      "statementEN": "Target the original P2 Deligne class with cusp weights0,1/3,2/3 and holomorphic anchor O(-2)+O(-1)^2. Exact v117 M0_EXACT has polynomiallambda³−1,trace0,order3;its joint representation with U is irreducible. Keep these exact matrix properties distinct from the numerical ODE identification there. Test whether the natural scalar/spin pushforward of existing C2 realizes this actual connection;physical selection of the direct sum as flavor module is not presumed."
    },
    {
      "id": "premise:primitive-reflection-split-and-controlled-geometric-variation",
      "titleEN": "Original reflection split with declared geometry variation",
      "statementEN": "Original pair A=(D+RDR)/2,B=(D-RDR)/2 on a declared common domain with fixed R and density-transport variation deltaD=-{h,D}/2. Trace identities hold finitely or under an actually proved differentiable relative-trace contract. Moving chi,mu,R,eta and domains remain separate. Geometric admissibility is not inferred."
    },
    {
      "id": "premise:finite-positive-heat-channel-endpoint-selection-test",
      "titleEN": "Finite data test of positive heat-channel values",
      "statementEN": "Algebraic test on C2:R=diag(1,-1),A=2I,B=sigma_x,D=A+B,chi1,common scaleD(s)=exp(-s)D and fixed eta phase. Compare normalized positive finite heat measures with identical endpoint operator values for a necessary data sufficiency test. Neither is asserted to be P1 or the same fully geometry-dependent transfer channel."
    },
    {
      "id": "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
      "titleEN": "Ramified holomorphic half-form trace of the given C2 spin line",
      "statementEN": "Retain actual E:y²=x⁴−1, its already supplied Q fixed nontrivial NS NS spin-line class alpha and normalized Szego kernel. Holomorphic trace includes sqrt(dz/dx), while ordinary flat coefficient p_*alpha remains separate. No extra Q linearization phase, positive equal-time CAR covariance or smooth circle domain is assumed."
    },
    {
      "id": "premise:theta-square-modular-transport-with-distinct-geometric-clock",
      "titleEN": "Theta-square modular action with distinct geometric Q",
      "statementEN": "Test standard S/T action on three theta squares as a representation of a marked elliptic family, retaining weight and central phases. Geometric Q:z->iz at fixed tau=i is the S homology change, not an already supplied T moduli path. Do not assume this family action has the same origin as spatial monodromy of fixed four-punctured P2."
    },
    {
      "id": "premise:fixed-three-slot-permutation-and-original-compiler-comparison",
      "titleEN": "Fixed three-slot permutation and original compiler comparison",
      "statementEN": "Test the explicitly proposed fixed three-slot P_nat candidate from v417 against the P_* pullback of the v117 pair in the existing September dictionary. Q or G remain fixed on the same named comparison carrier. This coordinate identification is the tested ansatz, not an established physical identification of all native E8 representations or clock carriers."
    },
    {
      "id": "premise:same-marked-elliptic-annulus-massless-conformal-metric-family",
      "titleEN": "Conformal metric family of the same marked massless annulus",
      "statementEN": "Study the existing smooth midpoint-annulus source on the same complex square curve with fixed spin, cut and face markings and massless geometric chiral Dirac operator. g_sigma=exp(2sigma)g for arbitrary smooth real sigma, with canonical spin lift and bulk/boundary L2 transport derived from volume densities. On the fixed complex curve this includes all Hermitian metrics. Connection, mass and complex structure do not vary. An unchanged original reflection/clock requires invariant profiles; otherwise transport the symmetry as well. No identification with the unresolved full marked equator graph, primitive P1 measure or physical time. The averaging lemma expressly retains the given free conditional CAR quantization, source-independent integrable total weights and nonzero normalization."
    },
    {
      "id": "premise:retained-zero-branch-defect-on-common-pin-geometric-history",
      "titleEN": "Retained zero-branch defect on a common Pin geometry history",
      "statementEN": "The original normal-zero branch k=pi/2,b1,c+i carries the retained positive quarter defect Pi. Compare the given pure D0 sea C0 and C0+Pi,both evolved by the same D_s=exp(-s h/2)D0 exp(-s h/2). The profile and tested step/pulse histories are named diagnostic inputs. Relative geometry response is Tr(U Pi U* partial_sD_s). It is not defined into the primitive P1 action response or a thin local seam map."
    },
    {
      "id": "premise:positive-joint-car-source-tested-against-full-geometric-projector",
      "titleEN": "Test a positive joint CAR source against the full geometric projection",
      "statementEN": "Consider an arbitrary normalized positive state on the specified joint charged two-face CAR algebra,without assuming quasifreeness or U1 invariance. The geometric target is the existing closed chiral annulus graph P_A with both marked faces,W=1/2 and original NS B_Sigma. Actual identity C_source=P_A is an explicit condition of the uniqueness theorem and an unresolved P1 source equation,not a fact inferred from geometry or RP. A finite error test applies only on a genuinely P_A reducing CAR block. Complete Dirac vector source,OS Padm and physical time are not identified with this chiral scalar target. No freely chosen purification supplies missing physical cross correlations."
    },
    {
      "id": "premise:real-marked-elliptic-complex-structure-family-with-transported-spin",
      "titleEN": "Explicitly changed marked elliptic modulus family with transported spin",
      "statementEN": "Consider E_rho:y²=x⁴+i rho x²−1 for real |rho|<2 with the continued original nontrivial spin partition,both original dividing real structures and free Moebius glide. Expressly continue free chiral Cauchy quantization on the two-face annulus normalized by its primitive A cycle. Q and the original inversion act between rho and minus rho fibers;their original fixed-fiber action is expressly relaxed. The mixing formula conditionally assumes an arbitrary positive normalized source-independent law on this new family. Neither admission in the fixed C2 compiler nor P1 measure support,variance,full marked graph domain,physical time or an interacting source is derived."
    },
    {
      "id": "premise:actual-elliptic-half-form-l2-trace-on-full-marked-equator",
      "titleEN": "Actual L2 half-form trace on full marked equator",
      "statementEN": "Retain supplied square elliptic curve, flat metric and NS spin line. On the full ramified equator sqrt(dz/dx) transports actual L2 norm to |dx|. Keep holomorphic kernel, orthogonal analytic range, positive CAR covariance and H1 vertex domain distinct. No new channel metric or free vertex condition."
    },
    {
      "id": "premise:genuine-d4-unitary-stable-parabolic-orbifold-descent",
      "titleEN": "Genuine stable unitary D4 orbifold descent",
      "statementEN": "The expressly specified stable determinant-trivial parabolic rank3 branch has genuine mark-preserving D4 linearization with Coxeter fiber c=diag(1,i,-i) and regular cubic meridian M=a². Apply Mehta Seshadri to this object. Do NOT identify the concrete A0* ODE with it merely from C4 rotation."
    },
    {
      "id": "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
      "titleEN": "Unchanged A0* Fuchsian equation and actual C4 clock",
      "statementEN": "Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed."
    },
    {
      "id": "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
      "titleEN": "Recovered genus2 cover with retained coefficients",
      "statementEN": "Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner."
    },
    {
      "id": "premise:given-square-nsns-elliptic-unit-charge-flat-connection-family",
      "titleEN": "Given elliptic NS source with an explicit unit-charge flat unitary probe",
      "statementEN": "On existing E=C/(Z+iZ) with original nontrivial NS/NS spin line and fixed H1_NSNS domain,calculate K_z=(-i partial_x+2pi v)+i(-i partial_y+2pi u),z=v+iu,as an explicit unit-charge probe. L_z=K_z*K_z,referencez0,gauge-periodic descent and positive theta-line convention are specified. Complex structure stays fixed;Q acts covariantly on external connection sources. This defines neither primitive P1 measure,physical hypercharge embedding,positive KMS state for every temporal twist,v472 Berry comparison map,nor z(alpha_EM). Parameter curvature and flat spacetime connection remain distinct."
    },
    {
      "id": "premise:normal-even-sea-car-source-and-canonical-graded-hs-double",
      "titleEN": "Normal even sea CAR source with canonical graded HS doubling",
      "statementEN": "For the algebraic source test use the already given sea Fock/CAR carrier,with faithful even normalized traceclass density rho and its standard HS space,Omega=sqrt(rho),L_A X=AX,R_A X=XA,Gamma X=Pi X Pi. Gamma is the canonical GNS implementer of source parity fixing Omega. Partner fields are represented in the fixed mode-index chart by b_j=−Gamma R_aj;this assumes no physical second P1 boundary. The finite saturation theorem covers arbitrary faithful even finite densities;the separate all-mode route requires the actual normal HS carrier,a complete covariance eigenbasis and saturation in every mode. For the free elliptic connection,rho is the already derived original thermal density,not a newly chosen geometry or temperature. TomitaJ,OSTheta,classical doubling and physical time remain distinct until actually mapped."
    },
    {
      "id": "premise:marked-e8-regularized-charged-grade-response",
      "titleEN": "Marked regularized E8 charged state and sector-grade response",
      "statementEN": "Existing positive E8_1 lattice vacuum source with original D5/A3 marking and 48 retained charges beta: beta^t P5 beta=5/4, beta^t P3 beta=3/4, beta²=2. The regularized charged vertex state has free preparation parameter u=r² in (0,1). N5,N3 are strongly commuting nonnegative oscillator grades; q5,q3 in [0,1] parametrize spectral readout. Keep original C/J matrices. u=48c3^4, q=exp(-2alpha), physical preparation, instrument and common time do not follow."
    },
    {
      "id": "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
      "titleEN": "Native Pauli translations and frozen Gaussian phase class",
      "statementEN": "Native theta-translation target is P_nat=N64/mu4 from v783 in frozen four-component frame,with actual sigma and J=iI. Code quotient L/(1+i)L is the distinct duality-twisted context module. G31 has center mu4;full Clifford matrix group has center mu8 and additional coset zeta8 G31. Retain these concrete actions and phases."
    },
    {
      "id": "premise:ordinary-rigidified-genus-two-theta-determinant-functor",
      "titleEN": "Ordinary rigidified theta determinant functor",
      "statementEN": "A=Jac(C), E_L=S0 tensor L of degree1 on genus2. D_L=det H0(E_L) tensor det H1(E_L)^(-1),or dual convention;Poincare family rigidified at marked q0. Then O(2Theta) and four holomorphic sections with standard symmetric linearization. No additional Pfaffian,metaplectic factor,or marked-point determinant."
    },
    {
      "id": "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
      "titleEN": "Relative spin and reference Hardy cable on original three-cover",
      "statementEN": "Compare holomorphic Hardy shifts M_z on S0 tensor L and the same degree-zero coefficient line L over the original pi:C→P1_z. Spin half-forms give boundary norm; Fredholm convention is det kernel tensor inverse det cokernel. Relative line is spin line tensor inverse reference line. This defines a mathematical sewing contract, not an established identification with physical D_rel/D_ref or state."
    },
    {
      "id": "premise:same-spin-hardy-shift-against-identity-with-grading-retained",
      "titleEN": "Seam shift versus identity on same spin space retaining grading",
      "statementEN": "On original three-cover use E=S0 tensor P_spin with proved equivariant Nm_Dq(P_spin)=O. Compare M_z with M_1 on same half-form Hardy space in det kernel tensor inverse det cokernel convention, retaining determinant parity. Native complex module leaves global alpha sign free. This is a mathematical realization, not an assumed physical Cauchy/Calderon identity."
    },
    {
      "id": "premise:standard-chiral-spin-trace-on-original-cubic-disk-pullback",
      "titleEN": "Massless spin trace on original cubic disk pullback",
      "statementEN": "Exactly C:eta²=1-w⁶, z=eta/(1-w³), S0 with S0²=K and H0(S0)=0. Conditionally consider the massless chiral spin operator on three normalized disk components and the compatible smooth ambient trace with half-form boundary norm integral|psi²|. Strong operator closure is not replaced by L2 range. No identification with the actual P1 operator is assumed."
    },
    {
      "id": "premise:conditional-three-sheet-negative-sea-car-source",
      "titleEN": "Three-sheet CAR source retaining negative-sea orientation",
      "statementEN": "On the given full half-form boundary space let PH be the threefold Hardy projection,C=I-PH the occupation covariance of a normalized positive charged CAR state,and U=M_z the ambient unitary. V=ran(PH-U PH U*) is the given three-dimensional q defect with existing c,Q,beta fiber markings. This explicitly conditional source retains old negative sea and positive winding. It asserts no P1 origin,physical time or freely chosen identification with the elliptic source."
    },
    {
      "id": "premise:marked-theta-frame-with-explicit-primitive-gaussian-root-normalization",
      "titleEN": "Completed theta frame with explicit primitive Gaussian integral normalization",
      "statementEN": "Start with completed Wq=H0(Jac(C),O(2Theta)) tensor Nq^-1, beta=i, fixed Schrodinger frame e_x for x in F2², a unit norm-line trivialization and actual alpha=zeta8 V. The same-spin representative also retains odd B_O^-1 and its alpha sign. For affine d planes A and stabilizer phases phi in mu4 explicitly choose r(A,phi)=(1+i)^(2-d) sum(phi(x)e_x)/sqrt2. Gaussian integer numerators,norm squared2 and the central i orbit are the arithmetic construction. This is not deduced from complex dimensions and does not assert P1 selection,physical length normalization or uniqueness among all Heisenberg-stable lattices."
    },
    {
      "id": "premise:two-theta-lattice-voas-with-given-geometric-faithful-c12-lift",
      "titleEN": "Two theta lattice VOAs with a given faithful geometric C12 lift",
      "statementEN": "Lattices Lambda0 and Lambda1=zeta8 Lambda0 come from the explicitly normalized theta construction. Use their unitary lattice VOAs with standard cocycle. On object0 the existing faithful C12 lift c0 with geometric action i sigma is given; beta0=c0^9 lifts i and sigma0=c0^4 lifts sigma. T is any standard-cocycle VOA isomorphism lifting actual lattice isometry alpha01=zeta8 V. Branch-one marks are transported. No T²=1,[T,beta0]=1,full G31 splitting,common local VOA or physical P1 identification is assumed."
    },
    {
      "id": "premise:connected-local-same-conformal-compiler-extension-unselected-support",
      "titleEN": "Local conformal compiler extension without preselected sector support",
      "statementEN": "U=V_D5 tensor V_A3 carries its fixed unitary conformal structure and marked discriminant chart C4² with q(a,b)=(5a²+3b²)/8. W is a connected local unitary VOA extension with the same conformal vector and finite-dimensional weight spaces. No M_(1,1), exact support or holomorphy is assumed. Existing classification yields U,D8,E8plus,E8minus. Modular S is the finite discriminant Fourier after the common Jacobi factor and correct background transport. This is a mathematical class, not asserted membership of original P1."
    },
    {
      "id": "premise:four-d8-sectors-with-fixed-affine-source-time",
      "titleEN": "Four D8 source modules with fixed affine time",
      "statementEN": "Mathematical parent of the four D8*/D8 modules 0,v,s,c with eight identical Heisenberg oscillators, source charge chart p and N≥0. H=8(N+|p|²/2+delta.p),delta_j=(j+a)/8−1/2,0<a<1,Q=sum p_j. Original quarter cases are a1/4,3/4. Conformal L0, individual Cartan charges and totalQ remain distinct. This mathematical completion does not assume a physical P1 realization of the Ramond space or a local field map."
    },
    {
      "id": "premise:marked-local-e8-completion-with-original-source-time-and-euclidean-clustering",
      "titleEN": "Joint marked local E8 completion with original time and Euclidean clustering",
      "statementEN": "Joint candidate C1 to C4 of LOCAL-TIME-COMPATIBILITY: fixed D8 current net, local even unimodular lattice extension on the same eight Cartan channels, original Omega and H=8(L0+delta.a0) as positive Euclidean clustering transfer, retained q twice-root marking, all E8 currents included as admissible local observables, clustering of all bounded local two-point functions. This is the precise candidate class being tested, not asserted joint consequence of P1. Sector-penalty addendum retains the same irreducible multiplicity-free finite-index Z2 net, D8 action, interval motion and vacuum representation."
    },
    {
      "id": "premise:specified-petersen-shell-and-full-family-finite-recursions",
      "titleEN": "Specified Petersen shells and full finite family recursion",
      "statementEN": "v808: ten two-element subsets of five marked slots, disjointness adjacency and radial P=[[0,1,0],[1/3,0,2/3],[0,1/3,2/3]] on H_pi with pi=(1,3,6)/10 and Y=diag(6,-4,1). v486/v487: M=[[1,0,0],[0,1/2,1/6],[0,1/6,1/2]], deck swap Delta of final two slots. v395: given affine E8 adjacency A,T_net=(A+2I)/4 and given 1:6 scheduler. These finite operators are compared without assuming identification with P1 fields,electromagnetic charge or physical time."
    },
    {
      "id": "premise:marked-oriented-quarter-spin-and-two-object-vertex-transport",
      "titleEN": "Marked oriented quarter spin and two-object vertex transport",
      "statementEN": "Positively oriented marked quarter turn z->iz of normal two-plane with Spin(2) lift a=+/-exp(i pi/4),a²=i; existing genus2 source (C,S0,Dq,Q) and selected beta; existing lattice vertex objects F0,F1,unitary T:F0->F1 and beta1=T beta0 T^-1. Continued oriented quarter step and geometric reversal remain distinct arrows. An open P1 amplitude functor is not assumed."
    },
    {
      "id": "premise:natural-single-face-inclusion-in-given-family-calderon-graph",
      "titleEN": "Natural single-face inclusion in the given family Calderon graph",
      "statementEN": "Given positive invertible M of v486/v487 family recursion;C=M²(I+M²)^-1,X=M(I+M²)^-1 and Pi=[[I-C,X],[X,C]] on doubled six-space. Tested inclusions are the two coordinate faces. No geometric P1 shell space or its embedding is thereby derived."
    },
    {
      "id": "premise:oriented-five-slot-hodge-candidate-with-explicit-basis-readout",
      "titleEN": "Oriented five-slot Hodge candidate with explicit basis readout",
      "statementEN": "Ordered orthonormal basis e0,...,e4,its volume form and v=sum e_i. On Lambda²C5 consider new mathematical candidate C=*(v wedge .). Conditional Born test explicitly sets two-words as measurement basis,U(t)=exp(-itC) as generator ansatz and input-label-dependent disjointness filter. These readout data and choice of C are not derived physical P1 rule."
    },
    {
      "id": "premise:given-five-slot-exterior-source-with-retained-complement-index",
      "titleEN": "Given five-slot exterior source with retained complement index",
      "statementEN": "V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone."
    },
    {
      "id": "premise:given-full-e8-current-source-with-fixed-carrier-su5",
      "titleEN": "Given full E8 current source with fixed carrier SU5",
      "statementEN": "Actual weight-one E8 Chevalley source from tfpt_explorer.current_block_geometry._actual_current_source and v498. Given D5/A3 frame uses first5/last3 standard coordinates. Carrier SU5 inside D5 has roots e_i-e_j,i,j<5. Retain full E8 source,cocycle,compact form and group actions. Physical P1 realization of this already given current source is not assumed proved."
    },
    {
      "id": "premise:specified-inclusive-current-response-with-invariant-metric",
      "titleEN": "Specified inclusive current response with invariant metric",
      "statementEN": "For an explicitly specified irreducible insertion sector and input/output modules,let B_a be actual current brackets in Killing-orthonormal basis. If sum B_a*B_a=kI,E(rho)=sum B_a rho B_a*/k denotes mathematical inclusive response with unread insertion index. Reduced response uses tensor chart transported by group action. This defines tested reader,not asserted selection of physically executed P1 instrument or original time."
    },
    {
      "id": "premise:specified-old-j20-instrument-in-fixed-six-mark-duad-chart",
      "titleEN": "Specified old J20 instrument in fixed six-mark duad chart",
      "statementEN": "Actual twenty jump events U_l(I-D_l) per mark from compiler-correlated-event-clock-20260919/source_channel.py;J20 effect3I/5,normalized jump channel Psi=(5/3)J20. Retain common duad labels of ten basis states. Comparison chart does not provide linear SU5/native group identification of Bell10=Sym²C4 with Lambda²C5 or already selected P1 apparatus."
    },
    {
      "id": "premise:specified-conjugate-su5-covariant-petersen-channel",
      "titleEN": "Specified full SU5 covariant channel with Petersen support",
      "statementEN": "H=Lambda²C5 in given oriented unitary duad basis,target dual H. T is CPTP and T(R rho R*)=barR T(rho)barR* for R=Lambda²U,U in SU5. Basis transitions to same or intersecting duads vanish. This is explicitly a mathematical conditional premise,not assumed physical P1 event covariance."
    },
    {
      "id": "premise:fixed-three-plus-two-mark-and-typed-original-degree-clock",
      "titleEN": "Fixed three plus two mark and typed original degree clock",
      "statementEN": "V=C5,P rank3 color projector,G_P=S(U3xU2),X=(-2,-2,-2,3,3),original U5=exp(2pi iX/5). Literal slot cycle c=(01234) is distinct and moves P. Covariant transport over Gr(3,5) concerns different marks,not full SU5 covariance within one fixed marked instrument. Continuous marks are not six old outer event marks or135 D8 frames."
    },
    {
      "id": "premise:specified-cptp-source-process-with-p5-saturation",
      "titleEN": "Specified CPTP source process with positive P5 saturation",
      "statementEN": "In fixed dual H=Lambda²C5 dictionary,T is a CPTP channel with Choi J_T,trace10. Require Tr(P5 J_T/10)=1 for rank5 projector from epsilon amplitudes. Sufficient conditional contract,not already proved P1 premise or arbitrary P_A state expectation. No assumed fullSU5 covariance,Petersen population or observed Kraus register."
    },
    {
      "id": "premise:original-native-pauli-and-v419-f20-source-words",
      "titleEN": "Original Pauli and v419 F20 source words",
      "statementEN": "Use frozen v783 two-qubit Clifford generators, existing Pauli16 and central mu8, and actual cyclotomic v419 C5,G matrices. A constructed source-word F20 subgroup is available; its physical seam selection is not assumed."
    },
    {
      "id": "premise:two-actual-source-events-with-coherent-record-access",
      "titleEN": "Two actual events with coherent record access",
      "statementEN": "Compose the actual unmarked sixty-event source twice, preserving phases. Additionally grant coherent access to all 3600 ordered histories and an active heralded record contraction after fixing a Hodge dictionary. This resource and selection are not derived P1 dynamics."
    },
    {
      "id": "premise:stipulated-e8-h8-with-original-color-center-selector",
      "titleEN": "Stipulated E8 H8 module with original color-center selector",
      "statementEN": "Retain stipulated E8 lattice extension with H8=8K_alpha,alpha=1/4 or3/4,actual rational Weyl dictionary M and original marked color center on first three carrier slots. Apply its P_sing after the carrier theorem. No intertwiner to the primitive P1/OS space is assumed."
    },
    {
      "id": "premise:actual-single-source-event-coherent-stinespring-record",
      "titleEN": "Coherent Stinespring record of actual single source event",
      "statementEN": "Use actual60 uniformlyweightedsourceoperations withtheirphases anddilationVsrc=sum_l|l>⊗U_l/sqrt60. GrantcoherentaccesstothisC60record andactivemeasurementofspecifiedeffectasresource. Reducedchannelalonedoesnotprovephysicalrecordcarrier ormeasurement. MarkedOmega andSpin5transportremainexplicitcarrierdata."
    },
    {
      "id": "premise:native-pauli-clock-family-with-marked-f20-inclusion",
      "titleEN": "Native Pauli clock family with marked F20 inclusion",
      "statementEN": "Use actual native Pauli four, frozen sigma, transported scalar-square theta alpha, and explicit native C,G word pair intertwined with v419. Retain all six alternating Pauli forms. Do not assume P1 selects this conjugate F20, one form, or any current contraction."
    },
    {
      "id": "premise:given-e8-fold-matrix-with-retained-source-charge-and-p2-grading",
      "titleEN": "Given E8 fold with retained source charge and P2 grading",
      "statementEN": "Use the same explicit Weyl matrix M from v16-operator-pullback-20261014/fold-results.json, mu_alpha=(j+alpha q)/8 with q=(1)^8 and alpha=1/4 or3/4, Qsource=(Mq).H, and original P2 Cartan charge X=(-2,-2,-2,3,3,0,0,0). Given D5+A3 target frame and compact E8 current representation. Do not assume raw local P1 spinor-field map, executed spectral filter, new physical time or changed source phase."
    },
    {
      "id": "premise:given-eightfold-even-car-quotient-with-marked-charge-and-source-time",
      "titleEN": "Given eightfold even CAR quotient with marked charge and source time",
      "statementEN": "Use existing fold eta_r(x)=psi((x+2pi r)/8)/sqrt8, local even rank8 CAR algebra on punctured quotient circle, fixed D8 Cartan chart and q=(1)^8, original current normal ordering/Weyl rule, and declared K_alpha source time. DHR sector labels/local von Neumann statement use standard locally normal even-CAR reference/Haag-dual vacuum-net representation. Assume neither normal local P1 single-interval identification,primitiveOS time,spin-structure sum nor bounded sharp spinor field."
    },
    {
      "id": "premise:ordinary-weyl-product-and-explicit-reflection-type-comparison",
      "titleEN": "Ordinary Weyl products and explicitly specified reflection type",
      "statementEN": "Compare the given chiral current Weyl relations under a real linear profile map L, retaining scalar linearity/conjugation and product preservation/reversal as separate explicit types. Transfer of the OS Grassmann word type to ordinary Weyl products is the tested identification hypothesis, not a proved P1 property. An oppositely oriented face pair remains a conditional target type."
    },
    {
      "id": "premise:existing-normal-thermal-source-with-bounded-neutral-insertions",
      "titleEN": "Existing normal thermal source with bounded neutral insertions",
      "statementEN": "Use the already given thermal sea representation of the free elliptic NS source with H>=0, finite Z_beta=Tr exp(-beta H), W=beta/2, rho=exp(-beta H)/Z and its HS standard space. Neutral even insertions including existing current Weyls are bounded in the source von Neumann algebra. Their imaginary-time conjugates are not assumed everywhere bounded; ordered heat products define the functional. The general HS Gram formula needs only an existing normal density, not Gaussianity. This comparison premise asserts neither physical P1 source, second geometric field family nor physical time identification."
    },
    {
      "id": "premise:finite-reflected-spectral-weight-preservation-test",
      "titleEN": "Finite test of the generic spectral RP preservation inference",
      "statementEN": "Test only the generic inference used in old measure proofs that a pointwise positive reflection-symmetric spectral weight exp(-Tr f(D²)) preserves existing RP. Test class: classical reflected finite halves,K0=[[10,9],[9,10]],D(s,t)=[[2s,1],[1,2t]],s,t=plus/minus1,f(u)=exp(-u). No full geometric/BRST/branch or P1/P2 realization of these data assumed. General-profile formula uses finite positive Laplace measure;the9/10 threshold is not asserted for arbitrarily small profiles."
    },
    {
      "id": "premise:finite-faithful-car-gns-source-completion",
      "titleEN": "Declared faithful finite CAR GNS source completion class",
      "statementEN": "At most two CAR modes are supplied with complete normalized CAR state moments, positive definite Gram and internal quarter invariance. The additional selfadjoint transfer preserves the CAR cyclic space, satisfies explicit finite bounds and has the supplied reference eigenvalue. One-transfer data supply linear constraints; all other supplied words are exactly replayed. The actual control oracle is the previously given quarter source; neither its data nor the finite representation ansatz is derived from P1/P2 here."
    },
    {
      "id": "premise:same-gapped-quarter-source-as-borchers-translation",
      "titleEN": "The same given quarter energy as Borchers translation",
      "statementEN": "Use exactly the already given full chiral quarter source H_alpha, alpha1/4 or3/4, with spectrum containing0 and least positive spectral point1/4. The proposed standard-pair bridge identifies U(s)=exp(is H_alpha) as its strongly continuous translation group and requires unitary modular conjugation V_t U(s) V_t*=U(exp(-2pi t)s) for all real s,t. This is an additional proposed identification to be tested, not an original P1 consequence."
    },
    {
      "id": "premise:original-v252-real-finite-block-and-selfdual-field-test",
      "titleEN": "Actual finite KO6 block and tested selfdual ansatz",
      "statementEN": "Given the existing v252 constructor with selfadjoint D_F, antiunitary J_F, J_F²=+I, J_F D_F=D_F J_F and J_F Gamma_F=-Gamma_F J_F. Test the additional direct Pfaffian identification through B_F=<J_F.,D_F.> and a universal internal rechoice of J at unchanged D_F. Control parameters of the published constructor class are not selected physical TFPT values. A total spacetime domain or Grassmann source law is not presumed derived from P1."
    },
    {
      "id": "premise:full-projector-car-marginal-and-commuting-joint-algebra",
      "titleEN": "Full projector covariance in a positive joint source",
      "statementEN": "Conditional theorem: a positive normalized joint state has full projection covariance P on the actually fully realized CAR algebra. The further unital C* algebra commutes with this CAR algebra. These assumptions are a source contract to test, not already derived P1 data; one face or incomplete neutral measurements do not replace them."
    },
    {
      "id": "premise:actual-quarter-neutral-vacuum-current-core",
      "titleEN": "Actual neutral vacuum current space of the quarter source",
      "statementEN": "Retain the supplied one-copy quarter CAR source alpha1/4 or3/4, negative sea Omega, actual level1 currents J_n with adjoints, H_alpha=N+Q²/2+(alpha-1/2)Q, common finite-energy core, existing local current net and original transported stress/winding comparison. Work precisely on the neutral cyclic Q0 space; elliptic Gibbs/HS state and charged sectors are distinct data. No physical P1 source map is assumed."
    },
    {
      "id": "premise:actual-local-weyls-and-finite-fiber-coordinate-target",
      "titleEN": "Actual full local Weyl system and finite spectral matrix fibers",
      "statementEN": "The existing actual local current net contains U_s,V_t with U_s V_t=exp(2ist)V_t U_s for all real s,t. The additional target identification tested is a unital complexlinear star image in the ordinary almost-commutative coordinate class A_sp, a subalgebra of continuous sections of a finite matrix/endomorphism bundle of positive rankN. This class is an explicitly chosen analytic realization, not implied by a smooth center alone. The full operational Seedop A_loc is not identified with A_sp."
    },
    {
      "id": "premise:neutral-current-recognition-with-actual-time-state-and-local-image",
      "titleEN": "Sufficient original current contract with actual time, state and local image",
      "statementEN": "Conditional recognition contract on the relevant eight-channel neutral current cycle: common invariant word domain with adjoints and level1 CCR, actual self-adjoint H>=0, H Omega=0, [H,j_a,n]=-8n j_a,n and Q_a Omega=0. Local statements require actual Fourier/smearing and support dictionary; reflected two-face claims require the actual common reflection representation. Thermal variant assumes actual beta KMS with legitimate unbounded-word extension; full joint zero-mode law and delta remain source data. This contract is not assumed proved from P1 and is not necessary for every coupled P1 proposal."
    },
    {
      "id": "premise:constant-finite-dirac-product-mixed-current-test",
      "titleEN": "Constant Dirac product with mixed current generators",
      "statementEN": "Assume the existing normal-independent two-component collar A=-i partial_theta+alpha, alpha=1/4 or3/4, Gamma=diag(1,-1), Jn=[[0,-1],[1,0]], S=Jn Gamma. In the supplied complete complex CAR system consider smooth one-face quadratic generators fI,fGamma,fP_R under actual HS/implementability conditions. For the product test Phi is a constant finite self-adjoint coefficient with B_Phi=Gamma A-S tensorPhi on the same H1 domain. A is internally scalar. Reducing projections are constant and reduce every Fourier momentum. For v252 also retain actual gamma_F and {Phi,gamma_F}=0. No physical P1 selection, separate chiral determinant, new vacuum or identification of tangential time with original OS Hamiltonian is presumed."
    },
    {
      "id": "premise:paired-quarter-external-lowest-block-candidate",
      "titleEN": "Paired quarter source and tested lowest-block selection",
      "statementEN": "Given B_a=2(A_a directsum A_(1-a)) on periodic H1,0<a<1,equal internal copies,j=exp(-i theta) K with summand exchange,and full spectral two-face graph G(B),ell>0. The external candidate claims Hcar=ker(|B|-lambda1) follows from the original primitive gap filter. Test that identification,not every P1 source. Physical CAR field map,original J/Clifford transport,OS reflection and time are not presumed identified."
    },
    {
      "id": "premise:canonical-recomplexified-graded-boundary-clifford-typing",
      "titleEN": "Geometric Clifford boundary with explicit changed complex structure",
      "statementEN": "Assume the existing free product class B=Gamma A or actual smooth tangential odd finite coefficient B_Phi=Z A-S Phi with total grading Z tensor gamma_F. Apply the standard Clifford boundary functor on the underlying real space with NEW complex structure Ical=i_old Gamma_tot and real structure C0=i_old gamma_n; the dual face has -C0. C0 is old-linear and new-antilinear,not identified with original charge J. This differs from full complex CAR quantization of both independent normal copies. State conclusions use the full graph as the actual quantum covariance in this functor. Its physical selection from P1/P2 is not presumed proved; Phi is a fixed classical background. Keep the fixed normal-independent product collar; a(theta) is smooth Hermitian and even,Phi(theta) smooth Hermitian and odd. No quantization of these bosonic backgrounds."
    },
    {
      "id": "premise:fixed-frame-graded-normal-dependent-source-family",
      "titleEN": "Fixed graded normal-dependent classical source family",
      "statementEN": "Assume fixed normals N,fixed gamma_F and fixed product trivialization,smooth selfadjoint even A(r),odd Phi(r),Ical=i_old Z gamma_F and C0=i_old N. A compatible finite regulator preserves these identities and adjoints; alternatively supply actual closed elliptic Cauchy data with Lagrangian Green form and grading invariance in the continuum. Normal dependence is an explicit extension of the old constant-product premise. State conclusions assume actual Clifford graph quantization per background. Only the additional integrated-moment identity takes an already given common bosonic weight and integrability as inputs; they are not presumed derived from P1."
    },
    {
      "id": "premise:given-quarter-many-body-source-and-compact-dirac-comparison",
      "titleEN": "Given quarter many-body source and tested compact Dirac comparison",
      "statementEN": "Given the already constructed limiting source in toe_research_20260909.tex with H=sum |j-1/4| n_j^exc and Q=sum n_b-sum n_d. Test only the added direct unitary identification of this FULL many-body time generator,including neutral/even sector,with |D| or positive affine energy rescaling in the usual compact finite-dimensional elliptic Dirac type with finite coefficient rank and finite p-summability. This identification is neither asserted as an original P1 theorem nor assumed true. Primitive boundary definition does not explicitly prescribe D_coll=H or every summability hypothesis."
    },
    {
      "id": "premise:actual-full-v252-unimodular-p2-gauge-lift",
      "titleEN": "Actual full v252 gauge lift and original P2 comparison",
      "statementEN": "Given the full unchanged v252 constructor pi,J_F,gamma_F,D_F and its symbolic Yukawa/Majorana inputs. Compare real gauge lift U=pi(u)J_F pi(u)J_F^-1 on the connected unimodular branch lambda det(m)=1 with original oriented P2 carrier E3+E2,Y=(-1/3)^3+(1/2)^2. No full Spin10 source action is presumed. A cyclically fixed neutral family line is considered only with an expressly supplied sigma=(123) and eigenvalue1; its original physical selection is not assumed."
    },
    {
      "id": "premise:fixed-local-quarter-channel-in-constant-odd-source",
      "titleEN": "Fixed local quarter channel in a constant odd source coefficient",
      "statementEN": "Given the existing Clifford graph source h=A_alpha g-i g Phi with A_alpha=-i partial_theta+alpha,alpha1/4 or3/4,Hermitian involution g and constant selfadjoint odd Phi. Compare fixed local map V_e f=f tensor e,g e=e,unit e,at fixed beta>0 and identical momenta/references. Original elliptic comparison uses actual W1/2 normalization,beta4pi and unchanged fold/normal-ordering reference. If classically averaged,a positive probability law on such constant Phi with fixed e,p,beta is explicitly supplied. This describes neither complex Pfaffian weights,moving field dictionaries nor general quantum-boson families."
    },
    {
      "id": "premise:actual-diagonal-lepton8-common-insertion-contract",
      "titleEN": "Actual reducing lepton8 contract with common insertions",
      "statementEN": "Given unchanged v252 with the existing diagonal integer control Yu11,13,17;Yd19,23,29;Ye31,37,41;Ynu1,2,3;MR1,4,9, its actual gauge lift and grading, p1/4 and four adjoint/J-real completed original quaternion one-forms q[D,b]. The generation0 lepton8 is proved reducing for these matrices. Source=target tests only automorphisms of this given tuple."
    },
    {
      "id": "premise:one-e8-bracket-weyl-pairing-with-single-anchor-dressing",
      "titleEN": "One E8 current trilinear as the same Weyl quadratic with one anchor mark only",
      "statementEN": "Test only literal B_h=κ(x,[h,y]),h in(10,6),x,y in(16,4), as the local quadratic coefficient of the SAME left four-dimensional Weyl multiplet with Lorentz epsilon. In each fixed spin/charge channel the family form omega is skew. Allow linear combinations F(X)omega G(X) for only ONE X=diag(3,-1,-1,-1) and arbitrary polynomials. Other original family generators, independent Dirac variables, derivative vertices, multiple omega factors and different field maps are outside this class."
    },
    {
      "id": "premise:spin10-su4-family-four-cycle-quarter-lift-class",
      "titleEN": "Complete Spin10/SU4 family-four-cycle quarter-lift class",
      "statementEN": "Given original E8 roots and Spin10×SU4/Z4 embedding. Candidates are g=[g5,eta C4],C4 a family four-cycle,eta^4=-1,g5 compact inSpin10 and g of exact E8 order4, equivalently g5^4=-1Spin. Allow all SU4 conjugates. The original SM subgroup inside Spin10 is marked; preserving it is tested as an additional subclass. No physical identification of mark rotation and native clock is assumed."
    },
    {
      "id": "premise:family-four-cycle-lift-commutes-with-original-sm",
      "titleEN": "Additional pointwise SM preservation by the Spin10 lift",
      "statementEN": "Within the given family-four-cycle quarter-lift class additionally require g5 to commute pointwise with original G_SM insideSpin10,Y=(-1/3,-1/3,-1/3,1/2,1/2),and original colorSU3/weakSU2 blocks. This exact symmetry premise defines the tested candidate subclass, not a newly derived P1 vacuum rule."
    },
    {
      "id": "premise:native-third-clock-current-word-pairing-class",
      "titleEN": "Native third clock and actual current-word pairing",
      "statementEN": "Given original D5+A3 E8 embedding, native toral third b=(-1,-1,-1,0,0,-1,0,0) and its coherent C12 field lift. Test K(x,w y) on g1 using complex-bilinear invariant K and actual ad_u/group letters. In the lepton pairing the carrier color charges vanish and actual family4 sigma phases have multiplicities2+2. A one-Higgs two-class subclass permits one generic fixed h in g2 and otherwise only functions of those same two sigma projectors. Do not presume physical Weyl-field type, temporal ordering, the arbitrary A3 torus or a marked three-plane."
    },
    {
      "id": "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
      "titleEN": "Constant odd circle-source coefficient with existing sea and full boundary graph",
      "statementEN": "In the existing Clifford chart on L2(S1,K) with finite K let h0=(-i∂theta+alpha)gamma,alpha=1/4 or3/4,gamma*=gamma,gamma²=I. Supply constant selfadjoint odd Phi,{gamma,Phi}=0,and V=-i gamma Phi,h=h0+V on common periodic H1. Compare given CAR sea projectors P_-(h0),P_-(h) and complete pure two-face projector G_ell(h),ell>0,including crossings. This is the existing source class with classical background, not physical selection from P1 or quantization of dynamic bosons."
    },
    {
      "id": "premise:fixed-scalar-quarter-full-jloc-pfaffian-candidate",
      "titleEN": "Direct full Jloc Pfaffian at unchanged scalar quarter parameter",
      "statementEN": "Test new direct source closure beta_Dalpha=<Jloc.,Dalpha> in existing old-complex collar with N,Z,S=NZ,Jhat=I⊗J_F,Jloc=S Jhat,Dalpha=N(∂r+Z(-i∂theta+alpha I)−S Phi),alpha=1/4 or3/4. Phi retains existing selfadjoint,J_F and oddness identities; fields and scalar quarter parameter remain unchanged. Claim is same antisymmetric Pfaffian source directly equal to primitive spectral action. Do not presume a J-odd charge connection, additional paired holonomy sectors or a new relative log profile as original consequences."
    },
    {
      "id": "premise:fixed-quarter-cover-deck-normal-and-convergence-selection-tests",
      "titleEN": "Fixed quarter cover, deck as normal and convergence-only selection tests",
      "statementEN": "Use existing longitudinal NS tuple B_cov=2(A1/4⊕A3/4),V=Tpi,u_cov=[[0,exp(ix)],[I,0]],with actual H1 domains and old complex types. Test only claimed local old-complex-linear normal multiplication on this same two-sector coefficient space,and convergence alone selecting dt/t. Relative heat pair is A1/4² versus A1/2²; no alternative measure is presumed a full admissible original TFPT source."
    },
    {
      "id": "premise:fixed-original-aps-quarter-domain-and-constant-odd-insertion",
      "titleEN": "Fixed original APS quarter domain and constant odd insertion",
      "statementEN": "Given product collar with p=n+alpha,alpha=1/4 or3/4,finite graded K,h0=p gamma_F,h=h0-i gamma_F Phi for constant bounded selfadjoint odd Phi. Retain x0 in RanP_-(h0),xell in RanP_+(h0),ell>0. Exterior/CAR transfer and reference are used only under their given contract. No physical state selection is assumed from elliptic realization."
    },
    {
      "id": "premise:mass-only-full-deck-relative-and-ordinary-heat-trace",
      "titleEN": "Mass-only deck-odd part under ordinary heat trace",
      "statementEN": "Narrow candidate: full local deck tau=S R_r with transported A and reflection-even Phi on a common stable domain,so Dref=D0,Drel=ZPhi. Test literal primitive Tr f(Drel/chi)-Tr f(Dref/chi),allowed f(x)=exp(-x²),on a nonzero infinite-dimensional geometric Hilbert space,without added UV cutoff or alternate trace. This is not assumed for all P1 realizations."
    },
    {
      "id": "premise:closed-antiperiodic-scalar-wall-with-fixed-hermitian-coefficient",
      "titleEN": "Closed antiperiodic scalar wall with fixed Hermitian coefficient",
      "statementEN": "Test The reviewed additional closed Green-source construction on finite circle length2ell,scalar anti-I spinor clutch,H1 domain,fixed finite Hermitian Phi,smooth real periodic scalar sigma(r). N²=-I,Z²=S²=I,S=NZ,Q=N partial_r+Z sigmaPhi,D=Q+pS. Explicit inverse additionally assumes ∮sigma=0. Neither global clutch nor Green=original Schwinger source is assumed from local C_faces."
    },
    {
      "id": "premise:scalar-spectral-heat-covariance-with-geometric-time-reflection",
      "titleEN": "Scalar spectral heat covariance and actual time reflection",
      "statementEN": "Test only the general inference for scalar translation-invariant Gaussian covariances on R with reflection tau->-tau. Single test C_s=exp[-s(-partial_tau²+omega²)],s>0,omega>=0. Class theorem additionally assumes real,even,continuous ordinarily positive definite c,c(0)>0,C1 at0 and positive reflected Hankel form. No claim that original selects this covariance. Already assumed OS-positive channels,fermionic/matrix reflections,contact/distribution kernels and purely spatial smoothing are different contracts."
    },
    {
      "id": "premise:given-global-quaternionic-sm-mass-loop-with-fixed-yukawas",
      "titleEN": "Given global quaternionic SM mass loop with fixed Yukawas",
      "statementEN": "Use already fully derived v252/v254 particle LR one-form family M_H=(q(H) tensor I_nf)diag(Yup,Ydown),q(H)=[[phi1,phi2],[-barphi2,barphi1]],with fixed Yukawa matrices and common represented/trivialized SM gauge space. Determinant-winding test requires nowhere-zero H along closed loop and invertible Yukawas. Normal geometric bundle clutch is not identified with this global matrix; Majorana and genuine additional bundle transport are separate data."
    },
    {
      "id": "premise:bounded-relative-operator-positive-laplace-and-compact-source-pair",
      "titleEN": "Bounded relative operator,positive Laplace profile and compact source pair",
      "statementEN": "Dref is actually selfadjoint on its fixed compact elliptic source domain,V=V* bounded and P any infinite-rank orthoprojection. Negative trace theorem assumes nonzero positive Laplace F(x)=∫e^(-sx)dμ,F(V²) a defined bounded operator and F(Dref²) trace class. Positive pair-heat theorem uses D=Dref+V on same domain and trace-class reference heat for every positive t. Whether actual original Drel is bounded zero order must be checked against full actual reflection lift and principal symbol; not generally assumed."
    },
    {
      "id": "premise:given-normal-spin-clutch-weak-orbit-family-and-u2-linearization",
      "titleEN": "Given normal spin clutch,weak orbit family and U2 linearization",
      "statementEN": "V=C² with actual SM action e^(it/2)U is supplied. N=CP1 normal spin sphere,W=P(V) separate weak orbit,L=O_W(-1) tautological,Q=V/L. Given degree-one clutch becomes explicit family g(w,φ)=e^(iφ)Pw+I-Pw,E=(O_N1⊠L)⊕(O_N0⊠Q),with split vertical connection and actual H1 domains. E8 application additionally retains named half-root λκ and mixed-carrier line j6. W is not assumed an already original physical parameter space; orbit/dual-section functor is tested as mathematical comparison."
    },
    {
      "id": "premise:given-normal-orbit-and-four-copy-natural-spin-family",
      "titleEN": "Given normal orbit family and four-copy natural spin lift",
      "statementEN": "N=CP1_N and W=P(V) are distinct bases. Supplied SM color C=3_(Y−1/3) and V=2_(Y+1/2) carry E=C⊕(O_N1⊠L)⊕(O_N0⊠Q),Q=V/L=detV⊗L*. D=detE has normal degree1 and is SM neutral. For four integral m_j consider W_m=ΛevenE⊗⊕D^m_j; already proved natural joint lifts have Σm=−2. mA=(0,0,−1,−1) is only a supplied representative. Literal kernels use previously specified split vertical spin connection; virtual family classes persist under smooth variation. A1+1D anomaly interpretation needs actual quantization of these modes; N×W is not assumed physical spacetime."
    },
    {
      "id": "premise:fixed-v117-orthogonal-d3-cartan-identification",
      "titleEN": "Additional fixed orthogonal identification with the D3 Cartan",
      "statementEN": "For the Cartan test only, identify the v117 rotation triple orthogonally with the last D3 coordinate block of the fixed marked D5+D3 E8 roots. Tested lifts are blockwise signed coordinate permutations. This is not an operator identity implied by original SU3⊂SU4 embedding or a physical chirality identification."
    },
    {
      "id": "premise:given-original-su3-to-su4-family-vector-action",
      "titleEN": "Existing SU3 family-vector embedding into SU4 four",
      "statementEN": "Use original SU3⊂SU4 embedding with4=3+1 and existing E8 branches (45,1),(1,15),(16,4),(bar16,bar4),(10,6). A supplied family-vector rotation R acts by U=diag(R,1), with actual tensor/exterior powers on these branches. This does not identify original v117 connection with physically used marked family connection or derive original joint operator source."
    },
    {
      "id": "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
      "titleEN": "Supplied split carrier with actual q sign lines on genus-two cover",
      "statementEN": "Given existing split carrier E3⊕E2 with unitary split connection onX and actual unitary flat q linesL0,L1,L2 on old coverC:w³=(z²−1)/(z²+1),η²=1−w⁶,product1 andπ*Fv117=L0⊕L1⊕L2. Pull these data toX×C and combine with declared alignment to mA slots. This does not selectX,E,mA or alignment as original P1 quantum source."
    },
    {
      "id": "premise:given-relative-unit-seam-on-specified-collar-faces",
      "titleEN": "Relative unit seam on explicitly assigned collar faces",
      "statementEN": "In existing product collar,test original relative unit gluing v1=Uv0 on an explicitly assigned pair of labeled faces. Scalar block has h e_n=(n+α)e_n and U e_n=e_(n+1),α=1/4 or3/4. Actual original Γ±-to-face assignment,orientation and three-cabled spin trace map are not assumed derived."
    },
    {
      "id": "premise:whole-constant-odd-coefficient-on-scalar-unit-clutch-domain",
      "titleEN": "Whole constant odd coefficient on same scalar unit-clutch domain",
      "statementEN": "Test supplied whole h=Aγ_F−iγ_FΦ with constant Hermitian odd Φ,internally scalar A=−i∂θ+α and U=e^{i_oldθ}I on D_U={ψ∈H1:ψ(ell)=Uψ(0)}. Hence [A,Φ]=0 and U*ΦU=Φ. Original Γ±-to-face assignment remains an explicit premise. Cited v252 coefficients are previously checked constructor inputs,not selected physical masses. Variable Φ,noncommuting connections or charged noncentral clutches change these premises."
    },
    {
      "id": "premise:declared-q-column-to-v252-generation-slot-comparison",
      "titleEN": "Declared comparison of actual q columns with supplied v252 generation slots",
      "statementEN": "For operator comparison identify actual ordered horizontal q columnsG with three supplied generation slots of v252 full_D basis. D_E=Gbase^-1U_FbarGbase acts on particle families,barD_E on antiparticles; Φ remains given full_D constructor with its Y_f and symmetricMR. Retain F5 Ical,C0,T_faces,NS domain and full graph covariance. This alignment is declared comparison input,not derived from kernel count,H0,equal dimensions orP1. Selects no mass,state,physical time or native action permission."
    },
    {
      "id": "premise:declared-q-column-to-v252-chiral-slot-comparison",
      "titleEN": "Alternative chiral comparison of q columns with actual v252 P2 carrier",
      "statementEN": "For this explicitly alternative comparison identify actual G columns(L0,L2,L1) with supplied generation slots through whole signed P2 dictionary. D_E acts on gamma_F positive,barD_E on negative. Retain unchanged full_D with Y and symmetricMR,F5 structure,faces,graph state and given time. Do not silently replace earlier particlewise hypothesis. No P1 selection,global trivialization,new state/time or physicalE8gauge action assumed."
    },
    {
      "id": "premise:original-hard-holonomy-and-closed-triangle-readout-contract",
      "titleEN": "Original hard-holonomy contract with pure closed-triangle trace",
      "statementEN": "Read original45 flavor sources defineY from canonical minimal paths of a Hermitian family connection andPi_triangle=Hol12Hol23Hol31 as ordered closed holonomy,delta=argtrace. DisplayedPi includes neitherKstr nor extraZ6operator. Nonreal asymptotic is a readout contract to test,not completed physical derivation. Active source retains absolute wall selector;no automatic physicalconnection=v117."
    },
    {
      "id": "premise:given-original-e8-cx-current-cocycle-and-compact-adjoint",
      "titleEN": "Given original C/X current source with E8 cocycle and compact adjoint",
      "statementEN": "Use the actual supplied level-one E8 current source C in1x4 and X inbar5x4, original cocycle and compact adjoints. The expressly restricted initial seed keeps only family labels1,2,3. Check current Lie words without presupposing geometric q/p access, a finite Phi coefficient or physical P1 source selection."
    },
    {
      "id": "premise:original-d5-base-current-action-on-given-p2-e8-source",
      "titleEN": "Original D5 base-current action on supplied P2 and E8 carrier",
      "statementEN": "Original D5_1 x A3_1 base net and explicit P2 Clifford carrier supply full45-dimensional D5 operator action including20 non-U5 roots. Its zero modes act with the existing Chevalley cocycle on the supplied compact E8 currents; no primitive P1 preparation or history selecting a word is presumed."
    },
    {
      "id": "premise:bare-c3-positive-kernel-with-real-diagonal-yukawa-readers",
      "titleEN": "Bare positive C3 kernel with real diagonal Yukawa readers",
      "statementEN": "For this restricted analytic class only, take the displayed positive circulant H3 with real parameters and strictly positive eigenvalues, and Y_f=L_f H3_f^-1/2 R_f with real diagonal readers. This is not assumed to be the original P1 consumer or full Pstr compression."
    },
    {
      "id": "premise:common-leading-distance-flavor-readers",
      "titleEN": "Common leading triple distances with equal two-leg weights",
      "statementEN": "Restricted candidate class only: arbitrary shared real triple x, sector positive scales/offsets and permutations, single leg or equal-weight same-list two legs. Not a P1 axiom. Different lists/weights, full sums and extra operator histories lie outside."
    },
    {
      "id": "premise:original-closed-real-delta-transport-action",
      "titleEN": "Original closed real delta transport action",
      "statementEN": "Original EM3 action on its invertible closed epsilon0 branch with real delta, fixed U6 and all three cusps. Use actual common Gbase dictionary U6=diag(M0,-M0) and fixed marked P0. This is not a newly chosen independently projected physical variation."
    },
    {
      "id": "premise:four-original-diagonal-paths-and-regularized-endpoints",
      "titleEN": "Four original diagonal paths with regularized endpoints",
      "statementEN": "Actual original v117 connection and already proved G along the four diagonal0-to-infinity classes, regularized target z^-D and fixed G metrics. Geodesic reading uses canonical complete hyperbolic metric of the given conformal class, or original real-reflection invariance; not an arbitrary physical metric. No original four-path summation prescription is assumed."
    },
    {
      "id": "premise:native-clock-adjoint-compensation-for-hardypair",
      "titleEN": "Tested native adjoint-clock compensation of Hardy operator",
      "statementEN": "Only The reviewed restricted candidate: actual96 Hardy endomorphism and original weak creator, native clock=-i gammaF acts by conjugation, and proposed combined fourfold adjoint average. Not a P1 axiom or a one-sided charged-Hom phase."
    },
    {
      "id": "premise:declared-positive-cubic-hardy-direction-for-gram-differential",
      "titleEN": "Declared Hardy direction for the original cubic Gram differential",
      "statementEN": "Comparison at the original unregulated positive cubic block with declared V=-kappa M0P0, actual y/delta and already calculated Hardy phase. This is not a claim that the original physical source selects this whole V_adm. Preserve actual Pstr commutation and other C6 branches at the original source contract."
    },
    {
      "id": "premise:whole-same-mu01-induced-ns-halfmode-reader",
      "titleEN": "Whole unchanged induced mu01 reader on original NS halfmode",
      "statementEN": "Unchanged already defined induced mu01 input, original three q cables and J-supported p_(r+1), Phi0 and NS halfmode, fixed G/R roots, actual normal Clifford action and both graph faces. Complete evaluation of the same reader, not a freely selected whole physical source or C6 branch."
    },
    {
      "id": "premise:whole-six-original-induced-inputs-at-fixed-kinetic-ns-reader",
      "titleEN": "All six original induced inputs at the fixed kinetic NS reader",
      "statementEN": "Evaluate the six existing offdiagonal mu_ab in the original induced NS/Hardy kinetic reader, Phi=0, finite positive ell_NS and half-frequency. Carry actual G_a input and J E^(b-1) output maps, same continuation, metric, spin, both graph faces and normal symbol. Do not identify individual twist lines or assume a physical combination or multiplicative compression of field products."
    },
    {
      "id": "premise:canonical-finite-particle-hole-corner-of-given-kinetic-graph",
      "titleEN": "Canonical finite particle-hole corner of the given kinetic graph",
      "statementEN": "Use canonical E and Eh corners of the given pure kinetic NS/Hardy graph at finite positive ell, actual J and Hom maps and normal projector, unnormalized finite CAR trace with sixteen carriers per family, and ordinary adjoint quadratures. No identification with whole unsmoothed Z or complete J_F/KO field."
    },
    {
      "id": "premise:bare-unsmoothed-crossface-quadratic-on-given-graph-vacuum",
      "titleEN": "Bare unsmoothed cross-face quadratic on the given graph vacuum",
      "statementEN": "Test only bare equal-time CAR quadratic T_mu=J* M_mu with actual geometric multiplier and canonical finite spectral cutoffs on the given graph vacuum. No smearing, sewn insertion, heat evolution or source-dependent contact prescription. Original quotient denominator is fixed Zref[0,0,0]."
    },
    {
      "id": "premise:given-original-two-stage-admissibility-complex-and-blocked-weight-caller",
      "titleEN": "Given original two-stage admissibility complex and blocked weight caller",
      "statementEN": "On the printed closed branch QFT2 gives commuting selfadjoint K_r, Delta_adm=sum K_r² and its Hodge projector. QFT4 additionally uses local C6 Green kernels and diagonal weights from transport counts, carrier labels and retained selector weights. Review this given source contract without asserting new physical provenance or choosing a new state."
    },
    {
      "id": "premise:actual-constant-weak-quarter-cap-with-coupled-normal-energy",
      "titleEN": "Actual constant weak quarter source with old boundary space and coupled normal energy",
      "statementEN": "Given full96 source h_p=p gamma_F+V with V=tQ gamma_F-i gamma_F D_F selfadjoint, finite, constant and independent of quarter p. Retain old rank48 P0,p=1_(p gamma_F<0), existing exterior/CAR caller and coupled ground energy E_p=Tr(h_p 1_(h_p<0)) for the cap comparison. No original physical selection of P0,V,ell,source measure or energy subtraction is assumed."
    },
    {
      "id": "premise:whole-product-dirac-with-standard-normal-clifford-double",
      "titleEN": "Whole product Dirac operator with standard normal Clifford clutch",
      "statementEN": "Given the whole normal-independent product interval, D=N(partial+B), B=Z tensor A-S tensor Phi with N²=-I, N*=-N, B*=B, {N,B}=0, [Gamma_tot,B]=0 and {Gamma_tot,N}=0. Standard invertible double joins D and -D by v(0)=Nu(0), v(ell)=-Nu(ell). Retain actual full96 coefficient and charge/real types. No prior derivation of this clutch or whole global cylinder from the P1 measure is assumed; a local collar alone is insufficient."
    },
    {
      "id": "premise:full-independent-even-odd-matrix-coefficient-class",
      "titleEN": "Full independent finite even and odd coefficient class",
      "statementEN": "Both grading sectors are nonzero; A and Phi independently range over every self-adjoint even and odd matrix. This stronger coefficient class is not asserted to be the original SM source."
    },
    {
      "id": "premise:whole-fermi-two-face-projection-and-diagonal-isometric-compression",
      "titleEN": "Whole Fermi two-face projection and common isometric compression",
      "statementEN": "Finite self-adjoint H, positive ell and one isometry V on both faces. G has the full Fermi and cross blocks. This tests closed lossless reduction and does not impose reduction on an open physical subsystem."
    },
    {
      "id": "premise:actual-v252-sm-coefficients-and-internal-ko6-without-extra-mixing",
      "titleEN": "Actual v252 SM coefficients and internal KO6 structure",
      "statementEN": "Original v252 full_D, rep, grading and Kswap, arbitrary Yukawas and symmetric Majorana, SM connection and quark-preserving momentum. No extra quark-lepton mixing or full normal real structure is assumed."
    },
    {
      "id": "premise:separable-normal-real-map-with-actual-jodd-gauge-and-typed-quarter-image",
      "titleEN": "Given normal-independent product collar, internal KO6 and separable normal antiunitary ansatz. J-odd actual gauge connection and scalar quarter image transport are separate premises and cases.",
      "statementEN": "Given normal-independent product collar, internal KO6 and separable normal antiunitary ansatz. J-odd actual gauge connection and scalar quarter image transport are separate premises and cases."
    },
    {
      "id": "premise:actual-p2-six-multiplet-gauge-real-coordinate-frame-class",
      "titleEN": "Fixed actual v252 left/opposite algebra, graded real P2 gauge representation, gamma and J. Six inequivalent positive-grade irreps with family multiplicity3. Constant coordinate frames are classified, without claiming they fix extra numerical Phi/clock/family operators.",
      "statementEN": "Fixed actual v252 left/opposite algebra, graded real P2 gauge representation, gamma and J. Six inequivalent positive-grade irreps with family multiplicity3. Constant coordinate frames are classified, without claiming they fix extra numerical Phi/clock/family operators."
    },
    {
      "id": "premise:original-higgs-radial-family-on-common-compact-product-domain",
      "titleEN": "Original radial Higgs one-form family at fixed Yukawas/Majorana on the given compact AP normal double times tangent circle with common H1 domain, fixed smooth connection and product algebra. Complex K-homology is compared with full source covariance.",
      "statementEN": "Original radial Higgs one-form family at fixed Yukawas/Majorana on the given compact AP normal double times tangent circle with common H1 domain, fixed smooth connection and product algebra. Complex K-homology is compared with full source covariance."
    },
    {
      "id": "premise:positive-laplace-profile-finite-three-moment-comparison",
      "titleEN": "Positive finite Laplace measure and three finite positive moments. Identification of the original profile variables and independent physical moment values is explicitly not supplied by this mathematical comparison.",
      "statementEN": "Positive finite Laplace measure and three finite positive moments. Identification of the original profile variables and independent physical moment values is explicitly not supplied by this mathematical comparison."
    },
    {
      "id": "premise:existing-ap-positive-source-factor-and-declared-squared-energy-comparison",
      "titleEN": "Existing AP source factor and explicitly squared-energy comparison",
      "statementEN": "Given self-adjoint invertible tangent reader of the constant original quarter class, beta=2ell and existing AP gluing factor Q=exp(-beta|h|), with full orientationR. Squared u=(beta|h|)^2 is an explicit comparison variable, not an assumed physical whole bosonic action identification."
    },
    {
      "id": "premise:actual-v252-entire-yukawa-majorana-family-with-compatibility-only",
      "titleEN": "Whole original v252 family under finite compatibility conditions",
      "statementEN": "Four arbitrary complex3x3 Yukawas and complex symmetric3x3 MR in original full_D, with fixed original algebra,gamma,JF. Impose only Hermiticity,gamma oddness,JF reality and order zero/one. Generic quotient uses only R014 constant U(3)^6 coordinate changes. No whole TFPT source rule, extra fixed clock or action selector assumed."
    },
    {
      "id": "premise:original-invariant-word-domain-with-nested-readouts",
      "titleEN": "Given original invariant word domain and nested readouts",
      "statementEN": "Actual operators and adjoints preserve common word domain D; original orthogonal P<=R preserve D. Formal free variables retain order. Analytic evaluation requires common inverses and domains separately. No new physical source, operation selector or time assumed."
    },
    {
      "id": "premise:original-single-beta-return-with-native-cartan-j-word-alphabet",
      "titleEN": "Original single-root return with native Cartan J",
      "statementEN": "Same complete original single-beta S and actual Fock adjoint as SOURCE-RETURN-MEMORY.txt, L=Sdagger S on neutral grade4 dimension726 with the original five quartics. Native linear J with Ju=i u,Jubar=-i ubar and its adjoint retained. Algebraic word responses of this supplied source only; no selected physical history or full E8 alphabet claimed."
    },
    {
      "id": "premise:original-regulated-full-source-with-actual-measure-and-legs",
      "titleEN": "Whole original source caller with actual measure and legs",
      "statementEN": "Original v42 Z_k integral exp(-S_adm-V_R+Jphi) with fixed original action,measure,domain and reference. Analytic statements require finite relevant integrals/derivatives and nonzero Z_k[0]; otherwise coefficientwise only. Actual field fibers retain Jacobians and Berezin ordering. Distinguish structural P_adm, configuration readout, positive-time half and state projection. No new measure or original source coupler assumed."
    },
    {
      "id": "premise:finite-reflected-positive-quadratic-ir-regulator-class",
      "titleEN": "Finite reflected positive quadratic IR regulator class",
      "statementEN": "Two real bosonic halves with no fixed-plane fields, reflection swaps them. Real symmetric A,C and PSD R=[[A,C],[C,A]]. Universal preservation over all finite positive RP original measures; no silent extension to complex/graded fermionic cases. A fixed original source can admit additional regulators. IR regulator is not a physical selector."
    },
    {
      "id": "premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber",
      "titleEN": "Actual shared real Higgs consumer and supplied boson fiber",
      "statementEN": "Original real AF one-form convention q(H)=[[barh2,h1],[-barh1,h2]] with supplied four Yukawa matrices across all families/colors. Keep distinct lepton and quark matrices. H fiber is an argument of same full original S_adm with measure,reference,regulator,eta and higher vertices. Finite Berezin algebra and required finite boson moments; analytic limits separate. Affine shift applies to affine Yukawa coupling; retain any additional H dependent fermion vertices as actual insertions. No new physical measure or Yukawa selection."
    },
    {
      "id": "premise:original-graded-rp-reference-and-even-local-reflected-half-action",
      "titleEN": "Supplied joint graded RP reference and even local reflected half action",
      "statementEN": "Given actual joint graded RP reference omega0, same original antilinear Theta,positive-half algebra and twisted product. In the supercommutative Euclidean path the actual even interaction is Vplus+ThetaVplus with strict half support and no unchecked fixed-plane/cross terms. B=exp(-Vplus),relevant coefficient integrals exist and omega0(ThetaB B)>0. A bosonic/fermionic RP product supplies one such reference; RP marginals of a coupled source alone do not. These hypotheses are not declared derived physical original data."
    },
    {
      "id": "premise:original-constant-higgs-fiber-and-symmetric-majorana-spectral-consumer",
      "titleEN": "Original constant Higgs fiber and symmetric Majorana spectral consumer",
      "statementEN": "Given actual whole v252/v254 real96 q(H) one-form consumer,four fixed complex3x3 Y and complex symmetric MR between right neutrino singlets. Constant H,real coordinates without1/sqrt2,no fixed nontrivial weak connection. Matrix spectral shift z>0. All-mode result uses supplied scalar-quarter product circle h=(n+alpha)gamma-i gammaPhi,alpha1/4 or3/4 with its original domain and mu²>0. Extension to global Padm,reference or APS requires established common unitary transport."
    },
    {
      "id": "premise:literal-archived-geometric-residue-and-common-higgs-field-comparison",
      "titleEN": "Literal archived residue and common Higgs-field comparison",
      "statementEN": "Compare exactly printed bulk coefficients in archived v42 section013 and v45 metrology source002,ED_bulk=-R/(24pi²)-u/(48pi²),GammaD4_bulk=kin/(16pi²)+u²/(16pi²)+Ru/(96pi²),Gamma_grav=-6chi²ED+GammaD4,and stated target potential with muPhi²(chi0)=chi0²wH²/(8pi²)>0,lambda=1/(16pi²). Same field normalization u=Phi*Phi>=0,fixed positive chi0,flat R0 background. Remaining complete relative/reference/eta/zero-source terms are not presumed zero. No automatic Wick or Legendre identification,no claim this exhausts current theory."
    },
    {
      "id": "premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer",
      "titleEN": "Local common Higgs residue contract and conditional product consumer",
      "statementEN": "Local source test assumes P=-(nabla²+E),R positive on spheres,same local linear trace for Res1 and FP0,E=-R/4-X(H),no extra H-dependent curvature/connection terms,fixed smooth interior and unchanged boundary data. Relative subtraction requires both operators of same type. Boundary/eta/nullity results use explicitly fixed regular domain branch. Actual whole96 Higgs family with supplied Y and symmetric MR is additionally evaluated through explicitly conditional standard product Dirac with spin4. Original spacetime/compression/reference/continuation map is not thereby derived."
    },
    {
      "id": "premise:whole-variable-higgs-bound-reference-and-conformal-dirac-map",
      "titleEN": "Whole variable Higgs response with bound reference and original scale sandwich",
      "statementEN": "Given ordinary spin4 product realization with unchanged96 Y/MR,fixed Clifford connection,H only order zero,and no H-dependent first-order coefficient of its square. Evaluate separately already supplied full collar lifts S Rr and S gammaF Rr without selecting either. Common reflected double with invariant metric/trace,transported common full domain,unchanged Y/MR under supplied base pullback,covariantly constant DM. H changes compactly in interior or closed double. Local geometric full/reference pair,not primitive bounded-Drel contract. Original Dsigma=fDf,f=e^-sigma/2,holding sigma fixed in H variations;distinguish unscaled and jointly scaled reference. Scale test assumes Brel0 or already transported mass chart;actual Brel must be evaluated in complete original sum."
    },
    {
      "id": "premise:original-inner-higgs-central-scale-and-finite-affine-source-map",
      "titleEN": "Original inner Higgs fluctuation with central scale and full affine source",
      "statementEN": "Same given anchor and same a,b in real oneform contract;f positive real bounded invertible or local common core,[f,a]=[f,b]=0,JfJ^-1=f,transported domain. Whole original96 H consumer with unchanged Y/MR,Hstar=(0,1),L(Hstar)=DY. Compare same inner change before/after scaling. Given finite full H fiber at fixed sigma/other fields;transport all vertices,reference,eta,sources and absolute Z0. q^4 Jacobian only for flat four-real measure,otherwise pushforward. No new Brel definition or unchecked continuum measure theorem."
    },
    {
      "id": "premise:given-normal-higgs-mode-realization-and-distinct-module-types",
      "titleEN": "Given normal Higgs modes and distinct module types",
      "statementEN": "Given3+2 carrier V=(3,1)-1/3+(1,2)1/2 with conjugation on End_C(V),given colorless H=(1,2)1/2,real-linear insertion;normal2D spin,weakSU2 and spacetime spin distinct. Reuse original normal B_Ea and Higgs/wedge results. Whole kernel/Gram formulas apply only when actual normal realization is given selfadjoint B or supplied doubling with finite constant kernel and actual scale fBf/domain,prescribed S and insertions on their domains. No new profile,normal metric,physical measure,or index-operator/Brel identification."
    },
    {
      "id": "premise:given-product-clifford-grades-parallel-projection-and-complete-relative-block-reader",
      "titleEN": "Given Clifford/form grades,parallel projection and complete relative block reader",
      "statementEN": "Existing whole96 Higgs consumer L(H)+DM,unchanged Y/MR;given conditional spin4 product with fixed Clifford connection. Distinguish ordinary internal two-form from Clifford-valued full notation. Heat comparison assumes parallel spin-compatible orthogonalP and compact interior variation;P+ is actual internal test,not identified with normalP or printedI48/P2. Block formulas exact for same finite regulated operator;infinite domain/relative trace/continuation require original contract. FixedP for affine Hjets;moving frames retain actual induced terms. No choice of physical normal operator,measure,profile,gap or free parameters."
    },
    {
      "id": "premise:original-positive-admissibility-reader-and-given-total-chiral-product",
      "titleEN": "Original positive admissibility reader and given total chiral product",
      "statementEN": "Padm is spectral in its actual positive Ladm=Dadm*Dadm on RanPstr and original domain. Finite low spectral subspace and fixed positive threshold only in named residue test;distinguish heat zero modes from zero-excluded zeta,constant nullity and no threshold crossing for comparing Hjets. Total chirality only in existing conditional Spin4×96 consumer,original GammaF,Y/MR,scalarf and grading-stable selfadjoint domain. Whole even spectral identity needs oddK and summable functions;check reference separately. No Ladm=Ksigma²,normalH=Padm or internalhalf=totalchirality identification. No new geometry,trace,metric or state choice."
    },
    {
      "id": "premise:whole-original-scale-congruence-and-specified-normal-energy-data",
      "titleEN": "Whole original scale congruence and specified normal energy response",
      "statementEN": "Given whole K=fK0f on transported domain, smooth positive f and original whole96 Higgs consumer. Boundary trace and metric use existing conformal transport. Profile recovery only on same homogeneous collar D0=N(partial_r+B), N*=-N,N²=-I,{N,B}=0,fixed Y/MR and sigma=sigma(r); complete first energy-transfer response of all given quarter modes must be supplied as data,not inferred from P(0). Spectral variation uses ordinary cyclic trace,justified continuation,interior variations and explicit reference/zero convention. Exterior Brel,other domains and weights remain separate."
    },
    {
      "id": "premise:given-whole-green-energy-source-and-conditional-scale-response",
      "titleEN": "Given whole Green/Poisson producer and conditional scale response",
      "statementEN": "Same existing homogeneous collar D0=N(partial_r+B),N*=-N,N²=-I,{N,B}=0 and whole given constant96 Higgs/MR family with quarter gap≥1/4. AP normal double has length2ell;APS comparison retains old fixedP_-(h0). Scale identities use actual shared transported domain and justified resolvent variation. DynamicHiggs derivative retains original whole weight,nonzeroZ0 and differentiable regulated source;no free normal metric,vertex norm or replacement of originalTr_rel."
    },
    {
      "id": "premise:current-original-spectral-action-and-fixed-ordinary-moment-dictionary",
      "titleEN": "Current original spectral action and fixed ordinary coefficient convention",
      "statementEN": "Actual current tfpt2section010:273-315 and v255/v259 statements;ordinary4D coefficients defined byTr exp(-tK²),justified interior asymptotics and actual domain/trace/reference. Known positive boundaryQ not automatically whole bosonic action orlogdet. Entire positiveLaplace mixture class with finite m0,m1,m2. Full original96H/MR R031consumer remains conditional,on specified fixedH reference branch;subtract other actualreference jets explicitly. No newY/scale/profile/trace orfree correction."
    },
    {
      "id": "premise:original-whole-spinor-and-entropic-curvature-consumers-with-given-higgs-response",
      "titleEN": "Original whole spinor and entropic curvature consumers with given Higgs response",
      "statementEN": "ExistingconditionalR031Spin4x96Diracconsumer withLichnerowiczE=−R/4,whole spinconnection,ordinaryconstanttrace/moment,closedorinteriorgeometryandactualreference. Separateactualv475vacuumconsumer−Trlog(I−betaX)on0/1/2formswithX2=2R_abcdonunorderedpairsandunchangedbeta/Einsteinpin;smallcurvatureinlogdomain. Wholealgebraic4Dcurvaturetensor,no maxsymmetricrestrictionbeforevariation. ExistingR031/R045HiggsconsumerwithallY/MR,specifiedbrokenstationarybranchandpositivequadraticradialoperatoratfixedbackground. Retainwhole source,boundreference,Z0,determinants,highervertices;no newlyphysicallyselectedfields,normsorcouplings."
    },
    {
      "id": "premise:actual-original-four-ghost-commuting-projection-admissibility-complex",
      "titleEN": "Actual original four-ghost commuting-projection admissibility complex",
      "statementEN": "Original Qadm=sum eta_j†K_j on H tensor Lambda(C4),with the actual four commuting orthogonal penalty projections,positive finite lambda_j and the supplied positive Dadm spectral calculus. Original macro iC means iota_C,not i times C. Separate normal S2,physical4D geometry,internal representations and auxiliary ghost degrees. Partial ghost trace needs no base trace class;full trace/determinant requires its actual regulator/reference. No physical ghost measure or Brel identification added."
    },
    {
      "id": "premise:actual-smooth-normal-family-with-supplied-unitary-horizontal-connection",
      "titleEN": "Actual smooth normal family with supplied unitary horizontal connection",
      "statementEN": "Actual selfadjoint normal B_Ea family or supplied doubling with smooth finite constant kernel rank,common domain or actual unitary transport and supplied unitary horizontal Hilbert-bundle connection including normal measure. R035 T=WS(Sdagger W²S)^−1/2 applies only for actual fBf transport. Reduced inverse requires isolated0 and sufficient form differentiability. Positive norm restriction concerns the supplied connection kinetic form,not a newly added boson operator. Parallel seed and scalar W derivatives are an explicit subclass only. Index chooses neither B(x),horizontal connection nor physical metric."
    },
    {
      "id": "premise:fixed-original-o1-section-consumer-and-actual-normal-first-order-placement",
      "titleEN": "Fixed original O1 section consumer and actual normal first-order placement",
      "statementEN": "Whole original V=H0(CP1,O(1)) with fixed holomorphic structure;continuous positive scalar normal multiplier W and actual R035 G/T normalization. B0T claim separately requires kerB0=V. First-order normal B=c^a nabla_a+Phi with actual shared domain and horizontal transport only on explicit product chart. No B_Ea=Brel identification. Whole original K=fDgeo f+Brel has exterior Brel;exterior placement alone does not imply no field dependence."
    },
    {
      "id": "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
      "titleEN": "Original quark Higgs consumer and actual positive conditional source mixture",
      "statementEN": "Given whole96 Phi(H)=L(H)+DM with original q and fixed supplied Y/MR;existing constant common quarter circle p=1/4,ell>0,h=p gammaF−i gammaF Phi,second-face C_H. Existing charged left-quark CAR subalgebra is conditionally quasifree with A_H tensor I_color3 and zero anomalous pairs. Actual full normalized H weight must give a positive mixture including Z_F/reference/eta and all factors. Strictness requires nonconstant u=HdaggerH and a nonzero quarkY. No new physical96-fold integration,measure derivation,general variable H(x)/connection or3+1D assumption."
    },
    {
      "id": "premise:fixed-rank-bounded-cutoff-with-ordinary-noncompact-higgs-volume",
      "titleEN": "Fixed finite rank and bounded cutoff with ordinary noncompact Higgs volume",
      "statementEN": "Explicit realization to test,not actual primitive measure derivation:entire O1 coefficient H in C2 with ordinary linear d4H at fixed Gram/background;Hermitian K_N(H),Kref_M(H) of fixed finite ranks,real globally bounded f,all H/reference dependence allowed. Only actual nonzero finite affine Berezin/Pfaffian polynomials,no new96-fold measure. Pure eta phase unit modulus. IR claim at fixed rank and fixed bounded S_B as epsilon|H|2 regulator vanishes. Evaluate other actual measures/support/Jacobians/additional action/unbounded f or joint rank limits separately."
    },
    {
      "id": "premise:whole-constant-original-quarter-source-positive-traceclass-profile-and-flat-higgs-volume",
      "titleEN": "Whole constant original quarter source and positive trace-class baseline on ordinary Higgs volume",
      "statementEN": "Already given whole constant h_H=(n+alpha)gammaF−i gammaF Phi(H) on original H1 quarter domain,alpha1/4or3/4,original96 Hermitian odd Phi(H)=L(H)+DM with fixed Y/MR. Positive Laplace F with finite baseline Balpha=sum_n F((n+alpha)^2/chi^2),fixed chi. Actual geometric mode cuts,optional full positive trace insertion0<=W<=I. Same genuine reference product with finite fixed baseline. Measure test explicitly ordinary d4H onC2,not asserted primitive measure. R031 compact even product only with actual grading-compatible domain and finite baseline."
    },
    {
      "id": "premise:given-o1-mode-isometry-and-weak-invariant-positive-higgs-covariance-marginal",
      "titleEN": "Given O1 isometry and additional weak-invariant positive Higgs covariance marginal",
      "statementEN": "Named identifiability test only:original normal O1 space C2 with actual supplied normalized embedding T and compatible unitary WEAK SU2 identification,normalspin2/weak2/spin4 distinct. Even additional actual positive normalized invariant H marginal with EHH*=cI,c>0 is GRANTED,not derived from index/P=T T*. Fourth moments only where finite. Four real H coordinates and original whole96 Phi/Y/MR unchanged. Fourier readout requires actual positive original Euclidean field source/commuting image and H=T*varphi_N,not a replacement for their origin."
    },
    {
      "id": "premise:literal-whole-source-localization-and-geometric-readout-contracts",
      "titleEN": "Literal whole source and existing localization and geometry contracts",
      "statementEN": "Source audit of existing full E8 current representation,named68D single-word realization,P1 boundary datum,conditional4D selector,free v1000 tensor Hessian and v1013 Hamiltonian class,and explicit Lean axiom compositions. No common physical localization identification assumed.27 website cards and distinct unchanged frozen registry inventoried as metadata;inflation relations only on supplied leading-order branch at common externalN and fixedc3. No current empirical check or statistical independence proof."
    },
    {
      "id": "premise:actual-proper-local-current-weyls-and-bare-native-code-compression",
      "titleEN": "Actual proper-local current Weyls and bare native-code compression",
      "statementEN": "Given full E8_1 Cartan source with actual J-positive neutral Fock embedding and unchanged five homogeneous grade4 codepolynomials,Gram96/8/8/8/1. P is observedcode only,not originalPadm. Bounded Weyls from smooth real8vectorprofiles on any disjoint nonempty propercircleintervals,no Fouriertruncation. Mode1 displacements ae0 andb(e0+e1),real a/b,orthogonal mode1 components0,all higher modes retained. Analytic compact-moment construction provides actual profiles. Test only ordinary product/commutator ofPAP/PBP against whole local word readout. No physicaloperation,newcoupling,4D identification orstate choice assumed."
    },
    {
      "id": "premise:actual-elliptic-quarter-supported-current-and-interval-car-modular-test",
      "titleEN": "Actual elliptic quarter source with supported current and interval CAR modular-time test",
      "statementEN": "Unchanged given free CAR source of original elliptic midpointannulus:occupation c_alpha(r)=(1+exp(4pi(r+alpha)))^-1,alpha1/4 or3/4,entire original theta charge law/current Weyl source. Actual sourcecircleintervalI and extensionbyzero L2(I) embedding. Compared geometricclass:realC5 pointdiffeomorphisms I ontoI,generatorcontinuous atfixed endpoints,unchanged weight1 current smearing f→f composed gamma^-1,arbitrary scalar affine current shifts. No fieldmixing,changed dictionary orprimitivephysicalmeasure identification assumed. Preserve existing constructive neutralMoebius vacuum as distinct provedstate."
    },
    {
      "id": "premise:actual-elliptic-two-face-projection-with-genuine-regional-support",
      "titleEN": "Actual elliptic two-face projection with genuine regional supports",
      "statementEN": "Given originalfree ellipticquarterCAR source c_r=(1+exp(4pi(r+alpha)))^-1,alpha1/4 or3/4,X=sqrt(C(1−C)),fullprojectionP=[[1−C,X],[X,C]] inalreadyprovedpositive transportedtwofacechart. PreserveoriginalGreen/RP/gradedHS dictionary. Regionalembeddings areactualextensionbyzero fortwononemptypropercircleintervals withopencomplements. Partnercomparison retainsgivensourcestate/linearCAR embedding. No primitiveP1measureidentification,newpurification,geometrychoice orGaussianizationafterHiggsintegration. Fullintervalsubalgebra andsingle supportedprobe aredistinctsubsystemcuts."
    },
    {
      "id": "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source",
      "titleEN": "Actual original rightup color triplet with fixed family vector and even color source",
      "statementEN": "Given original96 Phi(H),gamma_L+1,gamma_R−1,fixedp1/4,ell>0. Samefixed eigenvector of GIVEN Yu*Yu,y²>0,inall3originalrightupcolors;notnewphysicalstateselection. M*M=u diag(Yu*Yu,Yd*Yd) givesactualt(u)=1/2+p tanh(ell sqrt(p²+y²u))/(2sqrt(p²+y²u)) on(a,b],a1/2,b(1+tanh(ell p))/2. Reader assumespositiveevenstateinvariantunderoriginalconstantSU3;finite modularlogrequiresfaithfuldensity. Forcednonlinearity and positivemixturetestONLYadditionallyunderR054positive normalizedwholeHmixturewithnonconstantradialu,includingwholedet/Pf,Ref,Eta,Z_F,Z0. Generalreaderdoesnotrequiremixture. No primitiveP1measure,physicaltimeorfull96modularrestrictionclaim."
    },
    {
      "id": "premise:original-common-positive-constant-higgs-law-over-whole-quarter-tower",
      "titleEN": "One original common positive constant Higgs source over the whole quarter mode tower",
      "statementEN": "Samegivenoriginal96Yukawa/Higgs/Majoranaconsumerh_H(p)=p gamma−i gammaPhi(H),samefixedrightupfamilyvectorofgivenYu*Yu,y²>0,allp=n+alpha,n≥0,alpha1/4or3/4,onefixedell>0. Originalellipticnormalizationell2piretained. ONEpositivenormalizedfulllawoverfiniteconstantu=H*Hyieldsallaveragedconditionalt_p(u)=1/2+p tanh(ell sqrt(p²+y²u))/(2sqrt(p²+y²u)). AllRef/Eta/det/Pf/Z0andotherintegratedweightsbelongtothisSAMElaw,notrefittedpermode. NoHmomentorcompactnessassumption. Extra conditionalfermionverticesorH(x)changingthegivenconditionalformareoutofscope. NoidentitywithprimitiveC_Sigma/physicalcarrier/originassumed."
    },
    {
      "id": "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables",
      "titleEN": "Original sixty E8 events with unrefined record and typed Doily observables",
      "statementEN": "Given unchanged Gaussian E8 rays z in C4 of squarednorm4,r_z=I−zz*/2,actualH10=Sym²C4 in originalBellbasis,U_z=Sym²r_z and uniformunrefinedrecordbranchesB_z=U_z/sqrt60. Fifteen nontrivialPauliW_p are directionsmodulosign,Pi±rank2inC4,not15orthogonalsites. OriginaltensormapF defines J_p=F*(W_p⊗I+I⊗W_p)F and rank3 Q_p±=F*(Pi_p±⊗Pi_p±)F onH10. Namedpreparation/finaleffect are mathematicalprobes,notderivedphysicalstate. Noidentitywithstopped/refinedPetersenreader,physicalcuspclockor13Octoberloadedreflection."
    },
    {
      "id": "premise:given-e8-current-vacuum-net-and-original-grade-two-descendant-with-standard-split",
      "titleEN": "Given E8 current vacuum net with original grade2 descendant and strictly nested intervals",
      "statementEN": "SamealreadygivencompactE8_1latticevacuumnetwithOmega/fullL0,originalD5vector10⊗A3Sym²C4isometryE0atweight2andunchangedSU4currentaction. rho(u_z)E0=−iE0(I10⊗U_z),J0(X)E0=E0(I10⊗dGamma2X). ForalreadygivenstrictlynestedcircleintervalsclosureI⊂J,standardsplitfollowsfromfullcharactertraceclassandReehSchlieder. StandardformfixesWwithWABW*=A⊗BforAinA(I),BinA(J)′. Nophysicalregionselection,rawP1derivationofnet/vacuum,replacementoforiginalellipticsourceor3+1spacetimeassumed."
    },
    {
      "id": "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion",
      "titleEN": "Given original elliptic quarter source with supported scalar current insertion",
      "statementEN": "ExistingfreeannulusCARquantizationwithD_a=−i∂+aonperiodicH1,a=1/4and3/4,b=4pi,originalsea/current/H_a. Independentquarterblocksinonegivenmarginalarenotannulusfaces;wholeexistingtwofacegraphretained. ExecuteforwardD_a+epsilonfthroughallrealsmoothsupportedtestinsertionswithsameoriginalnormalization/time. Nochoiceofphysicalf,primitiveP1measure,net/vacuumor3+1derivedbyassumption."
    },
    {
      "id": "premise:original-quark-particle-color-group-counting-on-whole-constant-quarter-source",
      "titleEN": "Original color group counting on the whole constant quarter quark source",
      "statementEN": "Sameoriginalconditionalquasifree36-labelquarkPARTICLECARsubspaceperp=n+a,a=1/4or3/4,b=4pi,h=pgamma−igammaPhi,M=q(H)diag(Yu,Yd),q*q=uI2. GivenYremainfixed. ActualrealSU3liftusespiandJandactsidenticallyonL/Rcolor,notrawleftpiandnot96independentphysicalfermions. Retainwholemodetower,bothquartersatSAMEH,andallcomplement/ref/eta/ZF/H0/Z0inwholeweight. Boundedglobalgroupinsertionnotalreadyidentifiedwithlocal4D,EMormetricsource. PositiveHmixtureonlyunderactualpositivecompleteweight."
    },
    {
      "id": "premise:given-whole-quarter-graph-and-canonical-diagonal-original-color-lift",
      "titleEN": "Given whole quarter graph and canonical diagonal original color lift",
      "statementEN": "GivenwholeG(C)twofaceprojectionandC=(1+exp(4pihH))^-1fromoriginal36quarkparticleCARandgivenY. Sameactualpi/JSU3liftonbothcopiesofthedisplayedcommonSOURCEfiber,[C,U]=0,det36U1. Twoquartersarenottwofaces. OriginalCARRIERPsingandfixedZref[0]quotientretainedverbatim;NOidentificationofcarrierselectorwithoneface/diagonalFockprojectionorPF. Finiteoriginalregulatorsandconvergentfullmodecharacters;positiveHmixtureonlywithactualcompletepositiveweight."
    },
    {
      "id": "premise:original-marked-color-center-on-whole-e8-lattice-current-source",
      "titleEN": "Original marked color center on whole stipulated E8 lattice field source",
      "statementEN": "ExistingstipulatedunitaryE8_1lattice/currentnetinactualD5+A3targetframe,ColorA2=e1-e2,e2-e3,originalcentert=p1+p2-2p3mod3andneutraloscillators. GivenoldWardlambdaA=e3+e6andwholeweak(10,6)block;retainY/Flavor/Alpha,wholefields/clocks. ExecutePsingonTHISbranch,assumenoP1/OS/Padm/P_F/96CARintertwiner. Properlysupportedlocalcurrentswithactualdomains/adjoints. Extensiontheoremonlyintegrallattice/superlatticewithSAMEconformalvector. ReusenativeJboundarywithoutidentifyingJwithsourcequarterfoldorphysicaltime."
    },
    {
      "id": "premise:original-fixed-color-and-folded-ns-cartan-interface",
      "titleEN": "Original fixed color action and actual folded NS charge frame",
      "statementEN": "Retain unchanged E8 root representation, actual rational M in fold-results.json, NS charge space M Z8 and even M D8, R069 color A2=e1-e2,e2-e3 and center w=e1+e2-2e3. Reuse existing four-module AIA parent with actual cocycle/spin/quarter transport. Assume no common physical96-matter map, local inclusion, new gauging, measure law or spacetime from this data identification."
    },
    {
      "id": "premise:actual-thermal-quarter-source-and-retained-spin-parent-mixed-word",
      "titleEN": "Actual thermal quarter source and retained spin parent in mixed words",
      "statementEN": "Given original free CAR frequencies r+alpha,alpha1/4 or3/4,beta4pi,actual eightfold r=8n+j. Use its H=8(L0+delta.p),delta_j=(j+alpha)/8-1/2 and already retained four-module D8 AIA parent with original eps_ext cocycle. Mixed analytic words of actual four R070 color-spinor roots and all eight original odd vector channels,on ordered real cylinder strips with correct adjoint scalars and absolute NS/R trace normalizers. WHOLE P_NS B P_NS yields an explicitly constructed positive extension of given free source,not physical P1 selection. Restrict original color center only at whole-word endpoints. Optional NORMAL whole-parent KMS result only on B(H_parent) at SAME H/beta;no new physical KMS requirement or spin-structure sum."
    },
    {
      "id": "premise:actual-eightfold-arc-residue-source-and-fixed-spin-cartan-insertion",
      "titleEN": "Actual eightfold arc/residue fold and fixed color Cartan insertion",
      "statementEN": "Given actual eta_r=psi((x+2pi r)/8)/sqrt8,chi=Ualpha*eta,Ualpha(r,k)=exp(2pi i(k+alpha)r/8)/sqrt8,both quarters and old point-split bilinears with sea/reference. Original scalar Weyl profiles act diagonally in ARC chart and may differ on different arcs. q=M^T beta for four fixed color spinor roots and unchanged M. b is a smooth real periodic supported test;no new physical state or measure. Distinguish full even CAR on union from additive join of separate even arcs."
    },
    {
      "id": "premise:actual-original-ns-color-center-continuous-density-and-coordinate-net",
      "titleEN": "Actual NS color center,continuous density source and original coordinate algebras",
      "statementEN": "Given original CAR sea r<0,Jm=sum:a_r*a_(r+m):,both quarters,unchanged M and w=M^T(1,1,-2,0,...)=(1,-1,0,-1,-1,-1,0,-1). Z acts on a_r* by exp(2pi i w_(rmod8)/3),P0=(I+Z+Z²)/3 and neutralOmega. Actual Ualpha arc/residue fold and full original circle CAR region algebras given. Test entire continuous scalar current groups and ordinary coordinate supports. No P0=P_adm/P_F or physical P1 source intertwiner assumed."
    },
    {
      "id": "premise:actual-original-full-two-face-graph-and-local-matrix-operations",
      "titleEN": "Actual whole two-face graph and local matrix-operation class",
      "statementEN": "Given original G=[[1-C,X],[X,C]],C(p)=(1+exp(beta p))^-1,X=(2cosh(beta p/2))^-1,p=r+alpha,alpha1/4,3/4,beta4pi,existing wholeCAR source,unchanged M and periodic8fold B=8(-i∂x)+diag(k+alpha). Entire bounded matrix multiplication for reduction,entire smooth unitary multiplication for Fock implementation. No originalOS/Padm field intertwiner assumed."
    },
    {
      "id": "premise:original-blocked-transfer-algebra-and-marked-source-uniformity-audit",
      "titleEN": "Original blocked transfer and marked-source/uniformity audit",
      "statementEN": "Literal QFT004 C6 Green/retained weights/Padm route and Burnside-to-MPS-to-uniform-parent-gap inference. Distinct exact implication witnesses:same wholeCP transfer at fixed markO,and injective volume-varying canonical range3 parents. Not physical TFPT models or countermodels to whole master action."
    },
    {
      "id": "premise:original-bare-c6-fixed-analytic-half-power-and-literal-word-alphabet",
      "titleEN": "Original bare C6 analytic half-power and literal word alphabet",
      "statementEN": "Original v17U6,D_y=yI-deltaU6,Q=D*D+epsilon²I,C=(U+U*)/2,original algebraic delta and y1,1/3,2/3,epsilon>=0. Canonical analytic series with distinct directed letters and full absolute amplitude. No primitive physical measure/spacetime premise;original compressedKstr requires actual reduction proof."
    },
    {
      "id": "premise:actual-original-finite-v990-source-and-historical-parent-recovery",
      "titleEN": "Actual original finitev990 source and historicalparent recovery",
      "statementEN": "Unchangedv990.run andactualH_W0/OPS,suppliedparameters,originalGibbsweight;four-modeCAR onC6linktensorFockC4. Historicalv21/v42,microscopicCAR,given96Hsources inoriginalscopes;no primitivephysical3+1identification."
    },
    {
      "id": "premise:actual-original-finite-car-higgs-force-and-faithful-collective-source",
      "titleEN": "Actual original finite CAR Higgs force and faithful collective source",
      "statementEN": "Whole original real v252/254 oneform Phi(H),fixedYs,quaternionicHcoordinate and actual36quarkpart of givenquasifreesource. Gibbs/Legendre0<C<I,pairing0,YuorYdnonzero;finiteclasswith exactcontinuousSU2doubletaction. No primitivephysicalH/measure/time identification assumed."
    },
    {
      "id": "premise:actual-whole-circle-product-car-force-and-original-time-smearing",
      "titleEN": "Whole original circle CAR force and given time testing",
      "statementEN": "Original constant finite internal Higgs family,fixedYu/Yd,hp=p gamma-igammaPhi(Hstar),p=n+alpha,alpha1/4or3/4,ell>0 given. Pairing-zero quasifree Cp=(1+tanh ell hp)/2,factorizing even Fourier blocks,Ta=-igamma dPhi/dxa. Real Schwartz tests of same time;summable variance exact L2 criterion. No primitive H/physical3+1 or new measure/scale identification assumed."
    },
    {
      "id": "premise:original-constant-circle-local-higgs-force-and-hilbert-schmidt-time-source",
      "titleEN": "Original local Higgs derivative in given constant circle and Hilbert Schmidt time source",
      "statementEN": "Given original circle h=gamma(-i partialtheta+alpha)-igammaPhi(Hstar),periodicH1domain,alpha1/4or3/4,constantPhi/Hstar,fixedoriginalYs. Ta=-igamma dPhi/dxa Hermitian/odd,C=expit(2ell h),pairing0. Real localspace/time tests;strictlocality needs compact smooth supports allpointpairsdistS1>|t-s|. No primitivefield/physical3+1 or newHmeasure identification."
    },
    {
      "id": "premise:literal-archived-global-positive-kernel-finite-measure-map",
      "titleEN": "Literal archived globally positive kernel on finite measures",
      "statementEN": "v42section01631..148 andv45metrology00560..178:finite nonzerononnegative nu on[0,infty),Tnu(dt)=intK(s,t)dnu(s)/intpsi(s)dnu(s) dt,global lowerboundK>=m>0,Lebesguetargetdt,finitepositivedenominator. Scope exactlythiscombination,notactuallydifferentoriginalfinite-support/reference/integrablekernel."
    },
    {
      "id": "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction",
      "titleEN": "Given native Higgs quantum source and actual graded restriction",
      "statementEN": "Existing original96 oneform with fixed supplied Y/MR, non-KO-doubled36 quark part, Hermitian odd forces and given constant circle time. Finite faithful mode Gibbs C=expit K, K=2ell(p gamma+sum xa Ta),ell>0 and original quarter p. P is diagnostic gamma+ subspace, not identified with physical P_F/Padm. Conditional CAR quasifreeness at given background, not after dynamic H integration. Seed252,p1/4,ell.2,r.3 are constructor controls, not selected physical parameters."
    },
    {
      "id": "premise:fixed-puncture-spinor-extension-with-integral-selfdual-pairing",
      "titleEN": "Given spinor-meridian extension with integral selfdual charge pairing",
      "statementEN": "Fixed additive L=(D5+A3)+Z((1/2)^5,m0), m0=e0−1/4·1 from four oriented puncture meridians, actual product W(D5)×C4 action, positive real symmetric invariant form and integral unimodular total charge pairing. Root lengths, carrier scale, orthogonality and evenness are not additional premises. These common completion data are not a physical source derived from P1."
    },
    {
      "id": "premise:r096-same-constant-higgs-twoface-carrier",
      "titleEN": "Same constant Higgs and two-face carrier",
      "statementEN": "R096 compares the same original constant Higgs parameter on the same actual two-face CAR carrier and fixed source caller. Face labels are not internal chiral L/R labels. This is a conditional source comparison, not derivation of the primitive P1 identification."
    },
    {
      "id": "premise:r096-positive-normalized-contraction-mixture",
      "titleEN": "Positive normalized mixture of covariance contractions",
      "statementEN": "For the quantitative two-face defect mu is positive normalized, each conditional covariance P_H is self-adjoint with 0<=P_H<=1 on the same CAR space, and L is the fixed rank-six projector. Pbar uses precisely these weights."
    },
    {
      "id": "premise:r096-conditional-r054-color-wick-fibers",
      "titleEN": "Actual R054 color-symmetric quasifree fibers",
      "statementEN": "The four-word connection uses the actual constant color-symmetric conditionally quasifree R054 fermion fibers on the same carrier: <O>_H=24m(H)^2 and <N>_H=3m(H). The averaged source is not assumed quasifree."
    },
    {
      "id": "premise:r096-same-integrable-unnormalized-weights",
      "titleEN": "Identical integrable unnormalized weights and insertions",
      "statementEN": "The linear identity Z[O]=8Z[mN] uses identical integrable unnormalized weights and conditional fiber values on both sides. Positivity or finite complex normalization is not assumed for this linear statement. Physical use still requires deriving the mixed insertion from the original alphabet."
    },
    {
      "id": "premise:r096-real-face-quark-crossing-positive-radial-law",
      "titleEN": "Real face frame and positive nonconstant radial law",
      "statementEN": "The negative mixed covariance witness uses the original 36-dimensional quark particle module with one common real face frame, ell>0, p>0 and at least one nonzero original Yukawa singular value. Mu is positive normalized and u=H†H is not almost surely constant. Independent face gauge transport is not supplied."
    }
  ],
  "tasks": [
    {
      "id": "task:future-quotient-from-complete-r",
      "problemId": "problem:future-quotient-and-gns-reconstruction",
      "titleEN": "Future quotient from complete r",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:future-equivalence-minimizes-declared-answer-process"
      ],
      "requiredPremiseIds": [
        "premise:future-answer-functional"
      ],
      "successCriterionEN": "All finite sequences and allowed continuations have declared answers, so equivalence classes and induced operations are well-defined.",
      "nextActionEN": "Reuse the result only relative to this alphabet.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:conditional-gns-from-supplied-k",
      "problemId": "problem:future-quotient-and-gns-reconstruction",
      "titleEN": "Conditional GNS reconstruction from supplied K",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:positive-word-kernel-reconstructs-cyclic-gns"
      ],
      "requiredPremiseIds": [
        "premise:positive-word-kernel-null-stability"
      ],
      "successCriterionEN": "Complete positive K with reference, adjunction, and continuation stability determines the cyclic representation up to unitary equivalence.",
      "nextActionEN": "Reuse this conditional GNS result without marking K selection as solved.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:select-complete-k-from-original-source",
      "problemId": "problem:future-quotient-and-gns-reconstruction",
      "titleEN": "Select complete K from the original source",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:future-quotient-from-complete-r",
        "task:conditional-gns-from-supplied-k"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Original principles supply a concrete joint answer/K functional and experiment alphabet, positivity, reference, and null stability reproducing the intended physical source process.",
      "nextActionEN": "Derive K and its operation alphabet from P1/P2 and original source structure; no GNS theorem replaces this selection.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:read-operational-inputs",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Record the input status of the operational seed",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:operational-seed-is-input"
      ],
      "requiredPremiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "The defined seed data and the outputs induced from them are documented separately.",
      "nextActionEN": "Treat as established; do not count a later GNS construction as a source selector.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-physical-source-selector",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Find the original selector for source/state/event",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:read-operational-inputs"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "A rule derived from P1/P2 and original definitions jointly determines A_loc, omega, tau_t, events, and their field readout.",
      "nextActionEN": null,
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-native-source-common-time-thermal-family",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "The same source supplies Hamiltonian, time and thermal state",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:native-source-common-time-thermal-family"
      ],
      "requiredPremiseIds": [
        "premise:declared-native-round20-source"
      ],
      "successCriterionEN": "Finite spatial volume and original neutral scalar/charge source; no spatial continuum or P1/P2 selection claim.",
      "nextActionEN": "Reuse the existing proof within its scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-native-grade-carry-and-memory",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Marking and necessary memory are connected within the given source",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:native-grade-carry-and-memory"
      ],
      "requiredPremiseIds": [
        "premise:declared-native-round20-source"
      ],
      "successCriterionEN": "Given source, grade and J>0; the two-time kernel is neither a physical measuring instrument nor a universal three-dimensional memory realization.",
      "nextActionEN": "Reuse the existing proof within its scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-even-seam-global-operator-factorization",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "A common global seam-operator factorization exists",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:even-seam-global-operator-factorization"
      ],
      "requiredPremiseIds": [
        "premise:stipulated-even-e8-seam-lift"
      ],
      "successCriterionEN": "Global charge transports in the stipulated even completion; not local vertex insertions, an ordinary-local odd CAR/E8 inclusion or event dynamics.",
      "nextActionEN": "Reuse the existing proof within its scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-source-generated-marking-classification",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Reuse complete source-character classification",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:source-generated-marking-classification"
      ],
      "requiredPremiseIds": [
        "premise:full-normalized-charge-time-character-family",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:actual-chiral-opposite-quarter-domains"
      ],
      "successCriterionEN": "All four-torsion characters of the given source completely classified and their projectors reconstructed without target insertion.",
      "nextActionEN": "Reuse the result; do not restart the same finite family as a new search.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-conditional-seam-operator-reconstruction",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Reuse conditional joint seam reconstruction",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:conditional-seam-field-state-time-reconstruction",
        "finding:continuous-hardy-seam-classification"
      ],
      "requiredPremiseIds": [
        "premise:actual-wold-source-operator-hypotheses",
        "premise:charged-car-negative-sea-source",
        "premise:fixed-scalar-quarter-hardy-source"
      ],
      "successCriterionEN": "Analytic theorem with independent review in the explicitly supplied model.",
      "nextActionEN": "Use the result under these premises; do not search the same class again.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-same-source-seam-energy-selection",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Reuse the complete scalar energy theorem",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:same-source-seam-energy-selection"
      ],
      "requiredPremiseIds": [
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:charged-car-negative-sea-source"
      ],
      "successCriterionEN": "Analytic theorem with independent review in the explicitly supplied model.",
      "nextActionEN": "Use the result under these premises; do not search the same class again.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compare-process-first-reconstruction-routes",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Compare three process reconstruction routes using discriminating tests",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:read-operational-inputs"
      ],
      "resolutionIds": [
        "finding:process-composition-and-cyclicity-do-not-select-algebra",
        "finding:quartic-shape-selects-32-only-with-source-sign"
      ],
      "requiredPremiseIds": [
        "premise:typed-source-structures",
        "premise:process-composition-finite-controls",
        "premise:unmarked-five-traceless-hermitian-quartic"
      ],
      "successCriterionEN": "Observation, composition and stability routes have concrete conditional theorems/controls with added inputs; physical source derivation remains open.",
      "nextActionEN": "Source-derived interventions first; apply quartic theorem only after deriving the field, trace constraint and positive coefficient.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-native-joint-operator-object",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Reconstruct the actual common native operator object",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:native-symmetric-quartic-erasure-common-object",
        "finding:joint-native-algebra-normalizer-and-response-orbit",
        "finding:native-galois-intertwiner-unique-logical-marked-orbit"
      ],
      "requiredPremiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "successCriterionEN": "Connect at least three existing structures through actual intertwiners and algebra/commutant; type the clock actions.",
      "nextActionEN": "Reuse the common core and Galois map; begin no new dimension matching or abstract reset.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-native-source-event-menu-dynamics",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Classify native rates and coherent residual channels",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:reconstruct-native-joint-operator-object"
      ],
      "resolutionIds": [
        "finding:native-reflection-full-four-five-generators-rate-injectivity",
        "finding:complete-logical-readout-native-covariant-residual-classification"
      ],
      "requiredPremiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:fixed-complete-four-five-primitive-reflection-generators",
        "premise:complete-logical-nondisturbance-native-covariance",
        "premise:coherent-block-source-algebra-operation-menu"
      ],
      "successCriterionEN": "Separate primitive reflections from coherent algebra closure and determine the stated dynamical classes with their premises.",
      "nextActionEN": "Preserve rigidity with complete4/5 generators and the precisely scoped Dq class; do not call them physical source selection.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-common-clock-lift-and-original-event-menu",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Determine the common original clock lift and event menu",
      "kind": "assessment",
      "status": "open",
      "dependsOn": [
        "task:reconstruct-native-joint-operator-object",
        "task:classify-native-source-event-menu-dynamics"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Supply the actual common4/5/20 continuation of the existing coherent clock polynomial and the original-source event menu; jointly check normalization, erasure, products and full source time. Determine the complete4/5 generators or their currently free data from it.",
      "nextActionEN": null,
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-polar-mark-and-test-native-quarter-lifts",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Reconstruct original mark and test native clock continuation",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:reconstruct-native-joint-operator-object"
      ],
      "resolutionIds": [
        "finding:original-polar-mark-clock-centralizer-orbit",
        "finding:actual-quartic-code-product-stabilizer-quarter-exclusion",
        "finding:original-decoder-versus-native-quarter-polynomial-erasure-test"
      ],
      "requiredPremiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:original-marked-simplex-positive-polar-rule",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:original-erasure-decoder-and-same-native-quarter-polynomial",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "successCriterionEN": "Consistently connect actual positive polar transport, unchanged four-clock and original decoder; test product lifts and the same native polynomial continuation on a decisive input.",
      "nextActionEN": "Reuse these conditional theorems. Do not repeat the same three fixed points, product lifts or four reflection lifts without a changed premise.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-polar-fibre-and-test-native-parent-transport",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Classify polar fibre and test existing native selection mechanisms",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:reconstruct-polar-mark-and-test-native-quarter-lifts"
      ],
      "resolutionIds": [
        "finding:native-clock-compatible-polar-fibre-and-canonical-distance",
        "finding:native-moment-parent-and-product-path-selection-boundary"
      ],
      "requiredPremiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:original-native-fourth-moment-parent",
        "premise:local-product-code-orbit-geometric-parallel-transport"
      ],
      "successCriterionEN": "Completely classify actual clock-compatible marking fibre, characterize the original polar rule canonically and test existing moment parent/geometric product transport against the target operation.",
      "nextActionEN": "Reuse these scoped theorems; do not reoptimize this fibre or known parent without a new original interaction.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:test-original-current-response-and-native-code-dictionary",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Test original current response and actual code dictionary",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:classify-polar-fibre-and-test-native-parent-transport"
      ],
      "resolutionIds": [
        "finding:original-e8-current-response-and-full-quarter-lifts",
        "finding:literal-charged-current-register-dictionary-fails-quarter",
        "finding:native-cartan-code-inner-e8-stabilizer-excludes-marked-quarter"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark",
        "premise:original-coupled-determinant-event-cover",
        "premise:literal-charged-current-native-register-dictionary",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:compact-inner-e8-zero-mode-operation-class"
      ],
      "successCriterionEN": "Jointly test original nonscalar response, full clock order and actual current/register and Cartan-code maps.",
      "nextActionEN": "Preserve the conditional positive source response and do not retry either excluded dictionary using fitted current pulses.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:test-original-neutral-quadratic-and-first-mixed-source-response",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Test original neutral quadratic and first mixed source response",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:test-original-current-response-and-native-code-dictionary"
      ],
      "resolutionIds": [
        "finding:native-code-neutral-weight-two-action-and-global-clock-exclusion",
        "finding:original-neutral-root-mixed-response-derived"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:solely-neutral-local-weight-two-zero-mode-class"
      ],
      "successCriterionEN": "Test actual B48/R fields and complete neutral weight-two class on existing code; compute first joint source variation without a new coupling.",
      "nextActionEN": "Preserve separate exclusions; continue at ordered return response of actual combined source without declaring projection an execution rule.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-actual-mixed-ordered-code-erasure-return",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Derive ordered mixed code/erasure return",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:test-original-neutral-quadratic-and-first-mixed-source-response"
      ],
      "resolutionIds": [
        "finding:actual-mixed-ordered-return-on-native-quartic-code",
        "finding:mixed-return-spectrum-does-not-select-original-polar-mark",
        "finding:actual-mixed-return-fails-native-trimer-erasure-lift",
        "finding:strict-trace-gap-excludes-positive-mixed-return-reweighting"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:common-unnormalized-positive-return-erasure-test"
      ],
      "successCriterionEN": "Evaluate original isometry, actual code/erasure return and marking/clock comparisons without free coupling or intermediate projection.",
      "nextActionEN": "Preserve strict positive-reweighting exclusion; derive another original return insertion or longer charge-balanced history before claiming a new execution.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:test-full-source-return-code-closure-and-erasure-ward",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Test full source-return code closure and erasure Ward terms",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:derive-actual-mixed-ordered-code-erasure-return"
      ],
      "resolutionIds": [
        "finding:original-source-erasure-ward-terms-derived",
        "finding:uncompressed-original-mixed-return-does-not-preserve-code",
        "finding:original-root-response-sum-also-leaks-from-code"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles"
      ],
      "successCriterionEN": "Test full code closure with exact code-orthogonal witness and original sum; derive original source-erasure interchange without free coupling.",
      "nextActionEN": "First derive the originally specified full source operation/history with code closure (I-Pi)U_source Pi=0 and actual erasure action. If protection/recovery is required, derive it from same source. Do not insert code projection, postselection, measurement/reset rule, free longer history or independent20/5 normalization. Prior rank5 matrix is endpoint compression only; individual return and original240 sum demonstrably fail code closure. Only after full-operation test passes infer clock, marking and3+2 from its action. General original higher processes remain open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-full-source-return-exterior-memory",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Derive full source feedback and necessary memory",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:test-full-source-return-code-closure-and-erasure-ward"
      ],
      "resolutionIds": [
        "finding:original-full-source-return-exterior-feedback-derived",
        "finding:original-return-requires-memory-in-every-code-direction"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:specified-original-pair-ordered-response-composition"
      ],
      "successCriterionEN": "Retain actual original off-code states and compute feedback without fitted coupling or executed projection; decide whether same family admits closed five-dimensional linear continuation.",
      "nextActionEN": "Full feedback is derived for existing single pair: memory kernel B*D^kB, strict rank5 feedback Gram and Hankel rank lower bound10. Do not again use K^n as full history or build a freely chosen10D model. Next original-origin question: which actual P1-dependent field/boundary variation determines ordered insertion/history with4/5/20 readout and common time? Retain its complete source with charges, modes and memory. Code closure is required only for claimed closed code operations; do not impose it as a new P1 axiom. No clock/polar/3+2 origin claim without physical history selection; no fitted root weights, measurement/reset/projection rule or relative20/5 renormalization.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-all-mode-canonical-conformal-erasure-bridge",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Derive original all-mode conformal/erasure bridge",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:derive-full-source-return-exterior-memory"
      ],
      "resolutionIds": [
        "finding:native-conformal-primary-multiplicity-source-factorization",
        "finding:canonical-conformal-erasure-forces-primary-twenty-carry",
        "finding:all-canonical-stress-histories-scalar-on-native-code"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:canonical-source-stress-all-mode-history",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "successCriterionEN": "Derive actually original canonical geometric source histories including higher modes on4/5/20 and first forced erasure correction/native sector action without coupling choice; determine whether this class selects marked clock.",
      "nextActionEN": "Original canonical geometric route is now settled for ALL stress modes: common primary cycles on4/5/20, logically scalar action even with excursions/return, no R5/P2. Actual erasure Ward action additionally forces neutral weight5 twenty with fixed rho5 tensor bar rho4 action and norm78/85; no root/family branch required. Preserve this new source bridge. Next origin question within accepted native TFPT core: which actually original NONSTRESS field/boundary intervention and ordered insertion is allowed, and how does it act on full source with new carry, actual erasure and memory? Do not further vary pure conformal schedules, equate clocks from seed phases, or optimize freely combined carry/mode histories. Physical selection and polar/3+2 coupling remain open; assume no new measurement, projection, coupling or readout rule.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-full-local-cartan-insertion-and-ordering",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Check full local Cartan insertion and ordered product",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:derive-all-mode-canonical-conformal-erasure-bridge"
      ],
      "resolutionIds": [
        "finding:original-local-current-ope-forces-erasure-and-carry",
        "finding:all-real-local-cartan-profiles-erasure-third-bound",
        "finding:closed-cartan-weyl-histories-only-logical-phase"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-cartan-current-local-smearing-and-weyl-class",
        "premise:canonical-source-stress-all-mode-history",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "successCriterionEN": "Decide on actual original current field whether pure native erasure is local; derive regular carry and full local response and test stated ordered Cartan-Weyl class without fitted algebra.",
      "nextActionEN": "Full original local Cartan-current OPE now connects native4/5 with singular erasure20 AND regular primary carry20. Pure erasure is global Fourier mode, not local insertion; every actual local Hermitian Cartan profile retains further source modes, erasure norm fraction<1/3. Finite Cartan-Weyl histories are fully fixed and have only phase at closed code endpoints. Preserve bridge; do not optimize Cartan profiles/pulses or pure stress schedules. First open physical map: which original P1 boundary variation induces a specified NON-Cartan/composite insertion in accepted E8 source net, and how is its A/A*-invariant physical sector action derived? Determine actual insertion map and full ordered response with charges/carry/memory before logical compression. Do not identify code with H_adm, contour-extracted mode with local intervention or given field with selected coupling. Preserve prior root-zero-mode and paired-process exclusions without an all-E8/P1 no-go union. Physical time/state and polar/3+2 selection remain open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-full-local-source-hull-and-unprojected-returns",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Determine full local source hull and unfiltered returns",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:derive-full-local-cartan-insertion-and-ordering"
      ],
      "resolutionIds": [
        "finding:full-existing-local-e8-hull-of-native-code",
        "finding:full-local-quartic-wick-ladder-and-unprojected-native-actions",
        "finding:full-e8-current-products-fix-stress-and-exterior-ward-cancellation",
        "finding:full-source-simplex-does-not-select-original-polar-mark"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:native-g31-concrete-event-representation",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "successCriterionEN": "Determine minimal full source hull, products, exterior returns and symmetry decomposition without closedcode or newcoupling.",
      "nextActionEN": "Preserve17Oct correction:C5 is observer slice, not dynamically closed fundamental system. Full local hullH_E8 retains both20s/allcharges/modes. Complete quartic Wick ladder gives actual code/erasure mode action, fullM5 availability, same canonicalstress and newly UNMARKED originalW6 simplex from intrinsic10-ray geometry withoutW6input/fitrotation. Source recovers concrete separately used structure. Sixaxes live on intrinsic projective real locus; fullcomplex space has continuous additional minima, no physical real-state selection. None of15simplexpair planes is originalpolarP2. Next decisive bridge: which ORIGINAL seam/state/event data select actual transport/outcome and possible symmetry breaking in NOW derived UNCONTRACTED complex local source tensors? Compare their actual sector action with originalpolar/clocks first. No new minimizationrule fromM(w), selectingpairplane or newcoupling. PhysicalP1 pullback remains open, not automatic abstractreset. Keepfull exterior/memory paths and prior exclusions; invariantfullycontractedLINEAR returns are already scalar, not everycovariantchannel. No3+2/Flavor/timepromotion.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-unmarked-native-simplex-from-local-quartic-ope",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Derive unmarked native simplex from local quartic product",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:derive-full-local-source-hull-and-unprojected-returns"
      ],
      "resolutionIds": [
        "finding:unmarked-native-w6-simplex-from-full-quartic-ope",
        "finding:full-source-simplex-does-not-select-original-polar-mark"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:native-g31-concrete-event-representation",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "successCriterionEN": "Reconstruct a separately used native structure from full local product without its target coordinates; literal comparison only afterwards, physical selection separate.",
      "nextActionEN": "Preserve17Oct correction:C5 is observer slice, not dynamically closed fundamental system. Full local hullH_E8 retains both20s/allcharges/modes. Complete quartic Wick ladder gives actual code/erasure mode action, fullM5 availability, same canonicalstress and newly UNMARKED originalW6 simplex from intrinsic10-ray geometry withoutW6input/fitrotation. Source recovers concrete separately used structure. Sixaxes live on intrinsic projective real locus; fullcomplex space has continuous additional minima, no physical real-state selection. None of15simplexpair planes is originalpolarP2. Next decisive bridge: which ORIGINAL seam/state/event data select actual transport/outcome and possible symmetry breaking in NOW derived UNCONTRACTED complex local source tensors? Compare their actual sector action with originalpolar/clocks first. No new minimizationrule fromM(w), selectingpairplane or newcoupling. PhysicalP1 pullback remains open, not automatic abstractreset. Keepfull exterior/memory paths and prior exclusions; invariantfullycontractedLINEAR returns are already scalar, not everycovariantchannel. No3+2/Flavor/timepromotion.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:test-original-seam-state-event-data-on-full-field-tensors",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Test original seam/state/event data on full field tensors",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:reconstruct-unmarked-native-simplex-from-local-quartic-ope"
      ],
      "resolutionIds": [
        "finding:original-full-field-event-gram-reconstructs-relative-polar-mark",
        "finding:raw-event-state-positivity-does-not-execute-polar-normalization",
        "finding:determinant-cover-not-literal-full-cartan-lattice-event"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark",
        "premise:original-native-event-difference-fields-and-state-controls"
      ],
      "successCriterionEN": "Determine actual event/state response on fulloriginalfieldtensors and whether given normalization/sectoraction yieldsoriginalpolar/P2 withoutnewselectionrule.",
      "nextActionEN": "17Oct continuation: tested full native eventfields with allWick/Taylor terms. Positive RELATIVE responseR^−1/2 KW R^−1/2 literally reconstructsoriginalP2 withouttargetangle/SMcoupling. Do not labelphysicalselection: rawresponses nonorthogonal,GNS fixesmetric notpositiveprocessing; fullmarkedweight8statecontrol retainsdifferentnorms. Decisivenowconcretequestion: do ORIGINAL boundary/eventdata derive positive relative normalization and physical record/readout object in samefullfieldprocess? Determine actual variation of original relative spectralaction alongnative eventdirections withstate, coherentreference,output; do not fittheseobjects. Separate unmodifiedr fromcoupled determinantlifth: latter hasdifferentcoherentGram andno unchangedCartan-latticeautomorphismdictionary. Earlierchargedlift isdifferentrepresentation and remainsvalid. Retainjoint4/5/20/carry/charge/mode/exterior/memory action/time beforephysicalidentification. Noabstractreset,freelywhiteninginstrument,positiveroot/familyweights,closedC5 orphysical3+2/Flavor/timepromotion.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-intrinsic-event-geometry-and-composition",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Check intrinsic event geometry and composition",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:test-original-seam-state-event-data-on-full-field-tensors"
      ],
      "resolutionIds": [
        "finding:clock-free-quartic-product-spectral-sectors-and-native-five",
        "finding:six-complex-native-simplex-rays-from-holomorphic-product-quadrics",
        "finding:intrinsic-relative-response-covariance-and-state-boundary",
        "finding:intrinsic-event-composition-retains-shared-source-and-correlation-data",
        "finding:clock-free-event-geometry-fixes-clock-class-and-mark-orbit-not-member"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock"
      ],
      "successCriterionEN": "Testintrinsicgeometryunderbasis,state,localproducts,compositionwithoutpolar/clock/3+2selector;linkatleasttwoexistingTFPTstructuresorexactlyidentify missinginformation.",
      "nextActionEN": "User159c5316: donotautomaticallyreturntoinstrument/whiteningorigin. Intrinsicstructuretestcompleted: actualholomorphicquarticmultiplicationgivescanonical1+5+9andactualnative5intertwineratweight8;nineproductquadricsreconstructexactlysixCOMPLEXrayswithoutrealform,q,clock,N,P2input,thenliteraloriginalNmatch. Basis/metric/OPE-adjointcovariant;centralOPEtensorsalgebraicallyfixed,fullstateresponses/correlationsdependent. Fullcomposition/100erasureproductrulesretained;nosame-source/correlatedresponsefromtensoringmarginals. All15edges/60polarmarksconstructedclockfree;logicalnoncommutingpairsproduce40threeclockclassandsame60markorbit,noselectedclock/physical3+2. Nextextendsameactualproduct/correlationobjecttononcommutingoriginaleventhistories,oridentifyadditionalORIGINALseam/statedatumreducingS6/S5tofiniteflagq+twosubset;moreunmarkedalgebracannotbreakunique rank2selection. Native4/20/fullfieldclockliftsseparate,notquotientorderidentification. Nophysicalnullcomponentrule,couplingfit,closedC5,abstractreset. RawP1source/physicalstate/timeandfull3+2originremainopen.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:test-original-seam-state-data-on-sixty-native-flags",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Testoriginalseam/statedataon60nativeflags",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:classify-intrinsic-event-geometry-and-composition"
      ],
      "resolutionIds": [
        "finding:original-charged-seam-character-recovers-global-native-event-pair",
        "finding:internal-seam-vacuum-and-original-neutral-tensor-do-not-select-flag-root",
        "finding:actual-quarter-fold-shift-removes-native-symmetry-obstruction-without-flag-selector",
        "finding:fold-shift-equivariance-needs-actual-source-response-map-not-another-symmetry-no-go"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector"
      ],
      "successCriterionEN": "Withoutfittedclock/coupling/ruletestwhetheroriginaladditionaldataselectq+pair;distinguishinternalcharacter,vacuum,actualquarterfoldstate.",
      "nextActionEN": "Originalseam/stateon60flagstestcompleted: internalchargedcharacterrecoversglobalS01butnotq(fourorbit);originalR/48leavesq4↔5underexplicitfullsourceisometry,all4omissions. DONOTextendtoallP1/actualstateNoGo. Actualchargedquarterfoldg²hasorder8,notinternalZ4. Originaldαstabilizer1;oldSYMmetryobstructionGONE,butall60flagspassfixedpointtest. DerivefulloriginalCARcovariance/field/normalorderingtransport(F Cα F*,actualseam,adjoint,time)intocurrentnativeCartan/quarticfieldsandchargedintermediates. disshift/timediagnostic,notequaltovacuumexpectation/fullcovariance. Compareactualsource-definedresponsewith6rays/60flags;nofittedclock,compensation,coupling,maxoverlap,minimizer. Nomoreneutralvacuumtensorsasdselector,noabstractreset/closedC5. Retainpositiveglobalpairbridge;physical3+2/commonclock/stateoriginopen.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-fold-state-quartic-response-and-test-original-winding",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Derivefoldstatequarticresponseandtestoriginalwinding",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:test-original-seam-state-data-on-sixty-native-flags"
      ],
      "resolutionIds": [
        "finding:original-fold-covariance-current-counterterm-and-quartic-twisted-transport",
        "finding:fold-state-full-quartic-kernel-and-erasure-protected-low-order-response",
        "finding:original-fold-quartic-mean-and-spectral-responses-do-not-match-sixty-flags",
        "finding:original-winding-full-state-response-removes-vacuum-rank-two-shortcut"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport"
      ],
      "successCriterionEN": "Transportoriginalcovariance/normalorderingintocurrentnativefieldsandcompareactualresponse/originalwindingto6rays/60flagswithoutfittedclock/coupling/selection.",
      "nextActionEN": "Continue17Oct: originalfoldstate/fieldtransportexplicitinfixedconformalcurrentdictionary. SameFCFdiagonalizationnocopies,counterterm±δfromkernel,quarticYdFi=:fi(h+b/z):,full2point/allmodeBk;actualerasureforcesD3scalar85/256,anisotropyorder4. Direct6ray/60flagmean/kernel/spectraltestsNEGATIVE,norefit. ORIGINALglobalW4withcharge/time/ΓGonfullR_btested:unshiftedoverlaprank2,actualsourcecrossrank5,fullGrampreserved,time7/9. Novacuumchart2+3asphysicalselection. NoclosedC5/performedprojection,GmixesoppositepolarizationnotU4clock. FixedNScurrentidentitystillconditional,M/Oalonenophysicalselection. DerivePARTICULARoriginalobservable/interventionhistoryandadmissibleoutput/reference,thenevaluatewithcompletedtwistedresponse,retainingchargedz^(dβ),carry,modes,sourcetime. Nomoreneutralvacuumreplay/arbitraryspectrum/filters/fittedclockselector. Retainpositiveglobalseampair;physicalq/S,3+2/commonP1originopen,noabstractreset/promotion.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-original-density-geometric-response-and-time-winding-normal-form",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Derive original density/geometric response and whole time-winding class",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:derive-fold-state-quartic-response-and-test-original-winding"
      ],
      "resolutionIds": [
        "finding:original-source-global-time-winding-history-factorization",
        "finding:original-local-density-folds-to-correlated-root-current-and-erasure-response",
        "finding:original-current-all-mode-energy-and-geometric-stress-bridge",
        "finding:original-current-geometric-response-pair-has-no-common-polar-sector"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress",
        "premise:charged-car-negative-sea-source",
        "premise:fixed-scalar-quarter-hardy-source"
      ],
      "successCriterionEN": "Supply actual original field/process path with full state/charges/modes/erasure and exact ordered action, without fitting coupling/algebra/clock.",
      "nextActionEN": "17Oct original density/geometric bridge: all global time/winding words reduced, no more waiting-time/power scan. Original local c1 density folds to correlated non-Cartan root currents with fixed coefficients; full actual CAR state response, erasure20, all32 energy modes and original c1 stress Wards computed. Do not identify twisted folded Yd(T)/original Lcal+-1 with old unshifted stress/primary-vacuum theorem. Density/geometric Riesz response pair irreducible M5; mode30 rank2 matches no60polarflags, no Coxeter dictionary from number30. Next connect full local products/ordered responses of THESE originally fixed c1 density/geometric fields to existing intrinsic six-ray event geometry and original seam character/admissible output. No free root weights/selected profiles/new clock/measurement/filter/eigenvalue grouping. Retain every charge/carry/mode/correlation path and conditional physical reference; global pair retained, physicalq/S/P1/3+2 open. No abstract reset or closed-C5 axiom.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-original-full-current-kernel-field-products-and-seam-grading",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Derive full original current/field products and original seam grading",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:derive-original-density-geometric-response-and-time-winding-normal-form"
      ],
      "resolutionIds": [
        "finding:original-current-ordered-hall-kernel-and-actual-folded-field-products",
        "finding:original-seam-grades-full-density-geometric-products-and-energy-response",
        "finding:original-seam-complete-density-grading-not-sharp-32-input-sectors",
        "finding:original-density-all-profile-mean-work-scalar-on-native-packet"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "successCriterionEN": "Supply actual ordered source response without profile/clock fitting, retaining full folded fields/state/seam and testing sharp3+2 reading.",
      "nextActionEN": "17Oct full original current/field response available: exact Maya/Hall state intertwiner with all32 CAR vectors, closed multi-profile/time history kernel retaining ALL Gaussian tails, actual folded-field products on eight original preimages with same ordered Calpha/1-Calpha point splitting. No weight32 point-field identification. Internal seam grades products mod4; all four full energy classes strictly fullrank, commutant1, no sharp3+2 input reading. Mean density work scalar on wholeK4 packet; full coherence nonscalar. Next test ORIGINAL P1 boundary action and its claimed admissible physical variations/output data against THIS explicit full-field path: does it supply a selected source family/response functional or intrinsic event relation with fixed reference/admissibility? Name first underived dotD/dotB/dotQ or output functional and work there. Reuse existing P1-INSERTION-TANGENT/action-response-sewing results, no generic inverseKMS/composition replay. No free profile weights/modes29/30/newclock/measurement/positiveprocessing/mark-commutation axiom. Retain global pair/sixrays/60flags/E8 whole; physicalq/S/3+2/P1 open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-original-p1-gap-action-differential-and-test-native-spectral-component",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Derive original P1 gap-scale term and test direct native spectral bridge",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:derive-original-full-current-kernel-field-products-and-seam-grading"
      ],
      "resolutionIds": [
        "finding:original-p1-gap-normalized-action-covector-and-scalar-holonomy-class",
        "finding:original-p1-gap-car-component-not-native-sharp-32-event"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress",
        "premise:declared-p1-p2",
        "premise:typed-source-structures",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:charged-car-negative-sea-source",
        "premise:original-gap-normalized-primitive-relative-action"
      ],
      "successCriterionEN": "Evaluate explicit original source function without profile/measurement fitting and test smallest actually source-fixed3+2 bridge on full outputs. Keep physical overall selection separately open.",
      "nextActionEN": "17Oct originalP1 action source-audited including chi=1/lambda and full gap-scale term. It is a covector on GIVEN source variations; physical tangent/event not derived. Whole scalar-potential class of actual quarter source gauge equivalent to mean; fixedholonomy fixesgap/chi, not field response. Original canonical gapCAR projector(mode0/-1) tested on fullnative inputs: gap/complement rank5 each, nonprojective response, exterior rank5; NO sharp3+2 identification or local insertion. Do NOT replay this test/profile scan/KMSinverse/knownmasterbarrier/defectwellordering. Needed is first actual ORIGINAL family/connection from native local field/event arguments toD+,B_Sigma,bulk/domain/state, or actual minimal operator-fiber classification supplying it. Existing Higgsrank2/branchYukawa/d_disc* assumptions cannot replace this map. No arbitrary matrixpotential or linearj.F coupling. Two physical tasks remainopen; retain whole original E8/fields/correlations/sixrays/60flags/globalpair.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-scalar-first-order-source-fiber-with-actual-seam-time-ward",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Classify whole scalar first-order fiber with actual time-seam Ward",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:derive-original-p1-gap-action-differential-and-test-native-spectral-component"
      ],
      "resolutionIds": [
        "finding:complete-positive-scalar-first-order-circle-source-normal-form",
        "finding:fixed-source-time-seam-ward-rigidifies-scalar-principal-symbol-with-carry",
        "finding:unit-spectral-flow-gap-and-four-marks-do-not-imply-fixed-source-ward"
      ],
      "requiredPremiseIds": [
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures",
        "premise:positive-scalar-first-order-source-comparison-class",
        "premise:given-original-fixed-one-particle-time-winding-ward"
      ],
      "successCriterionEN": "Treat whole variable principal-symbol class/domains/marks/gauge transport/spectralflow exactly; distinguish stronger original operator relation frombareP1 index without fitting source.",
      "nextActionEN": "17Oct whole smooth positive scalar LOCAL firstorderfiber classified includinga(theta),state/marktransport/globalNcarry. No more scalar speed/profile scan. UnitSF+gap+quarterholonomy+fourmarks/quartercovariance do NOT force fixedtime-seamWard; exactk4control. SameactualgivenWard[B,Z]=Z forcesa1; continuousmarkedresidualfiber onlygaugetransport,globalNmod4timequarterphase/4Zseacarryexplicit. Sourcefiberresult,notWardorigin. Nextoriginalproof must supply physical localoperator/representation map and thisstrongerjointtimeseamrelation fromP1,or actualoriginalnon-scalar/nonlocaldirection withlocalization. Nochosenmatrixpotential/Yukawa/measurementrule. Do not promoteoneparticleunitarity tounchangedFocksea/Schwarzian/relativeaction. RetainwholeE8/products/sixrays/60flags/globalpair andtwoopenphysicaltasks;3+2notderived.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compare-four-native-starts-with-full-original-fold-state-response",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Compare four starts with complete original state response",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:test-original-seam-state-data-on-sixty-native-flags",
        "task:derive-fold-state-quartic-response-and-test-original-winding"
      ],
      "resolutionIds": [
        "finding:four-native-starts-have-distinct-original-fold-state-correlations",
        "finding:four-starts-full-joint-kernel-and-charged-covariant-transport",
        "finding:four-native-polar-marks-not-fixed-source-state-gauge-equivalent"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:four-starts-fixed-state-versus-whole-datum-comparison"
      ],
      "successCriterionEN": "Separatefixed-stateequivalencefromwhole-datumtransport;computeactualfield/charge/time/erasureresponsesandinvariantdifferencewithoutcoupling/selectionrule.",
      "nextActionEN": "18Oct: The four starts and polar planes have pairwise distinct correlation invariants in the SAME original fold/NS field dictionary. Whole E8 datum transport is covariance, not fixed-state symmetry or physical gauge proof; odd-CAR only separately transported passively. Do not maximize c1 or polar trace or repeat fixed-point/profile tests. Check the actual original preparation, event or output datum for which already distinguishable relation is instantiated. No fitted coupling, invented detector or four P1 theories. Retain full E8/erasure/time/carry response; physical source and q/S/3+2 remain open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:audit-original-source-minimality-and-domain-theorem",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Audit original minimality and analytic-domain assertion",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-minimality-does-not-reconstruct-operational-source",
        "finding:generic-first-order-relative-bound-zero-counterexample-and-correct-domain-repair"
      ],
      "requiredPremiseIds": [
        "premise:literal-boundary-minimality-and-first-order-domain-statements",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions"
      ],
      "successCriterionEN": "Locate the first missing or false implication in the original source and give a valid theorem with explicit hypotheses.",
      "nextActionEN": "Reuse the specific audit and conditional analytic repair; do not reactivate or mark the historical origin tasks solved.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:distinguish-classes-from-connection",
      "problemId": "problem:seam-family-connection-compatibility",
      "titleEN": "Separate classes from actual transport",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:joint-discrete-data-vs-connection"
      ],
      "requiredPremiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "The theorem listing singleton [nabla_F*] and Chern classes is recorded as a discrete/conjugacy-class statement; the common operator realization is kept separate and the lift formula is explicitly marked as conditional on A_E.",
      "nextActionEN": "Keep as a source gap; do not cite the discrete theorem as a definition of Phi or D_coll.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-compatible-joint-connection",
      "problemId": "problem:seam-family-connection-compatibility",
      "titleEN": "Derive the common connection from the original source",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:distinguish-classes-from-connection"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "The original collar action generates beta and family-local-system transport together without silently assuming parallelity.",
      "nextActionEN": "Specify explicitly how D_coll acts on the family local system and determinant direction.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:retain-sign-projector-counterexample",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Reuse the sign-projector counterexample",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:sign-projector-does-not-determine-time-magnitude"
      ],
      "requiredPremiseIds": [
        "premise:sign-covariance-only"
      ],
      "successCriterionEN": "For sign-only questions, account for the lost |H| channel.",
      "nextActionEN": "Do not equate OS/projector invariance with full dynamical invariance.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-conditional-full-transfer-reconstruction",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Reuse conditional full-transfer reconstruction",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:full-faithful-kms-or-transfer-recovers-magnitudes"
      ],
      "requiredPremiseIds": [
        "premise:known-faithful-kms-or-full-transfer"
      ],
      "successCriterionEN": "With full T or faithful KMS covariance, energy magnitudes are uniquely reconstructible.",
      "nextActionEN": "Reuse the formula while keeping TFPT identification of T open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-physical-full-transfer",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Identify the physical complete TFPT transfer",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:retain-sign-projector-counterexample",
        "task:reuse-conditional-full-transfer-reconstruction",
        "task:reuse-full-two-face-collar-reconstruction"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "The original source identifies the same complete transfer operator with scale, sign, domain, and state.",
      "nextActionEN": "Retain both finite endpoint traces, fiber comparison and normal length from the original source. Evaluate the full graph with the existing inverse reader. Do not identify the geometric deck lift with 2P_C−I. Establish CAR state identification and actual marking action from the same source; do not count a matrix generated from guessed B as a P1 derivation.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-full-two-face-collar-reconstruction",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Reuse complete collar reconstruction",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:reuse-conditional-full-transfer-reconstruction"
      ],
      "resolutionIds": [
        "finding:full-two-face-collar-recovers-signed-operator"
      ],
      "requiredPremiseIds": [
        "premise:actual-product-collar-two-face-data"
      ],
      "successCriterionEN": "The actual full graph relation determines the same signed operator with correct domains.",
      "nextActionEN": "Apply the existing inverse reader to actual source data; no further sign-only search.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-shared-register-homogeneous-gkls-time",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Classify homogeneous GKLS embedding of the shared register family",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:shared-register-gkls-embedding-exact-q-interval"
      ],
      "requiredPremiseIds": [
        "premise:specified-shared-s3-register-channel-family"
      ],
      "successCriterionEN": "The precise mathematical statement and premises have been reviewed in the original sources.",
      "nextActionEN": "Reuse this scope; infer neither physical selection nor a fresh kernel run.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:decide-fixed-m4-all-branch-homogeneous-time",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Decide every homogeneous GKSL logarithm of the fixed M4 channel",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:marked-m4-channel-all-powers-homogeneous-gksl-excluded"
      ],
      "requiredPremiseIds": [
        "premise:specified-marked-m4-clifford-channel"
      ],
      "successCriterionEN": "The precise mathematical statement and premises have been reviewed in the original sources.",
      "nextActionEN": "Reuse this scope; infer neither physical selection nor a fresh kernel run.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-derived-flavor-ratio",
      "problemId": "problem:flavor-ratio-amplitude-readout",
      "titleEN": "Reuse the derived flavor ratio",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:flavor-ratio-closed-absolute-anchor-open"
      ],
      "requiredPremiseIds": [
        "premise:declared-p1-p2"
      ],
      "successCriterionEN": "Treat 55/117 as fixed on exactly the stated discrete stratum.",
      "nextActionEN": "Do not start a new search for this ratio.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:select-absolute-holonomy-anchor",
      "problemId": "problem:flavor-ratio-amplitude-readout",
      "titleEN": "Determine the absolute holonomy amplitude",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:reuse-derived-flavor-ratio"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "A continuous U_f* derived from the original source fixes absolute amplitudes without reopening the ratio.",
      "nextActionEN": "Derive the wall selector for the absolute anchor from original data.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:separate-root-from-selector",
      "problemId": "problem:alpha-fixed-input-root",
      "titleEN": "Separate root calculation from source selection",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:alpha-equation-is-fixed-input-closure"
      ],
      "requiredPremiseIds": [
        "premise:declared-p1-p2",
        "premise:fixed-input-models-scoped"
      ],
      "successCriterionEN": "The closure equation for the defined rank-one projector and the still-open derivation of its inputs are documented as separate statements.",
      "nextActionEN": "Promote to a physical prediction only after deriving the seam projector and observable from the original source.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-alpha-inputs-and-transfer",
      "problemId": "problem:alpha-fixed-input-root",
      "titleEN": "Derive alpha inputs and Thomson transfer",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:separate-root-from-selector"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:declared-p1-p2",
        "premise:quarter-phase-retained"
      ],
      "successCriterionEN": "The projector, weights, parameters, and renormalized observable are derived from original principles and the same physical channel.",
      "nextActionEN": "Reuse canonical old-circle defect line and full-source state theorem. Check actual original P1 insertion/reference mapping and EM determinant norm. Do not identify marked D5 grade response5/4 with common time carrying exponent2; derive preparation, weights and Thomson transfer from the same channel.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:prove-alpha-positive-root-uniqueness",
      "problemId": "problem:alpha-fixed-input-root",
      "titleEN": "Establish the unique global positive root",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:alpha-global-positive-root-unique"
      ],
      "requiredPremiseIds": [
        "premise:fixed-em-seam-function"
      ],
      "successCriterionEN": "Analytic existence and uniqueness proof on the entire positive half-line for the same original function.",
      "nextActionEN": "Reuse the proof; recheck its assumptions if the seam response changes.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:state-fixed-function-scope",
      "problemId": "problem:gravity-flow-normalization",
      "titleEN": "Record scope of fixed original functional",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:matter-observations-do-not-fix-geometric-response"
      ],
      "requiredPremiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Possible non-identifiability from matter-only reads is not confused with freedom to change the original functional.",
      "nextActionEN": "Track the required full geometric source and normalization as an open proof step.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-geometric-modular-response",
      "problemId": "problem:gravity-flow-normalization",
      "titleEN": "Derive geometric modular response and area coefficient",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:state-fixed-function-scope"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "The same local state, algebra, normalization, and regulator yield the geometric modular flow and conical area coefficient of the fixed original functional.",
      "nextActionEN": "Connect the metric-dependent derivative of the original functional to microscopic horizon relative entropy using the same data.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-full-neutral-quadratic-matrix",
      "problemId": "problem:clock-linked-neutral-response-reconstruction",
      "titleEN": "Reconstruct all neutral quadratic matrix directions",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:four-clock-fields-complete-quadratic-response"
      ],
      "requiredPremiseIds": [
        "premise:native-current-clock-ope-access"
      ],
      "successCriterionEN": "Rational complete basis and inverse response map.",
      "nextActionEN": "Reuse the existing36-probe inverse; do not repeat three-sector or spectrum searches.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-clock-probe-physical-access",
      "problemId": "problem:clock-linked-neutral-response-reconstruction",
      "titleEN": "Derive physically admissible probe access",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:reconstruct-full-neutral-quadratic-matrix"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:native-current-clock-ope-access",
        "premise:declared-p1-p2"
      ],
      "successCriterionEN": "An original instrument and state transfer permit the generated mixed responses.",
      "nextActionEN": "Supply and test the actual field/instrument operator on the same source.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:construct-covariant-original-j-lift",
      "problemId": "problem:clock-source-covariant-transport",
      "titleEN": "Construct original J lift with complete time/charge action",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-j-covariant-source-transport"
      ],
      "requiredPremiseIds": [
        "premise:stipulated-e8-clock-tuple"
      ],
      "successCriterionEN": "All-charge intertwiner with original cocycle.",
      "nextActionEN": "Reuse the existing lift; derive physical frame or sector identification separately.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:interpret-clock-source-frames",
      "problemId": "problem:clock-source-covariant-transport",
      "titleEN": "Derive physical meaning of the frame orbit",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:construct-covariant-original-j-lift"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:stipulated-e8-clock-tuple",
        "premise:declared-p1-p2"
      ],
      "successCriterionEN": "An original operator/state contract determines whether frame change, sector or event.",
      "nextActionEN": "Compare charged instrument action with fixed or jointly transported marking.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:identify-neutral-response-blind-directions",
      "problemId": "problem:charged-twist-response-identifiability",
      "titleEN": "Determine twist blindness completely",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:neutral-vacuum-allword-twist-blindness"
      ],
      "requiredPremiseIds": [
        "premise:neutral-current-vacuum-insertions"
      ],
      "successCriterionEN": "Invariant-subspace proof for every allowed word and time.",
      "nextActionEN": "Treat equal neutral data across twists as an equivalence.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-twist-from-charged-data",
      "problemId": "problem:charged-twist-response-identifiability",
      "titleEN": "Reconstruct twist from charged responses",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:eight-charged-responses-reconstruct-twist"
      ],
      "requiredPremiseIds": [
        "premise:normalized-charged-primary-time-access"
      ],
      "successCriterionEN": "Explicit inverse of original basis responses.",
      "nextActionEN": "Use the existing eight-dimensional inverse.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-actual-charged-source-probes",
      "problemId": "problem:charged-twist-response-identifiability",
      "titleEN": "Derive actual charged source probes",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:identify-neutral-response-blind-directions",
        "task:reconstruct-twist-from-charged-data"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:declared-p1-p2",
        "premise:quarter-phase-retained"
      ],
      "successCriterionEN": "Original local fields/instruments supply the compared charged intermediate states with statistics and time scale.",
      "nextActionEN": "Test the first charged operator map on the same source; no additional neutral-moment search.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:native-field-response-discriminator",
      "problemId": "problem:native-charged-seam-selection",
      "titleEN": "Check native fields and response discriminator",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:native-opposite-charge-response-symmetry"
      ],
      "requiredPremiseIds": [
        "premise:native-full-charge-field-source",
        "premise:native-c-invariant-start"
      ],
      "successCriterionEN": "Explicitly retain T, actual adjoints and both propagation sectors.",
      "nextActionEN": "Reuse these original operators and the charged discriminator.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-native-seam-symmetry-breaking",
      "problemId": "problem:native-charged-seam-selection",
      "titleEN": "Derive actual marked seam/state action",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:native-field-response-discriminator"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:declared-p1-p2"
      ],
      "successCriterionEN": "The same original source supplies the marked field/state/time dictionary and its odd charged response.",
      "nextActionEN": "Test at the actual seam operator or selected state how the established symmetry is avoided; prescribing η is insufficient.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-constructive-seam-1",
      "problemId": "problem:constructive-seam-lift-state",
      "titleEN": "Finite search closed, actual winding and parity equivalence",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:constructive-phase-class-and-full-winding"
      ],
      "requiredPremiseIds": [
        "premise:fixed-car-crossed-half-charge-search"
      ],
      "successCriterionEN": "Global crossed operators; no local field equivalence or physical selection.",
      "nextActionEN": "Reuse the reviewed conclusion with its premises; do not repeat the unchanged search.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-constructive-seam-2",
      "problemId": "problem:constructive-seam-lift-state",
      "titleEN": "Positive finite-word state extension",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:constructive-positive-state-extension"
      ],
      "requiredPremiseIds": [
        "premise:fixed-car-crossed-half-charge-search",
        "premise:fixed-positive-crossed-state"
      ],
      "successCriterionEN": "No complete concrete Finsupp kernel instantiation, physical state selection or automatic K-invariance of the bare shift algebra.",
      "nextActionEN": "Reuse the reviewed conclusion with its premises; do not repeat the unchanged search.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-constructive-seam-3",
      "problemId": "problem:constructive-seam-lift-state",
      "titleEN": "E8 current group conditionally determines the P sign",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:constructive-current-group-selects-positive-p-lift"
      ],
      "requiredPremiseIds": [
        "premise:stipulated-even-e8-seam-lift",
        "premise:fixed-car-crossed-half-charge-search"
      ],
      "successCriterionEN": "Only the stipulated even E8 lift; full odd-Z8 sectors remain additional. No transfer of the different (9,1) source. The ±i path orientation is not selected.",
      "nextActionEN": "Reuse the reviewed conclusion with its premises; do not repeat the unchanged search.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-constructive-seam-4",
      "problemId": "problem:constructive-seam-lift-state",
      "titleEN": "The same shift functional hides distinct ground states",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:constructive-state-algebra-resolution-and-source-test"
      ],
      "requiredPremiseIds": [
        "premise:fixed-car-crossed-half-charge-search",
        "premise:fixed-positive-crossed-state"
      ],
      "successCriterionEN": "Normal ground densities in the supplied K space; no state selection from P1/P2. The ground space was already known.",
      "nextActionEN": "Reuse the reviewed conclusion with its premises; do not repeat the unchanged search.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-constructive-seam-5",
      "problemId": "problem:constructive-seam-lift-state",
      "titleEN": "No phase hit realizes the unchanged source",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:constructive-all-phases-fail-unchanged-source"
      ],
      "requiredPremiseIds": [
        "premise:fixed-car-crossed-half-charge-search",
        "premise:unchanged-quarter-car-qwz-source-comparison"
      ],
      "successCriterionEN": "Only the named unchanged CAR/QWZ representation with the same time. No TFPT no-go; choosing a state removes no added zero vector.",
      "nextActionEN": "Reuse the reviewed conclusion with its premises; do not repeat the unchanged search.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-partner-type-1",
      "problemId": "problem:seam-partner-charge-state-time",
      "titleEN": "Concrete pair operator; source neutrality is not hypercharge neutrality",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:partner-carrier-charges-and-state-types"
      ],
      "requiredPremiseIds": [
        "premise:oriented-p2-exterior-carrier",
        "premise:fixed-e8-fold-quarter-dictionary"
      ],
      "successCriterionEN": "Original carrier plus supplied E8 charge dictionary; no physical field identification.",
      "nextActionEN": "Reuse the reviewed result within its stated scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-partner-type-2",
      "problemId": "problem:seam-partner-charge-state-time",
      "titleEN": "Fixed quarter time splits the color/weak multiplet",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:partner-fixed-quarter-time-splits-sm-multiplet"
      ],
      "requiredPremiseIds": [
        "premise:oriented-p2-exterior-carrier",
        "premise:fixed-e8-fold-quarter-dictionary"
      ],
      "successCriterionEN": "Only the supplied affine dictionary. Backgrounds or time-dependent covariant symmetries have different premises; no general gauge-physics no-go.",
      "nextActionEN": "Reuse the reviewed result within its stated scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-partner-type-3",
      "problemId": "problem:seam-partner-charge-state-time",
      "titleEN": "Explicit conjugation for the existing sheet pairing",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:partner-original-carrier-cross-sheet-conjugation"
      ],
      "requiredPremiseIds": [
        "premise:oriented-p2-exterior-carrier"
      ],
      "successCriterionEN": "Representation with metric/orientation; J_C is not yet the actual boundary/OS conjugation. Two carrier labels are not two vacua.",
      "nextActionEN": "Reuse the reviewed result within its stated scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-partner-type-4",
      "problemId": "problem:seam-partner-charge-state-time",
      "titleEN": "Actual partner map between quarter domains",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:partner-chiral-quarter-conjugation-state-time"
      ],
      "requiredPremiseIds": [
        "premise:actual-chiral-opposite-quarter-domains"
      ],
      "successCriterionEN": "Given chiral source. No selection from P1/P2, no equal responses within one fixed twist, and no identification with affine r0.",
      "nextActionEN": "Reuse the reviewed result within its stated scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-joint-bilinear-hermitian-correction",
      "problemId": "problem:seam-partner-charge-state-time",
      "titleEN": "Bilinear sheet pairing is not Hermitian kernel selection",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:joint-bilinear-hermitian-correction"
      ],
      "requiredPremiseIds": [
        "premise:oriented-p2-exterior-carrier"
      ],
      "successCriterionEN": "Correction of the finite selection inference; no identification of I with the actual Calderon operator and no P1 countermodel.",
      "nextActionEN": "Reuse the reviewed conclusion with its premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-joint-quarter-transports-marking",
      "problemId": "problem:seam-partner-charge-state-time",
      "titleEN": "Actual quarter conjugation transports the supplied marking",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:joint-quarter-transports-marking"
      ],
      "requiredPremiseIds": [
        "premise:actual-chiral-opposite-quarter-domains",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:given-first-marked-quarter-character"
      ],
      "successCriterionEN": "Exact map of the supplied source and conditional E8 lift; first marking, source realization and physical event law are not derived from P1/P2. Both quarter domains remain explicit; no switch to another branch to solve a fixed-sector question.",
      "nextActionEN": "Reuse the reviewed conclusion with its premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-joint-fixed-time-marking-repair-excluded",
      "problemId": "problem:seam-partner-charge-state-time",
      "titleEN": "No time-stabilizing orthogonal repair of the fixed marking",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:joint-fixed-time-marking-repair-excluded"
      ],
      "requiredPremiseIds": [
        "premise:actual-chiral-opposite-quarter-domains",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:given-first-marked-quarter-character"
      ],
      "successCriterionEN": "Only fixed fold time and fixed 5+3 marking. Covariant marking transport is positively constructed; other sources or dynamical dictionaries are not excluded.",
      "nextActionEN": "Reuse the reviewed conclusion with its premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reuse-joint-spinor-not-source-coefficient",
      "problemId": "problem:seam-partner-charge-state-time",
      "titleEN": "Spinor16 is a state sector, not a 16-real one-particle field",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:joint-spinor-not-source-coefficient"
      ],
      "requiredPremiseIds": [
        "premise:oriented-p2-exterior-carrier",
        "premise:given-d5-a3-free-fermion-realization"
      ],
      "successCriterionEN": "Representation types of the supplied free realization; no selection from P1/P2 and no new spinor-CAR replacement.",
      "nextActionEN": "Reuse the reviewed conclusion with its premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:calibrate-typed-operator-synthesis",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Calibrate new search without supplying the target map",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:typed-operator-search-calibrated"
      ],
      "requiredPremiseIds": [
        "premise:declared-finite-operator-synthesis-inputs"
      ],
      "successCriterionEN": "Generate a known map, eliminate the wrong linearity type using a learned counterexample, and pass adversarial exact-verifier tests.",
      "nextActionEN": "Reuse calibration; an unchanged replay is not new research.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:synthesize-joint-source-operator-dictionary",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Synthesize a joint field, marking and transfer dictionary",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:calibrate-typed-operator-synthesis"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "The same generated map satisfies actual field products, adjoints, carrier marking, quarter domain, and state/time transport in a source-grounded representation.",
      "nextActionEN": "Continue F1 from R034/R035. Whole supplied96 inner Higgs producer and central scale/affine full-source map are evaluated. Resolve actual original B_Ea/bosonic-relative reduction into Brel and SAME Tr_rel,with first symbol/domain,normal mode embedding/metric and actual insertion into existing wedge-to96 H map. Use full Gram transport if actual Bsigma=fBf;retain induced connection/exterior memory. No bare5 mass,free overlap exponent,scale/Y/lift scan or new Brel definition. Retain original reference/eta/scale/trace/H0/Z0 and complete state/time/RP/Flavor/Alpha/E8/clocks. Decide common H and Einstein jets of actual producer before full H source closure.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:implement-positive-source-kernel-synthesis",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Search for the positive common source kernel itself",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:construct-certify-discriminate-finite-kernels",
        "task:repair-and-pass-collar-source-control"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Construct unknown positive word kernels from original relations and establish continuation stability and actual time/field action. A finite positive moment matrix alone is insufficient.",
      "nextActionEN": "Reuse existing kernel construction,exact completion and discrimination under plan C1/F1 and SEARCH-METHODS S3/S4. Read and update docs/research/fundamental-plan/progress.json and RESULTS.md on continuation. The offline replay confirms the two given complete finite clustering kernels with2245 moments each and ten length5 separators. This tool control is not physical source selection. New search requires a concrete originally derived source-control relation; do not optimize old classes or extremal objectives as a physical selector. Do not reactivate the stopped automation.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:construct-certify-discriminate-finite-kernels",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Automatically construct, certify and distinguish finite kernels",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:positive-kernel-construction-with-exact-discriminator"
      ],
      "requiredPremiseIds": [
        "premise:finite-positive-kernel-search-class"
      ],
      "successCriterionEN": "Generate unknown moments; exactly verify successful complete realizations while incomplete tables remain candidates; emit the shortest distinguishing word response.",
      "nextActionEN": "Reuse the implemented search and offline certificates. Do not count unchanged finite calibrations as new fundamental solutions.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:repair-and-pass-collar-source-control",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Repair search conditions against source types and collar controls",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:source-typed-kernel-search-controls"
      ],
      "requiredPremiseIds": [
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Feasibility is default; heat and thermal GNS controls use compatible representations without forced pure states.",
      "nextActionEN": "Reuse source types and controls; do not count extremal calibration as physical selection.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-canonical-collar-multifield-ray",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Reconstruct multi-field sewing of the canonically identified boundary source",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:repair-and-pass-collar-source-control"
      ],
      "resolutionIds": [
        "finding:collar-car-projection-multifield-ray"
      ],
      "requiredPremiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:actual-car-graph-and-oriented-boundary-pairing"
      ],
      "successCriterionEN": "State ray from CAR projection and operator ray from oriented boundary pairing; exact products and chronological composition, with absolute scalar explicitly missing.",
      "nextActionEN": "Reuse reconstruction once physical CAR covariance and boundary pairing are established. Do not replace interacting sources with free rules.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:retain-source-reference-amplitude",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Retain absolute reference amplitude in search",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:source-reference-amplitude-retained"
      ],
      "requiredPremiseIds": [
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Campaign, cache and direct certifier distinguish lambda and transfer type; no certificate under silent T Omega=Omega.",
      "nextActionEN": "Reuse parameterized path; derive lambda from the original source rather than solver bounds.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:integrate-given-free-source-jointly",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Integrate supplied free source including boundary response and scalar",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:joint-fermionic-source-schur-functional"
      ],
      "requiredPremiseIds": [
        "premise:given-complex-fermion-source-quantization"
      ],
      "successCriterionEN": "Direct Berezin integration and independent determinant formula agree including complex sources, Schur factor and signs.",
      "nextActionEN": "Use exact integration formulas after establishing provenance of actual K/measure; do not count a mode partition as geometric derivation.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-complete-nongaussian-car-link",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Convert the full finite CAR kernel into a link functional",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:complete-car-kernel-fixes-nongaussian-link-functional"
      ],
      "requiredPremiseIds": [
        "premise:complete-labeled-even-car-kernel"
      ],
      "successCriterionEN": "Exact roundtrip, sewing and trace with higher vertices and scalars.",
      "nextActionEN": "Reuse the reader for complete candidates; do not impose a free model.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:close-original-recursive-word-memory",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Close original recursive word reconstruction with memory",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:full-memory-schur-reconstruction-preserves-every-ordered-word-under-nesting",
        "finding:original-return-and-native-j-have-minimal68-dimensional-all-word-memory"
      ],
      "requiredPremiseIds": [
        "premise:original-invariant-word-domain-with-nested-readouts",
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:specified-original-pair-ordered-response-composition",
        "premise:original-single-beta-return-with-native-cartan-j-word-alphabet"
      ],
      "successCriterionEN": "Coefficientwise composition and complete minimal linear realization of the specified original alphabet.",
      "nextActionEN": "Reuse in F1; continue whole original source and original action consumer.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:retain-full-original-source-through-regulator-and-readout",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Retain whole original caller through scale and readout",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-full-source-regulator-flow-retains-normalized-kernel-and-vacuum-factor",
        "finding:full-reflected-quadratic-regulator-cone-preserves-every-rp-source"
      ],
      "requiredPremiseIds": [
        "premise:typed-source-structures",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:original-regulated-full-source-with-actual-measure-and-legs",
        "premise:finite-reflected-positive-quadratic-ir-regulator-class"
      ],
      "successCriterionEN": "Full functional pair rule,exterior legs and exact universal RP criterion in the specified regulator class.",
      "nextActionEN": "Reuse and execute actual original interacting source coupling; no new regulator candidate round.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-shared-higgs-source-and-local-rp-sewing",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute actual shared Higgs source with full matter words and local RP",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-shared-higgs-source-induces-fixed-yukawa-mixed-matter-words",
        "finding:local-even-yukawa-sewing-preserves-given-joint-graded-rp"
      ],
      "requiredPremiseIds": [
        "premise:typed-source-structures",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber",
        "premise:original-graded-rp-reference-and-even-local-reflected-half-action"
      ],
      "successCriterionEN": "Original whole one-form consumer and complete induced source rule with precise mixed coefficient; valid scoped common RP sewing.",
      "nextActionEN": "Reuse. Evaluate actual original H fiber,common reflection/locality data and mixed answers from same master.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reduce-whole-constant-original-higgs-spectral-fiber",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Reduce whole constant original Higgs spectral fiber",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:whole-original-constant-higgs-orbit-has-reduced-majorana-spectral-response"
      ],
      "requiredPremiseIds": [
        "premise:typed-source-structures",
        "premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber",
        "premise:original-constant-higgs-fiber-and-symmetric-majorana-spectral-consumer"
      ],
      "successCriterionEN": "Whole96 left rotation with Majorana and exact reduced determinant with first whole-circle jet.",
      "nextActionEN": "Reuse reduction and resolve actual source match R029.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:resolve-original-geometric-higgs-residue-sign-and-field-map",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Resolve original geometric Higgs residue sign and field map",
      "kind": "construction",
      "status": "open",
      "dependsOn": [],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:typed-source-structures",
        "premise:literal-archived-geometric-residue-and-common-higgs-field-comparison"
      ],
      "successCriterionEN": "Same complete original source explains H²/H⁴ signs and normalization in target potential,or a concrete original identification is corrected from source; no free extra action.",
      "nextActionEN": "Identify actual original normal field insertion and equivariant T from primitive source;execute whole imaginary-source restriction Zorig[iTj]/Zorig0,not chosen Gaussian prior or covariance alone. Keep complement/mixed fields and reference/eta/Z0. Radial classification only for actual invariant marginal;preserve all whole-theory results.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:evaluate-original-local-higgs-heat-coefficient-compatibility",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Evaluate local original Higgs heat identification and whole finite consumer",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-local-higgs-residue-linear-coefficients-fail-same-trace-heat-ratio",
        "finding:whole-original-higgs-moments-fix-conditional-local-kinetic-mass-quartic"
      ],
      "requiredPremiseIds": [
        "premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Decide first H²/RH² heat identification exactly and evaluate whole96 moments through named conditional consumer without choosing new Y.",
      "nextActionEN": "Use scoped R030/R031 and resolve original symbol/reference/continuation map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:evaluate-whole-variable-bound-higgs-reference-and-scale-map",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute whole variable bound Higgs reference and original scale map",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:whole-variable-original-higgs-bound-reference-response-and-forced-clifford-factor",
        "finding:original-symmetric-scale-map-fails-simultaneous-higgs-einstein-repair"
      ],
      "requiredPremiseIds": [
        "premise:whole-variable-higgs-bound-reference-and-conformal-dirac-map",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Evaluate both supplied reference jets with all H derivatives and test same scale map against Higgs and Einstein together.",
      "nextActionEN": "Resolve actual total Brel/H source and same original trace/field contract.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-inner-higgs-scale-and-normal-kernel-map",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute whole inner Higgs scale/source and normal kernel transport",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:whole-original-higgs-inner-scale-and-affine-full-source-transport",
        "finding:normal-higgs-mode-type-and-exact-kernel-metric-require-actual-relative-operator-map"
      ],
      "requiredPremiseIds": [
        "premise:original-inner-higgs-central-scale-and-finite-affine-source-map",
        "premise:given-normal-higgs-mode-realization-and-distinct-module-types",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Scale actual supplied whole Higgs vertex without double counting,retain full finite affine source,and determine typed whole normal kernel transport.",
      "nextActionEN": "Resolve actual bosonic-relative Brel/source trace map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-given-superconnection-grades-and-whole-normal-spectral-reader",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute given whole superconnection and normal spectral reader",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-superconnection-grades-and-weighted-heat-retain-higgs-kinetic-excursions",
        "finding:whole-normal-reduction-preserves-relative-spectral-reader-and-higgs-jets"
      ],
      "requiredPremiseIds": [
        "premise:given-product-clifford-grades-parallel-projection-and-complete-relative-block-reader",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Type-check ordinarytwoform/Higgsderivative;distinguish compressed andweightedheat;derive complete conditional normalblock/trace/source reader throughH4 withoutinventing originalblocks.",
      "nextActionEN": "Apply derived exact reader to actual original normal blocks.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:evaluate-own-admissibility-and-whole-total-chiral-spectral-readers",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Determine own-admissibility and whole total-chiral spectral readers",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-admissibility-own-spectral-reader-has-no-free-low-mode-residue-repair",
        "finding:whole-total-chiral-positive-spectrum-retains-higgs-kinetics-and-common-half-trace"
      ],
      "requiredPremiseIds": [
        "premise:original-positive-admissibility-reader-and-given-total-chiral-product",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Evaluate original admissibility heat/zeta/residues and given total-chiral product trace for all allowed spectral functions. Preserve zero modes,index,reference and domains;identify the unproved original operator map.",
      "nextActionEN": "Determine actual original Dadm to Ksigma realization map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-whole-scale-energy-profile-and-relative-flow",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Derive whole scale-energy map,normal profile and relative flow",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:whole-scale-energy-response-uniquely-reconstructs-normal-profile",
        "finding:original-relative-scale-flow-separates-residue-finite-part-and-local-anomaly"
      ],
      "requiredPremiseIds": [
        "premise:whole-original-scale-congruence-and-specified-normal-energy-data",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Derive exact whole scale/domain/normaltrace and spectral reader,reconstruct entire normal profile class from specified first energy response,separateFP/residue/anomaly with actualBrel defect.",
      "nextActionEN": "Execute original full energy response and actualBrel scale insertion.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-green-energy-producer-and-mixed-scale-readout",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original Green energy producer and mixed scale readout",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-whole-green-produces-energy-response-with-correct-orthogonal-trace",
        "finding:whole-mixed-scale-source-reads-bosonic-insertion-before-higgs-average"
      ],
      "requiredPremiseIds": [
        "premise:given-whole-green-energy-source-and-conditional-scale-response",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Supply whole originalR040energy response with correctstate projection and readW from specified original scale response with dynamicweight covariance.",
      "nextActionEN": "Determine actual original normal insertion/relative trace map without circular self-confirmation.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:resolve-current-spectral-action-argument-and-common-higgs-gravity-weights",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Match current action argument and common Higgs/gravity weights",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:current-original-spectral-action-triplet-fails-positive-laplace-class-unless-leading-relative-term-cancels",
        "finding:correct-current-argument-weights-link-whole-higgs-threshold-and-same-einstein-response"
      ],
      "requiredPremiseIds": [
        "premise:current-original-spectral-action-and-fixed-ordinary-moment-dictionary",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Translateactualcurrentmomentargument,testwholepositiveclasswithreferenceexception,evaluateexistingwholeH/Einsteinconsumerwithsameweights.",
      "nextActionEN": "Determineactualoriginalrelativeoperator/reference/source map,no freeprofileortracefit.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-whole-original-curvature-consumers-and-higgs-radial-source",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute whole original curvature consumers and Higgs radial source",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:whole-original-spinor-curvature-a4-has-no-independent-scalaron-r-squared",
        "finding:whole-original-entropic-curvature-corrects-max-symmetric-scalar-scale",
        "finding:given-whole-higgs-source-fixes-radial-curvature-susceptibility-without-extra-scalar"
      ],
      "requiredPremiseIds": [
        "premise:original-whole-spinor-and-entropic-curvature-consumers-with-given-higgs-response",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Testwholetensorspaceinsteadofmaxsymmetry;evaluateoriginalspinorandentropicconsumersseparatelywithsamepin;connectgivenHiggsresponsewithoutdoublecounting.",
      "nextActionEN": "Evaluateactualoriginaladditionalgeometricoperatorandfullrelativecurvaturesource.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-four-ghost-admissibility-source-and-geometric-type-test",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original whole four-ghost source and geometric type test",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-original-four-ghost-complex-preserves-base-selector-with-full-cohomology-and-distinct-traces",
        "finding:whole-original-admissibility-energy-source-recovers-constraints-but-cannot-replace-geometric-operator"
      ],
      "requiredPremiseIds": [
        "premise:actual-original-four-ghost-commuting-projection-admissibility-complex",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Evaluate whole actual ghost complex,cohomology,traces and energy source;compare geometric and selector operators by actual spectral type.",
      "nextActionEN": "Follow original geometric insertion and bound reference.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-moving-normal-kernel-derivative-and-source-response",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original moving normal kernel derivative and whole source response",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-moving-normal-kernel-fixes-induced-connection-and-full-scale-covariance"
      ],
      "requiredPremiseIds": [
        "premise:actual-smooth-normal-family-with-supplied-unitary-horizontal-connection",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Differentiate actual R035 kernel including matrix normalization,derive A/C/whole covariance from original B and retain whole mixed source;do not call additional premises an origin derivation.",
      "nextActionEN": "Follow actual normal-family producer and same bound reference.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:test-original-fixed-o1-source-and-normal-operator-placement",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Decide fixed original O1 source and normal operator placement",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:fixed-original-o1-source-rejects-nonconstant-normal-multiplier-and-fixes-placement-test"
      ],
      "requiredPremiseIds": [
        "premise:fixed-original-o1-section-consumer-and-actual-normal-first-order-placement",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Decide whole positive multiplier class on originalV,compare both operator placements with derivative/symbol and isolate actual original variation tensor.",
      "nextActionEN": "Execute original functional source producer with same bound reference.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:test-whole-higgs-mixture-against-covariance-only-modular-reader",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Compare whole Higgs mixture and covariance reader on invariant four-field witness",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:shared-original-higgs-mixture-has-invariant-color-fourpoint-wick-defect"
      ],
      "requiredPremiseIds": [
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Derive internal-frame invariant four-field test on actual original quark block and decide entire stated positive H-weight class analytically without choosing physical H measure.",
      "nextActionEN": "Execute actual original field/carrier and full mixed source map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:test-exact-bounded-cutoff-higgs-normalization-at-fixed-rank",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Test exact bounded cutoff on whole ordinary Higgs volume",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:bounded-fixed-rank-spectral-action-does-not-normalize-noncompact-higgs-volume"
      ],
      "requiredPremiseIds": [
        "premise:fixed-rank-bounded-cutoff-with-ordinary-noncompact-higgs-volume",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Decide stated finite-trace-to-measure inference on explicit whole Higgs volume class analytically without inventing original measure.",
      "nextActionEN": "Execute actual original field-source pushforward.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:test-whole-original-circle-joint-mode-ir-higgs-normalization",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Test whole original circle joint mode and IR Higgs normalization",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:whole-original-quarter-source-bounds-higgs-weight-uniformly-through-joint-mode-ir-limits"
      ],
      "requiredPremiseIds": [
        "premise:whole-constant-original-quarter-source-positive-traceclass-profile-and-flat-higgs-volume",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Decide R055 rank loophole on whole given original circle with actual Phi/reference and uniform proof,without new geometry or measure.",
      "nextActionEN": "Execute actual original source pushforward.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-original-o1-mode-covariance-versus-whole-higgs-law",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Test original O1 mode covariance against whole Higgs-law class",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-o1-covariance-leaves-full-radial-higgs-law-and-exact-fourier-source-readout"
      ],
      "requiredPremiseIds": [
        "premise:given-o1-mode-isometry-and-weak-invariant-positive-higgs-covariance-marginal",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Test first modekernel→sourcelaw identification without measure choice,classify whole added invariant class and name actual original-source readout with limits.",
      "nextActionEN": "Execute actual original field-source Fourier restriction.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-original-whole-process-localization-before-geometric-readout",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Reconstruct original localization from the whole process",
      "kind": "construction",
      "status": "open",
      "dependsOn": [],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:literal-whole-source-localization-and-geometric-readout-contracts",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Same original whole source determines actual localized subalgebra family and state/time action without freely supplied target geometry;prove causal/dimensional identification,physicalcarrier and subsequenttensorresponse. Distinguish source gap from exclusion.",
      "nextActionEN": "After R084 retain whole theory: under the hypothesized same scalar shift the complete coupled 36-quark constant-H circle yields relative determinant 1 despite nonzero H response; gamma+ marginal yields (1−z)^−18. One-sided shift of the FULL coupled space is S2 not S1 for nonzero mass. A mathematical whole-pair det2 reader exists and finite native checks indicate Higgs dependence; original Z0/ref/eta is not thereby fixed. Compare actual original seam shift, restriction and R080 ordered det2 source on same carrier/clock/reference/eta/Z0/PQ word contract and derive trace correction; no free regulator.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:test-bare-native-code-word-compression-for-original-locality",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Test bare native-code word compression against actual locality",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-disjoint-local-weyls-acquire-spurious-commutator-under-bare-native-compression"
      ],
      "requiredPremiseIds": [
        "premise:actual-proper-local-current-weyls-and-bare-native-code-compression",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Exactly compare actual disjoint local operations of same original source before/after codecompression and identify omitted word cancellation.",
      "nextActionEN": "Retain whole local word readout and execute original P1 local field map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:decide-original-quarter-geometric-local-time-and-interval-source-reader",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Decide original geometric local-time class and execute actual interval reader",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-quarter-current-state-excludes-nontrivial-geometric-local-point-time",
        "finding:actual-elliptic-interval-car-source-produces-local-modular-generator"
      ],
      "requiredPremiseIds": [
        "premise:actual-elliptic-quarter-supported-current-and-interval-car-modular-test",
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Test actualsupportedtimewitness andwhole statedclass againstactualwholestate;providepositivefreeCAR reader/domain/actualwordcheck.",
      "nextActionEN": "Execute original marked field/sewing map;retain bothscopedresults.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-actual-regional-two-face-partner-and-supported-charged-word",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute actual regional two-face partner and supported charged word",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-proper-two-face-regions-do-not-contain-pure-local-source-double",
        "finding:actual-elliptic-whole-environment-fixes-regional-car-partner"
      ],
      "requiredPremiseIds": [
        "premise:actual-elliptic-two-face-projection-with-genuine-regional-support",
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks"
      ],
      "successCriterionEN": "Compare actualregionalsourcecompressiononwholechargedwordandderivecorrectpartnerinsamesourcewithsupport/domaincontrol.",
      "nextActionEN": "Continueactualoriginalsource/insertionderivation,nofurtherfreepartnersearch.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-original-color-marginal-modular-law-and-complete-source-reader",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original color marginal, modular field law and complete class reader",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-original-color-triplet-has-spectator-dependent-modular-field-law",
        "finding:actual-color-marginal-has-complete-finite-source-reader-and-mixture-criterion",
        "finding:two-and-four-field-words-do-not-complete-original-color-triplet-source"
      ],
      "requiredPremiseIds": [
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture"
      ],
      "successCriterionEN": "ExecuteactualoriginalHdependentmarginalinsteadofchosenHint,deriveoddmodularlawandprovecompletequeries/classcriterion.",
      "nextActionEN": "Producetheactualoriginalfullsourceratios,retainingallphysicalopenbridges.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-common-higgs-law-from-whole-original-quarter-source",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Reconstruct common Higgs law from whole original quarter source tower",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:whole-original-quarter-occupation-tower-uniquely-reconstructs-common-radial-higgs-law",
        "finding:finite-original-tower-reader-and-existing-weak-symmetry-fix-shared-matter-responses",
        "finding:unchanged-free-quarter-source-cannot-be-nontrivial-integrated-higgs-mixture"
      ],
      "requiredPremiseIds": [
        "premise:original-common-positive-constant-higgs-law-over-whole-quarter-tower",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source",
        "premise:given-o1-mode-isometry-and-weak-invariant-positive-higgs-covariance-marginal"
      ],
      "successCriterionEN": "Wholeoriginalmodetowerinsteadofcopiesoffixedtriplet;exactinjectivity/constructiveinverse,finiteanswerreaderandactualcrosschannelconsumercomparisonwithoriginboundary.",
      "nextActionEN": "Deriveactualforwardmastertowerandoriginalfield/carriertransport.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-record-action-on-doily-and-ordered-source-response",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original record action on Doily and ordered whole source response",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-e8-record-doily-action-is-signed-p-plus-compatible-point-with-typed-sym2-lift",
        "finding:actual-e8-record-words-distinguish-order-and-retain-phase-beyond-fifteen-labels",
        "finding:literal-doily-incidence-output-and-strict-causal-order-on-fifteen-source-labels-excluded",
        "finding:actual-doily-context-record-characters-have-ranks-four-two-two-two"
      ],
      "requiredPremiseIds": [
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables",
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:actual-single-source-event-coherent-stinespring-record"
      ],
      "successCriterionEN": "Actualoriginalrecordmatricesinsteadofgraphcounts;typeC4/H10,decisiveliteralqroutingandorderedwitness,retainfullrecords/phasesandoriginboundary.",
      "nextActionEN": "Continueactualoriginalphysicalsource/local-eventdictionary.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:localize-original-record-process-and-test-unchanged-source-exterior",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Locally implement original record process and test unchanged exterior source",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:canonical-standard-split-localizes-original-source-record-words-with-full-descendant-companion",
        "finding:unchanged-global-sixty-event-source-fails-local-exterior-current-test",
        "finding:canonical-source-localization-changes-exterior-state-and-does-not-select-event-origin"
      ],
      "requiredPremiseIds": [
        "premise:given-e8-current-vacuum-net-and-original-grade-two-descendant-with-standard-split",
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables"
      ],
      "successCriterionEN": "Transportactualglobalcurrentdictionarytoexistinglocalalgebra,retainfullrecords/phases,immediatelytestoriginalstate/exterior,donotconfuseimplementationandorigin.",
      "nextActionEN": "Executegenuineoriginalsupportedsourceinsertionwithactualinside/outsidewordstate.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-elliptic-supported-insertion-and-causal-source-test",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original elliptic insertion,whole source and causal response",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-elliptic-fixed-holonomy-insertion-gives-local-operation-on-unchanged-source",
        "finding:original-quarter-pair-fixes-square-charge-law-half-response-and-real-quillen-norm",
        "finding:actual-elliptic-source-determines-all-path-normalized-causal-current-response"
      ],
      "requiredPremiseIds": [
        "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion",
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "successCriterionEN": "Sameoriginalinsertionproducesoperator,covariance,whole-state,Z0andlocal/exteriortimeresponsewithallchargesandbothfaces.",
      "nextActionEN": "Reuseentireclosedscalarclassandexecuteactualoriginalmarkednonabelian/mixedsourceinsertion.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-mixed-higgs-color-group-response",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Evaluate actual joint Higgs and color group source",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-higgs-quark-source-has-exact-whole-su3-counting-response",
        "finding:single-original-color-parity-separates-free-quillen-from-positive-higgs-integrated-source"
      ],
      "requiredPremiseIds": [
        "premise:original-quark-particle-color-group-counting-on-whole-constant-quarter-source",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion"
      ],
      "successCriterionEN": "ExecuteactualwholeSU3insertwithH,allmodes,normalizationandfreegeometricresponse;identifyfirstgenuinemixedanswer.",
      "nextActionEN": "Executeactualprimitivejointsource/referenceinsertion,retainingthreeexistingwordprobes.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-whole-original-graph-color-selector-and-relative-reader",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute whole original graph color reader with typed original center selector",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:whole-original-quarter-graph-color-response-is-relative-and-diagonal-singlet",
        "finding:original-center-selector-requires-typed-state-field-and-face-transport"
      ],
      "requiredPremiseIds": [
        "premise:given-whole-quarter-graph-and-canonical-diagonal-original-color-lift",
        "premise:typed-source-structures",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:original-quark-particle-color-group-counting-on-whole-constant-quarter-source",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:stipulated-e8-h8-with-original-color-center-selector"
      ],
      "successCriterionEN": "EvaluatewholeGdiagonalandrelativeactionanddecisivelydistinguishcarrierstate,chargedfieldandonefaceconditioning.",
      "nextActionEN": "Executeactualoriginaltypedcarrier/sourceintertwiner.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-color-fixed-field-source-and-first-graded-matter-test",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original color fixed source and first inherited grading test",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-color-center-fixes-whole-e6-a2-source-and-charged-ward-word-action",
        "finding:original-color-neutral-lattice-class-cannot-supply-odd-fields-by-inherited-superlattice-extension"
      ],
      "requiredPremiseIds": [
        "premise:original-marked-color-center-on-whole-e8-lattice-current-source",
        "premise:typed-source-structures",
        "premise:stipulated-e8-h8-with-original-color-center-selector",
        "premise:local-e8-current-response-realization",
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "successCriterionEN": "ExecuteoriginalColorselectoronwholeE8source,actualWard/weakfieldtypinganddecisivefirstCARgradingtest.",
      "nextActionEN": "Executeactualoriginalgradedsource/consumerintertwiner.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-color-spin-mixed-four-word-and-full-sector-sewing",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute actual original color-spinor CAR four-word and complete spin-sector sewing",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-color-spin-car-mixed-word-has-complete-thermal-source-and-cyclic-sewing",
        "finding:exact-original-ns-ramond-heat-equality-does-not-identify-fixed-color-restricted-source"
      ],
      "requiredPremiseIds": [
        "premise:actual-thermal-quarter-source-and-retained-spin-parent-mixed-word",
        "premise:typed-source-structures",
        "premise:original-fixed-color-and-folded-ns-cartan-interface"
      ],
      "successCriterionEN": "Produce entire original response with cocycle,time/modes/zero modes and absolute sector traces;independently recover actual kernel and full thermal sewing under SAME center.",
      "nextActionEN": "Reuse result. Compare actual original Z_adm/C_Sigma/P_F with this full answer and its spin seam,trace and insertions;no repeated vertex/theta/heat or free spin-measure campaign.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-color-density-and-coordinate-region-descent",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Decide actual color admissibility of density operations and coordinate regions",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-color-selector-admits-exactly-eighth-periodic-original-density-variations",
        "finding:actual-color-is-internal-exactly-on-eightfold-coordinate-source-regions"
      ],
      "requiredPremiseIds": [
        "premise:actual-original-ns-color-center-continuous-density-and-coordinate-net",
        "premise:original-fixed-color-and-folded-ns-cartan-interface",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Decide complete given scalar-variation class and coordinate regions with actual M/center/source;retain whole charged intermediate words and originaltime.",
      "nextActionEN": "Reuse result,continue primitive full source map without new profile or region choice.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-calderon-operation-and-full-source-response",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute actual whole seam-operation class and two-face response",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-whole-two-face-multiplier-reduction-is-only-constant-residue-diagonal",
        "finding:original-two-face-local-fock-implementation-and-exact-source-variation-differ-from-reduction"
      ],
      "requiredPremiseIds": [
        "premise:actual-original-full-two-face-graph-and-local-matrix-operations",
        "premise:actual-product-collar-two-face-data",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Analytically decide whole matrix multiplication reduction/implementation and exact original response;preserve Cauchy/Fock/OS types.",
      "nextActionEN": "Reuse result,execute actual original field/source map inOSconsumer.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-c6-entire-word-expansion-and-source-amplitude",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute entire original C6 word expansion with source amplitude",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-c6-half-power-has-exact-entire-positive-ordered-word-expansion",
        "finding:original-c6-whole-word-sewing-retains-source-amplitude-and-controlled-infinite-tail"
      ],
      "requiredPremiseIds": [
        "premise:original-bare-c6-fixed-analytic-half-power-and-literal-word-alphabet",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Analyticallydecidealloriginalwordlengths/intermediates,concatenation,absoluteamplitude,homogeneousdeltaresponsewithtailcontrol.",
      "nextActionEN": "Reuse result,execute original marked field/coupling call;no physical source replacement by definition.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-collective-higgs-force-source-and-mean-dual",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original collective Higgs force source and entire mean dual",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-original-higgs-force-has-complete-ordered-fermionic-determinant-source",
        "finding:finite-covariant-higgs-composites-have-no-nontrivial-positive-instantaneous-classical-law",
        "finding:actual-original-collective-mean-has-exact-ball-domain-and-relative-entropy-action"
      ],
      "requiredPremiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-finite-car-higgs-force-and-faithful-collective-source"
      ],
      "successCriterionEN": "Decideactualgaugeaction,wholeorderedsource,finiteclassicalreplacementclassandexactGibbs/Legendremeandomain.",
      "nextActionEN": "Reuse;continueprimitivefield/weightmap,noimposedm=HorGammaasbosonmeasure.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-allmode-force-with-actual-time-and-whole-source",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original all-mode force with actual time and whole source",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-uniform-allmode-force-clt-is-nonzero-only-before-fixed-time-smearing",
        "finding:original-unscaled-time-smeared-force-has-selfadjoint-whole-ordered-source"
      ],
      "requiredPremiseIds": [
        "premise:typed-source-structures",
        "premise:actual-whole-circle-product-car-force-and-original-time-smearing"
      ],
      "successCriterionEN": "Decide uniform dynamic candidate and construct actual unscaled whole ordered time quantum source.",
      "nextActionEN": "Reuse source;follow original supported field/weight map,no K=H.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:execute-original-local-spacetime-force-source-and-causal-lift",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original local space/time force source and causal lift",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-local-higgs-force-has-whole-centered-hilbert-schmidt-determinant-source",
        "finding:given-original-circle-force-source-generates-an-exact-causal-local-net"
      ],
      "requiredPremiseIds": [
        "premise:typed-source-structures",
        "premise:original-constant-circle-local-higgs-force-and-hilbert-schmidt-time-source"
      ],
      "successCriterionEN": "Decideactuallocalinsertion,wholeinfinitesourceandoperatorlocalityingivencircle.",
      "nextActionEN": "Reusesource;executeoriginalmastercarrierandcommonweight.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:explicit-e8-all-current-response-reader",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "titleEN": "Build an explicit248-current reader with complete Ward response",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:e8-current-dictionary-all-separated-responses"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization"
      ],
      "successCriterionEN": "Concrete fields, cocycle, statistics and all separated root/Cartan insertions in the same given E8 representation.",
      "nextActionEN": "Reuse e8_boundary_response.current_response. Existing task:synthesize-joint-source-operator-dictionary still requires the original physical insertion map; do not substitute a freely chosen coupling for its derivation.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:audit-actual-charged-scaling-source-reproduction",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "titleEN": "Reproduce actual charged source path to its first missing map",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:charged-scaling-microscopic-map-still-unspecified",
        "finding:original-slater-proxy-fitted-bound-fails-actual-norm",
        "finding:periodic-microscopic-zero-modes-distinguish-source-state"
      ],
      "requiredPremiseIds": [
        "premise:literal-microscopic-charged-scaling-and-v988-slater-data",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Audit the first original lattice-to-field dictionary and reproduce an energy probe on the actual unchanged state.",
      "nextActionEN": "Open task:synthesize-joint-source-operator-dictionary requires actual B_N on a named microscopic sector with refinement, localization and energy proofs. Explicitly retain the periodic half-zero-mode covariance or derive a different state rule. Abstract E8 extension and clock conjugacy retain their completed scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compare-four-independent-foundations",
      "problemId": "problem:fundamental-process-classification",
      "titleEN": "Check four independent starting classes and counterworlds",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:replicated-deterministic-consistency-iff-influence-dag",
        "finding:three-binary-processes-two-copy-reversible-classification",
        "finding:independent-poset-information-composition-consequences",
        "finding:reset-diagnosis-not-global-tfpt-underdetermination"
      ],
      "requiredPremiseIds": [
        "premise:foundational-reset-no-target-input",
        "premise:finite-event-poset",
        "premise:finite-deterministic-joint-replication-control",
        "premise:finite-update-observation-errors",
        "premise:finite-operational-composition-action"
      ],
      "successCriterionEN": "Check assumptions, necessary consequences and limits in each class; compare TFPT only afterward.",
      "nextActionEN": "Reuse the reviewed classification and general composition theorem within scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:assess-record-preserving-composition-principle",
      "problemId": "problem:fundamental-process-classification",
      "titleEN": "Jointly justify replica control and actual record persistence",
      "kind": "assessment",
      "status": "open",
      "dependsOn": [
        "task:compare-four-independent-foundations",
        "task:ground-observable-discriminator-constraints"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:foundational-reset-no-target-input"
      ],
      "successCriterionEN": "An independent principle justifies permitted composition and persistent readable records in the same process class; explicitly decide erasure operations, physical access restrictions and counterworlds. Choose no target internal algebra or TFPT number.",
      "nextActionEN": null,
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compare-minimal-observable-counterworlds",
      "problemId": "problem:fundamental-process-classification",
      "titleEN": "Compare minimal observation conditions and counterworlds",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:three-inequivalent-repeatable-observation-countermodels",
        "finding:repeatable-reports-do-not-imply-full-state-stability",
        "finding:finite-sequential-data-admit-classical-history-realization"
      ],
      "requiredPremiseIds": [
        "premise:repeatable-distinction-benchmark",
        "premise:three-explicit-observability-countermodels",
        "premise:finite-prefix-consistent-sequential-data"
      ],
      "successCriterionEN": "Explicitly check independent assumptions, at least three operationally inequivalent countermodels, shared consequences, concrete discriminators and whether they exceed definitions.",
      "nextActionEN": "Retain countermodels and identification limits; do not force a winner with fitted additional axioms.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:ground-observable-discriminator-constraints",
      "problemId": "problem:fundamental-process-classification",
      "titleEN": "Empirically ground a discriminator and access conditions",
      "kind": "assessment",
      "status": "open",
      "dependsOn": [
        "task:compare-minimal-observable-counterworlds"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:foundational-reset-no-target-input"
      ],
      "successCriterionEN": "Identify a concrete reproducible phenomenon with independently justified access/memory/context conditions separating remaining candidates; no silent new selection rule. Assess L1 consistency, L2 conditional necessity and L3 physical explanation separately.",
      "nextActionEN": null,
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:review-unbounded-pascal-source",
      "problemId": "problem:carrier-pascal-glue-formal-scope",
      "titleEN": "Classify the unbounded Pascal proof",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:pascal-carrier-rank-unique-unbounded-source-proof"
      ],
      "requiredPremiseIds": [
        "premise:pascal-carrier-exhaustion-equation"
      ],
      "successCriterionEN": "The precise mathematical statement and premises have been reviewed in the original sources.",
      "nextActionEN": "Reuse this scope; infer neither physical selection nor a fresh kernel run.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:review-finite-glue-source-scope",
      "problemId": "problem:carrier-pascal-glue-formal-scope",
      "titleEN": "Classify the formal finite glue scope",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:finite-carrier-glue-elements-orbits-and-halfway"
      ],
      "requiredPremiseIds": [
        "premise:specified-finite-carrier-discriminant-form"
      ],
      "successCriterionEN": "The precise mathematical statement and premises have been reviewed in the original sources.",
      "nextActionEN": "Reuse this scope; infer neither physical selection nor a fresh kernel run.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:define-marked-seam-transport-category",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Define marked seam category and factor formula",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:marked-seam-category-and-character-valued-full-lift-factor"
      ],
      "requiredPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "successCriterionEN": "Precise object class, complete proof and reproducible certificate within declared scope.",
      "nextActionEN": "Reuse proved theorem within scope; do not reopen as a new task.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-quarter-clock-four-puncture-sign-lifts",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Completely classify quarter-clock four-puncture lifts",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:quarter-clock-sign-lift-complete-four-puncture-classification"
      ],
      "requiredPremiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection"
      ],
      "successCriterionEN": "Precise object class, complete proof and reproducible certificate within declared scope.",
      "nextActionEN": "Reuse proved theorem within scope; do not reopen as a new task.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compute-quarter-central-quotient-restrictions",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Determine central class and all subgroup restrictions",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:quarter-lift-central-quotient-class-and-all-subgroup-restrictions"
      ],
      "requiredPremiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "successCriterionEN": "Precise object class, complete proof and reproducible certificate within declared scope.",
      "nextActionEN": "Reuse proved theorem within scope; do not reopen as a new task.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compute-native-g0-full-factor-class",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Determine full G0 cocycle and class",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:native-clock-reflection-full-factor-cocycle-trivialization"
      ],
      "requiredPremiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "successCriterionEN": "Precise object class, complete proof and reproducible certificate within declared scope.",
      "nextActionEN": "Reuse proved theorem within scope; do not reopen as a new task.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compute-native-456-local-cohomology",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Determine native4/5/6local cohomology",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:native-quartic-exterior-local-cohomology-distinguishes-clock-monodromies"
      ],
      "requiredPremiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "successCriterionEN": "Precise object class, complete proof and reproducible certificate within declared scope.",
      "nextActionEN": "Reuse proved theorem within scope; do not reopen as a new task.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-unrestricted-g31-reflection-monodromy",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Classify unrestricted G31 reflection monodromies",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:define-marked-seam-transport-category",
        "task:compute-native-g0-full-factor-class"
      ],
      "resolutionIds": [
        "finding:original-g31-reflection-census-and-all-integral-cohomology",
        "finding:all62-original-clock-obstructions-and-central-variants"
      ],
      "requiredPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "successCriterionEN": "Specify actual peripheral G31 conjugacy classes and completely determine product1 moduli with orbits/stabilizers.",
      "nextActionEN": "Reuse complete original reflection quadruple classification; do not reopen this case.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compute-lift-class-beyond-native-g0",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Determine lift class beyond G0",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:compute-native-g0-full-factor-class"
      ],
      "resolutionIds": [
        "finding:global-original-g31-character-lift-nonsplitting"
      ],
      "requiredPremiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension"
      ],
      "successCriterionEN": "Evaluate factor formula on an explicitly larger actual group and prove its class.",
      "nextActionEN": "Reuse the proved original nonsplitting theorem. Keep the central determinant class and character-valued monodromy lifts distinct; do not reopen this global question.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-reflection-equivariant-and-mapping-class-seam-lifts",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Classify additional reflection/clock equivariance and mapping-class quotients",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:classify-quarter-clock-four-puncture-sign-lifts"
      ],
      "resolutionIds": [],
      "requiredPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection"
      ],
      "successCriterionEN": "Define extra markings and morphisms and prove remaining classes relative to the present moduli.",
      "nextActionEN": "Fixed native T0/JT0 reflection lifts, R=J rotation, joint native case and pure mapping class quotient are now decided in MATH.SEAM.EQUIVARIANCE.SEARCH.01. A larger quotient over all allowed normalizer isometries or jointly transported reflection markings still needs its explicit category and complete classification. Do not promote scoped results to that stronger statement.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:completed-equivariant-study-0",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Equivariant lifting and divisibility by eight",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:orbifold-lift-criterion-and-determinant-eight-divisibility"
      ],
      "requiredPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "successCriterionEN": "Full proof and finite evaluation under explicit equivalence.",
      "nextActionEN": "Reuse proved theorem within its stated contract.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:completed-equivariant-study-2",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "All62clock obstructions and central transport variants",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:all62-original-clock-obstructions-and-central-variants"
      ],
      "requiredPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "successCriterionEN": "Full proof and finite evaluation under explicit equivalence.",
      "nextActionEN": "Reuse proved theorem within its stated contract.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:completed-equivariant-study-3",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Actual group comparison and central pushout exclusion",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-sign-lift-g31-group-comparison"
      ],
      "requiredPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "successCriterionEN": "Full proof and finite evaluation under explicit equivalence.",
      "nextActionEN": "Reuse proved theorem within its stated contract.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:completed-equivariant-study-4",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Complete invariants and explicit collisions",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:complete-g31-lift-invariants-and-explicit-collisions"
      ],
      "requiredPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "successCriterionEN": "Full proof and finite evaluation under explicit equivalence.",
      "nextActionEN": "Reuse proved theorem within its stated contract.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:e-series-slices-under-actual-quarter-clock",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Compare E6 and E7 slices with the actual quarter clock",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:e7-quarter-pairs-literal-native-g31-reflections",
        "finding:e6-root-subsystem-quarter-clock-discriminant-obstruction",
        "finding:e-series-square-cover-family-and-quarter-descent",
        "finding:e-series-integral-glue-and-normalization-nonidentifiability"
      ],
      "requiredPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "successCriterionEN": "Actual root action and an explicit dictionary to existing reflections; completeness proof within stated scope.",
      "nextActionEN": "Retain the established P1/P2→D5+A3→E8 and seed derivations. All four follow-up dictionaries are solved in MATH.SEAM.ESERIES.CLOSURE.04: full field lifts, fixed compiler, common covers with maximal intertwiner, and48/4/3/5/4 projector identities. The separate global noncentral lift class is now also decided and must not be reopened.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:completed-original-g31-character-monodromy-lifts",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Classify original character-valued G31monodromy lifts",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:compute-lift-class-beyond-native-g0",
        "task:classify-unrestricted-g31-reflection-monodromy"
      ],
      "resolutionIds": [
        "finding:all62-original-character-clock-lifts-complete",
        "finding:all17-original-character-monodromy-lifts-complete"
      ],
      "requiredPremiseIds": [
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "successCriterionEN": "Complete17/62census and normal-form action.",
      "nextActionEN": "Reuse proved classification.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:complete-e7-pair-all-field-dictionary",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Determine E7-pair action on all original lattice fields",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:e-series-slices-under-actual-quarter-clock",
        "task:compute-lift-class-beyond-native-g0"
      ],
      "resolutionIds": [
        "finding:e7-pair-full-lattice-field-character-torsor"
      ],
      "requiredPremiseIds": [
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "successCriterionEN": "Compare actual operators or weights; completely solve the fixed object class with explicit proof and direct certificate.",
      "nextActionEN": "Reuse the proved dictionary in MATH.SEAM.ESERIES.CLOSURE.04; preserve decided cases and exclusions.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:complete-native-compiler-e-series-cut-dictionary",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Completely connect E6/E7 cuts to the original compiler",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:e-series-slices-under-actual-quarter-clock"
      ],
      "resolutionIds": [
        "finding:e-series-complete-native-compiler-cut-dictionary"
      ],
      "requiredPremiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "successCriterionEN": "Compare actual operators or weights; completely solve the fixed object class with explicit proof and direct certificate.",
      "nextActionEN": "Reuse the proved dictionary in MATH.SEAM.ESERIES.CLOSURE.04; preserve decided cases and exclusions.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:complete-cover-clock-actual-carrier-dictionary",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Compare common covers and actual clock carriers",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:e-series-slices-under-actual-quarter-clock"
      ],
      "resolutionIds": [
        "finding:common-cover-clock-and-maximal-integral-phi12-intertwiner"
      ],
      "requiredPremiseIds": [
        "premise:existing-marked-cyclic-cover-and-burau-model",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "successCriterionEN": "Compare actual operators or weights; completely solve the fixed object class with explicit proof and direct certificate.",
      "nextActionEN": "Reuse the proved dictionary in MATH.SEAM.ESERIES.CLOSURE.04; preserve decided cases and exclusions.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:complete-shared48-fourthirds-fivequarters-consequence",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Prove shared representation consequence for48,4/3 and5/4",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:complete-native-compiler-e-series-cut-dictionary"
      ],
      "resolutionIds": [
        "finding:native-four-cut-projectors-unify48-fourthirds-fivequarters"
      ],
      "requiredPremiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "successCriterionEN": "Compare actual operators or weights; completely solve the fixed object class with explicit proof and direct certificate.",
      "nextActionEN": "Reuse the proved dictionary in MATH.SEAM.ESERIES.CLOSURE.04; preserve decided cases and exclusions.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:complete-joint-native-compiler-cover-covariance",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Completely decide joint compiler-field-cover construction",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:complete-e7-pair-all-field-dictionary",
        "task:complete-native-compiler-e-series-cut-dictionary",
        "task:complete-cover-clock-actual-carrier-dictionary",
        "task:complete-shared48-fourthirds-fivequarters-consequence"
      ],
      "resolutionIds": [
        "finding:complete-covariant-compiler-voa-source-and-weyl-closure",
        "finding:complete-fixed-jhat-cyclic-field-lift-and-associated-clock",
        "finding:relative-native-burau-clock-hom-faithful12-transport",
        "finding:e6-vertex-nonselection-survives-full-field-clock-phases"
      ],
      "requiredPremiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:existing-marked-cyclic-cover-and-burau-model",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:joint-native-compiler-cover-covariance-category"
      ],
      "successCriterionEN": "Actual common carrier with composing maps, minimal closure and complete lift/periphery/selection compatibility decision in the stated category.",
      "nextActionEN": "Reuse MATH.SEAM.ESERIES.JOINTSOURCE.05 as the complete joint mathematical connection. Retain all marks and relative carries; do not reopen excluded stronger identifications as uncomputed cases.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-canonical-compiler-field-source-from-c4",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reconstruct canonical local compiler field source from C4",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:complete-joint-native-compiler-cover-covariance"
      ],
      "resolutionIds": [
        "finding:marked-c4-glue-unique-local-e8-vacuum-source",
        "finding:canonical-vacuum-clock-preserves-e6-nonselection"
      ],
      "requiredPremiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:marked-c4-unitary-local-extension-reconstruction-class"
      ],
      "successCriterionEN": "Determine products, state, conformal dynamics and local extension in the exact labelled class without assuming primitive source selection.",
      "nextActionEN": "Reuse MATH.SEAM.ESERIES.SOURCE-RECONSTRUCTION.06 in its specified class and retain its extra realization premise.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:eliminate-redundant-c4-support-and-multiplicity-inputs",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Eliminate redundant sector and multiplicity assumptions",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:reconstruct-canonical-compiler-field-source-from-c4"
      ],
      "resolutionIds": [
        "finding:marked-generator-forces-e8-without-support-multiplicity-or-minimality-input"
      ],
      "requiredPremiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:connected-local-same-conformal-compiler-extension-with-generator"
      ],
      "successCriterionEN": "Derive support and multiplicities from the weaker connected local conformal hypotheses and classify all remaining extensions.",
      "nextActionEN": "Use SIMPLIFICATION.txt as the stronger theorem and retain its first realization premise; extra minimality models are unnecessary in this class.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:native-quarter-equivariant-markings",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Classify native equivariant markings",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:classify-quarter-clock-four-puncture-sign-lifts"
      ],
      "resolutionIds": [
        "finding:native-reflection-rotation-lift-classes-and-forgetful-images"
      ],
      "requiredPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection",
        "premise:fixed-native-reflection-rotation-character-markings"
      ],
      "successCriterionEN": "Complete classification with explicit objects, morphisms and direct original certificates.",
      "nextActionEN": "Reuse proved result in its stated scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:pure-quarter-clock-mapping-class-quotient",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Classify pure quarter clock mapping class quotient",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:classify-quarter-clock-four-puncture-sign-lifts"
      ],
      "resolutionIds": [
        "finding:quarter-clock-pure-mapping-class-complete-quotient"
      ],
      "requiredPremiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection",
        "premise:ordered-quarter-clock-pure-hurwitz-equivalence"
      ],
      "successCriterionEN": "Complete classification with explicit objects, morphisms and direct original certificates.",
      "nextActionEN": "Reuse proved result in its stated scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:complete-e6-incidence-and-lossless-tetrahedron-transform",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Determine complete cut algebra and lossless tetrahedron transform",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:complete-joint-native-compiler-cover-covariance"
      ],
      "resolutionIds": [
        "finding:e8-cut-five-orbital-incidence-algebra-complete",
        "finding:compiler-d8-frame-requires-full-d5-a3-flag",
        "finding:tetrahedron-incidence-lossless-e6-reconstruction",
        "finding:restricted-clock-lift-and-global-cover-audit-reconciled"
      ],
      "requiredPremiseIds": [
        "premise:standard-e8-root-cut-full-flag-incidence-category",
        "premise:joint-native-compiler-cover-covariance-category",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension"
      ],
      "successCriterionEN": "Determine all full orbitals, structure constants, incidences and information losses on actual root sets and reconcile the original clock comparison with the independent report.",
      "nextActionEN": "Reuse the complete finite theorem MATH.SEAM.ESERIES.INCIDENCE.07 and the bundled unchanged originals. Lossless evaluation does not choose its input signal.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:identify-scalar-glue-and-native-cyclic-clock-class",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Completely compare scalar glue and actual native compiler class",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:reconstruct-canonical-compiler-field-source-from-c4",
        "task:complete-e6-incidence-and-lossless-tetrahedron-transform"
      ],
      "resolutionIds": [
        "finding:double-scalar-quarter-is-marked-glue-with-two-step-index",
        "finding:scalar-quarter-two-involutive-e8-extensions",
        "finding:native-quarter-glue-inner-conjugacy-and-oriented-tetrahedron-flags",
        "finding:native-cyclic-compiler-inner-conjugacy"
      ],
      "requiredPremiseIds": [
        "premise:scalar-eight-channel-twist-and-explicit-compiler-charge-chart",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "successCriterionEN": "Determine the actual lattice map, all scalar extensions, full clock conjugacy and its tetrahedron-flag connection.",
      "nextActionEN": "Reuse SOURCE-RECONSTRUCTION.06 reproduction. For physical origin audit the actual microscopic field/refinement morphism; do not treat an abstract inner conjugator as its selection.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-actual-clock-doily-quartic",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify actual clock doily and quartic space",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:actual-clock-doily-ovoid-kernel-is-native-quartic-five"
      ],
      "requiredPremiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:unify-clock-glue-and-twisted-branches",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Determine common clock and glue description",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:glue-clock-twisted-sectors-share-marked-quadratic-module"
      ],
      "requiredPremiseIds": [
        "premise:marked-c4-unitary-local-extension-reconstruction-class",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-native-six-effect-instruments",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Classify all finite covariant instruments",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:complete-native-six-effect-covariant-instrument-classification"
      ],
      "requiredPremiseIds": [
        "premise:original-six-ovoid-covariant-instrument-category"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:connect-new-observable-to-existing-erasure-consumer",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Connect new observable to actual erasure output",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:native-six-effect-readout-on-existing-erasure-output"
      ],
      "requiredPremiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:separate-singlet-ray-from-physical-state-selection",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Separate singlet ray from physical state selection",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:relational-quartic-singlet-and-invariant-density-separation"
      ],
      "requiredPremiseIds": [
        "premise:relational-native-quartic-tensor-sector-without-state-selection"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:audit-feedback-loop-origin-premises",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Audit origin premises of the feedback loop",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:new-clock-feedback-origin-input-audit"
      ],
      "requiredPremiseIds": [
        "premise:declared-p1-p2"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compare-classified-channels-with-original-native-events",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Compare classified channels with original native events",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:classify-native-six-effect-instruments"
      ],
      "resolutionIds": [
        "finding:native-event-channel-cone-intersection-is-tenth-to-half"
      ],
      "requiredPremiseIds": [
        "premise:original-six-ovoid-covariant-instrument-category",
        "premise:native-clock-complex-reflection-and-quartic-subspace"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-original-seam-selection-of-native-observable-process",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Select the operational observable process from original seam action",
      "kind": "construction",
      "status": "open",
      "dependsOn": [
        "task:classify-native-six-effect-instruments",
        "task:connect-new-observable-to-existing-erasure-consumer",
        "task:audit-feedback-loop-origin-premises",
        "task:compare-classified-channels-with-original-native-events",
        "task:classify-minimum-native-ovoid-observation-stage",
        "task:close-original-quartic-erasure-derivative-dictionary",
        "task:identify-original-octic-field-and-test-clock-preparation",
        "task:derive-actual-quarter-fold-octic-stress-response",
        "task:reconstruct-octic-directly-in-original-car-and-geometric-jet",
        "task:recover-paper-microscopic-neutral-octic-chain",
        "task:correct-paper-source-identification-criterion",
        "task:repair-original-seam-ray-and-os-moment-identifications",
        "task:recover-older-circle-source-and-controlled-heat-closure",
        "task:close-direct-original-seam-defect-and-reweighting-interface",
        "task:close-original-spin-and-retained-source-defect-dictionary",
        "task:transport-original-seam-factor-through-faithful-kms-and-carrier",
        "task:close-pair-index-original-clutch-and-ns-limit-interface",
        "task:resolve-normal-index-line-and-full-source-pushforward-criterion",
        "task:compare-normal-connection-and-tetrahedral-cover-transport",
        "task:close-joint-lift-split-connection-and-native-clock-compatibility",
        "task:identify-native-cartan-four-and-global-joint-mark-transport",
        "task:complete-native-octic-under-existing-source-zero-mode-symmetry",
        "task:compute-source-w8-twopoint-and-assess-original-local-p1-map",
        "task:audit-older-seam-results-and-reconstruct-full-original-stress-cycle",
        "task:recover-original-winding-comparison-and-local-quarter-current-net",
        "task:assess-fixed-pin-descent-of-original-winding-conjugation",
        "task:resolve-full-pin-reflection-and-ns-cover-green-positivity",
        "task:realize-existing-quarter-source-on-concrete-elliptic-moebius-cut",
        "task:complete-full-elliptic-real-slots-and-test-marked-seam-and-p2-pushforward",
        "task:close-global-spin-kernel-and-test-modular-three-source-dictionary",
        "task:derive-real-equatorial-trace-and-recover-original-c4-monodromy-proof"
      ],
      "resolutionIds": [
        "finding:canonical-conformal-boundary-trace-fixes-existing-elliptic-cauchy-state",
        "finding:conformal-factor-averaging-preserves-given-free-boundary-wick-words",
        "finding:full-projector-covariance-and-positivity-force-all-car-words",
        "finding:actual-two-face-projector-reduces-free-source-test-to-cross-coherence",
        "finding:existing-elliptic-half-period-has-canonical-graded-gns-intertwiner",
        "finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law",
        "finding:source-spin-relative-poincare-normalization-closes-point-norm-family",
        "finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package",
        "finding:full-clock-norm-power-class-and-canonical-eighth-period",
        "finding:original-unit-winding-selects-one-inverse-norm-in-three-cabled-hardy-pair",
        "finding:original-boundary-audit-and-h1-point-restriction-limit",
        "finding:eta-phase-conventions-do-not-identify-relative-spin-reference-pair",
        "finding:same-spin-unit-shift-gives-native-module-class-with-odd-determinant-line",
        "finding:original-even-odd-operator-split-is-compatible-with-same-spin-seam-reference",
        "finding:four-session-summaries-remain-covered-with-superseded-norm-selection-task",
        "finding:elliptic-projector-and-weyl-results-retain-their-source-type-at-cubic-spin-bridge",
        "finding:cubic-spin-cauchy-range-is-three-hardy-with-strong-domain-distinction",
        "finding:original-negative-sea-three-mode-ket-is-dual-to-required-hardy-line",
        "finding:auxiliary-theta-route-needs-no-physical-cubic-bulk-or-eta-selected-dual",
        "finding:primitive-gaussian-theta-frame-constructs-e8-pair-with-retained-spin-action",
        "finding:existing-c12-lift-induces-coherent-two-object-e8-vertex-groupoid",
        "finding:actual-winding-functional-calculus-preserves-ns-ramond-split",
        "finding:single-chiral-cycle-exchange-selects-e8-in-four-extension-class",
        "finding:affine-source-involution-pairs-full-d8-sector-spectra",
        "finding:marked-local-e8-with-unchanged-source-time-fails-euclidean-clustering",
        "finding:original-parity-audit-does-not-supply-local-spinor-gauging",
        "finding:hypergraph-local-update-repaired-with-full-family-clock",
        "finding:petersen-polar-step-has-exact-double-cover-family-intertwiner",
        "finding:petersen-source-current-and-hodge-candidates-fail-physical-identification",
        "finding:a7-clock-direction-identifies-neutral-e7-zero-root",
        "finding:oriented-sewing-cocycle-distinguishes-continuation-and-reversal",
        "finding:calderon-single-face-compression-is-not-perron-projector",
        "finding:hodge-born-magnitudes-and-filtered-petersen-jump-match",
        "finding:five-complement-amplitudes-form-full-petersen-quantum-channel",
        "finding:original-twenty-events-factor-through-hodge-and-conditional-phase-record",
        "finding:actual-e8-mixed-current-response-is-full-clifford-channel",
        "finding:carrier-su5-centralizer-gives-direct-e8-petersen-response",
        "finding:su5-covariance-and-petersen-support-fix-complete-quantum-response",
        "finding:neutral-pair-witness-separates-old-events-and-hodge-response",
        "finding:original-degree-clock-is-not-carrier-slot-cycle-at-fixed-source",
        "finding:full-mark-transport-and-isospectrality-do-not-select-hodge-channel",
        "finding:original-pair-source-fixes-state-but-not-selected-epsilon-process",
        "finding:single-positive-process-saturation-selects-full-hodge-channel",
        "finding:original-five-slot-wedge-is-exact-e8-hodge-coefficient",
        "finding:native-pauli-f20-metric-and-quarter-bridge",
        "finding:two-actual-coherent-events-herald-hodge-at-one-over-twenty-five",
        "finding:original-color-center-removes-only-extra-h8-ground-state",
        "finding:marked-symplectic-functor-fixes-native-hodge-kraus-space",
        "finding:f20-record-repair-removes-chart-induced-three-plus-two",
        "finding:theta-scalar-square-lift-is-distinct-from-symplectic-f20-lift",
        "finding:full-admissibility-vacuum-test-needs-source-image-and-transfer-reduction",
        "finding:canonical-native-spin5-hodge-is-already-one-source-record-subchannel",
        "finding:native-hodge-record-selector-is-image-projector-not-kraus-kernel",
        "finding:irreducible-f20-four-cannot-host-original-independent-native-family-clock",
        "finding:native-hodge-is-exact-collective-five-current-action",
        "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
        "finding:six-hodge-responses-have-exact-full-current-barycenter",
        "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts",
        "finding:spin5-hodge-five-is-plucker-kernel-not-original-quartic-hessian",
        "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
        "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
        "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
        "finding:old-ward-root-generates-exact-charged-fifty-module",
        "finding:tp-charged-bracket-support-forces-entire-carrier-marginal",
        "finding:original-ward-and-p2-grading-select-smaller-creation-thirty",
        "finding:charged-source-quarter-recovers-inverse-internal-glue",
        "finding:state-independent-creation-branch-removes-whole-process-hodge-demand",
        "finding:given-source-current-constructs-half-kink-spinor-transport",
        "finding:neutral-ward-response-needs-no-spinor-observable-membership",
        "finding:actual-source-sector-transport-distinguishes-identical-hodge-marginals",
        "finding:ordinary-weyl-type-obstruction-to-single-chiral-os-anti-anti-reflection",
        "finding:given-two-face-source-derives-opposite-neutral-weyls-and-bounded-time-reflection",
        "finding:finite-ko6-pairing-does-not-supply-standalone-pfaffian-source",
        "finding:full-free-projector-forces-joint-commuting-source-factorization",
        "finding:actual-neutral-current-source-has-constructive-moebius-standard-pair",
        "finding:continuous-local-current-weyls-cannot-live-in-finite-coordinate-fibers",
        "finding:actual-folded-current-ward-and-state-determine-all-neutral-words",
        "finding:graded-boundary-clifford-typing-transports-full-scalar-and-finite-coupled-source"
      ],
      "requiredPremiseIds": [
        "premise:declared-p1-p2"
      ],
      "successCriterionEN": "Actually identify original P1 source on relevant local marked sector: jointly derive field generators,adjoint,products/cocycle,state map,seam/reflection and actual OS transfer. Determine physical admissible net through A/A* invariance. Do not presume the now excluded full-local E8 identification with unchanged H=8K and clustering as the target. A different time or restricted observable map needs original derivation and alone is not complete physics. Apply existing E8 reconstruction within proven scope; separately close electromagnetic readout and physical spacetime evolution. Charged generators may be intertwiners between superselection sectors. Pure neutral observable response requires neither every spinor as observable nor full localE8 extension; require stronger structures only for corresponding full-field claims.",
      "nextActionEN": "CURRENT29Oct14:24UTC: Reuse closed Clifford field/state/R/same-time diagram and actual v252/P2 SM wedge map. Free or exactly decoupled g+ channel locally carries entire old elliptic quarter source at beta4pi; do not reclassify its theta/nullmode law as missing. Constant fixed-channel test is complete: one old free occupation matches iff Phi e0;positive averages require almost-sure decoupling. Generic Yukawa/Majorana do not preserve additional SM+sigma fixed line. Do not infer whole NS cover winding/support from second spectrum. Spinor-CAR level4 was old; actual Y check confirms factor4 or12 with unchanged Ward charges. Now derive original common source with dynamical bosons and relevant field/sector operations from P1/P2; do not force entire interacting theory to remain old free source. Test which required physical readouts can follow through an original UV/sector map without changed current levels or new free couplings. Operational Seed already includes state/algebra/time; no universal extra measure requirement or second Fock construction on full OS space. The reviewed followup7 and the reviewed source followup11 actually received these corrected tasks; preserve Gemini. Full goal remains open pending real origin theorem.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:classify-minimum-native-ovoid-observation-stage",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Completely classify the minimum native ovoid observation stage",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:native-six-ovoid-observation-first-occurs-at-tensor-degree-three"
      ],
      "requiredPremiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:native-tensor-povm-and-coherent-source-category"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:close-original-quartic-erasure-derivative-dictionary",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Close the original quartic erasure derivative dictionary",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:original-quartic-erasure-and-hamming-octic-share-marked-ovoid-response"
      ],
      "requiredPremiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:native-clock-complex-reflection-and-quartic-subspace",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:native-tensor-povm-and-coherent-source-category"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:identify-original-octic-field-and-test-clock-preparation",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify original octic field and test clock preparation",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:native-octic-field-ray-is-explicit-but-retained-clock-stress-preparation-fails"
      ],
      "requiredPremiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-actual-quarter-fold-octic-stress-response",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive actual quarter-fold stress response",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:identify-original-octic-field-and-test-clock-preparation"
      ],
      "resolutionIds": [
        "finding:actual-quarter-fold-stress-has-nonzero-octic-eighth-jet"
      ],
      "requiredPremiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:reconstruct-octic-directly-in-original-car-and-geometric-jet",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reconstruct octic and geometric jet directly from original CAR",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:identify-original-octic-field-and-test-clock-preparation"
      ],
      "resolutionIds": [
        "finding:native-octic-is-an-original-even-car-current-composite",
        "finding:original-geometric-source-jet-and-partial-p1-seed-closure"
      ],
      "requiredPremiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "successCriterionEN": "Explicit map/classification in the stated contract.",
      "nextActionEN": "Reuse with all premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:recover-paper-microscopic-neutral-octic-chain",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Compose the existing microscopic paper theorem through the octic field",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:reconstruct-octic-directly-in-original-car-and-geometric-jet"
      ],
      "resolutionIds": [
        "finding:paper-microscopic-car-composes-with-native-octic-ward",
        "finding:microscopic-neutral-octic-has-controlled-smeared-limit"
      ],
      "requiredPremiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions"
      ],
      "successCriterionEN": "Compose existing original maps with actual operators/time and exact scope.",
      "nextActionEN": "Reuse as a resolved scoped result with its premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:correct-paper-source-identification-criterion",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Correct the original boundary criterion and redundant state premise",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:reconstruct-octic-directly-in-original-car-and-geometric-jet"
      ],
      "resolutionIds": [
        "finding:paper-seed-source-needs-local-image-not-global-equivalence",
        "finding:full-car-positive-time-forces-source-vacuum"
      ],
      "requiredPremiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions"
      ],
      "successCriterionEN": "Compose existing original maps with actual operators/time and exact scope.",
      "nextActionEN": "Reuse as a resolved scoped result with its premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:repair-original-seam-ray-and-os-moment-identifications",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Audit and repair original seam-line and OS moment identifications",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:correct-paper-source-identification-criterion"
      ],
      "resolutionIds": [
        "finding:original-winding-theorem-does-not-select-seam-ray",
        "finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel",
        "finding:original-os-step-needs-full-moments-not-connected-cumulants",
        "finding:graded-field-image-precedes-physical-observable-restriction"
      ],
      "requiredPremiseIds": [
        "premise:original-seam-pair-and-full-moment-os-statements"
      ],
      "successCriterionEN": "Locate the first missing operator and moment identification in the originals and prove a precise sufficient repair with countercontrols.",
      "nextActionEN": "Reuse the four scoped results with their premises; do not repeat a purely topological rank-one or cumulant-OS inference.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:recover-older-circle-source-and-controlled-heat-closure",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Recover older original source and controlled ground-mode closure",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:repair-original-seam-ray-and-os-moment-identifications"
      ],
      "resolutionIds": [
        "finding:older-original-circle-representative-already-realizes-ward-and-index",
        "finding:old-quarter-heat-transfer-has-controlled-rank-one-limit-and-odd-product",
        "finding:historical-em-rank-one-and-full-heat-traces-have-different-contracts",
        "finding:older-frg-functional-already-supplies-formal-full-moment-parent",
        "finding:earliest-c3-route-quantizes-level-but-needs-physical-kinetic-normalization",
        "finding:canonical-positive-circle-half-selects-the-toeplitz-line-and-sixth-order-correction"
      ],
      "requiredPremiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "successCriterionEN": "Identify earlier concrete operators/functionals at the originals, correct absence judgments, and decide whether full heat gives the later single-mode factor exactly or as a controlled limit.",
      "nextActionEN": "Reuse the old circle representation and full-moment definition. Add no new auxiliary source or repeat topology-only rank inferences.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:close-direct-original-seam-defect-and-reweighting-interface",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Close the direct old seam defect and actual reweighting contract",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:recover-older-circle-source-and-controlled-heat-closure"
      ],
      "resolutionIds": [
        "finding:old-seam-shift-canonically-gives-relative-car-line-and-fredholm-factor",
        "finding:old-index-coupling-removes-heat-map-and-has-sharp-residual-ward-test",
        "finding:original-admissibility-requires-image-membership-not-positive-half-or-commutation",
        "finding:old-closure-already-assumes-car-but-does-not-map-the-geometric-circle",
        "finding:historical-uv-map-infinite-mass-exclusion-already-proved-and-recovered"
      ],
      "requiredPremiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:full-graded-car-with-original-positive-time",
        "premise:historical-sf-sector-action-and-relative-normalization",
        "premise:original-admissibility-and-graded-source-interfaces",
        "premise:literal-positive-rg-map-on-finite-halfline-measures"
      ],
      "successCriterionEN": "Direct covariant line,relative determinant,old index coupling and exact residual-ratio criterion with original sources and independent review; not full physical completion.",
      "nextActionEN": "Reuse the result in its stated scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:close-original-spin-and-retained-source-defect-dictionary",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Close original spin and actual defect dictionary",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:close-direct-original-seam-defect-and-reweighting-interface"
      ],
      "resolutionIds": [
        "finding:a4-spin-lift-fixes-local-ns-and-unordered-quarter-pair",
        "finding:cover-winding-exchanges-quarter-sectors-before-its-square",
        "finding:retained-winding-preserves-local-support-and-neutral-time",
        "finding:marked-glue-square-is-the-e8-fermionization-character",
        "finding:fixed-canonical-d8-is-not-transported-source-d8",
        "finding:actual-winding-has-four-module-e8-defect-extension",
        "finding:ramond-lift-sign-is-common-intertwiner-basis-gauge"
      ],
      "requiredPremiseIds": [
        "premise:original-a4-same-moebius-order-four-pin-lift",
        "premise:fixed-marked-glue-and-retained-source-d8-frame",
        "premise:standard-four-d8-module-parent-with-retained-subtheories",
        "premise:full-graded-car-with-original-positive-time",
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "successCriterionEN": "Check A4 action,quarter/cover winding,neutral support/time and full affine extension preserving CAR/E8 words; decide whether new apparent signs are basis changes.",
      "nextActionEN": "Reuse the closed mathematical connections; test physical source and response identity separately.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:transport-original-seam-factor-through-faithful-kms-and-carrier",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Transport original seam factor through faithful KMS source and carrier",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:close-original-spin-and-retained-source-defect-dictionary"
      ],
      "resolutionIds": [
        "finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class",
        "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor",
        "finding:schur-carrier-plus-complement-preserves-original-relative-determinant",
        "finding:v258-forward-source-gap-is-reused-not-solved-by-inversion",
        "finding:one-sided-source-and-real-em-norm-need-response-map-not-chiral-phase"
      ],
      "requiredPremiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:same-original-circle-trace-class-covariance",
        "premise:existing-finite-orthogonal-carrier-on-same-source"
      ],
      "successCriterionEN": "Prove exact finite-beta factor,compression boundary and sufficient Schur transport on the same source without asserting physical EM functional identity.",
      "nextActionEN": "Reuse these results and the earlier v258 provenance audit.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:close-pair-index-original-clutch-and-ns-limit-interface",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Resolve pair index,original carrier clutch and actual NS limit interface",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:transport-original-seam-factor-through-faithful-kms-and-carrier"
      ],
      "resolutionIds": [
        "finding:trace-class-pair-index-fixes-relative-factor-without-primitive-ray",
        "finding:matrix-clutch-degree-connects-weak-determinant-class-without-ray-selector",
        "finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index",
        "finding:inner-carrier-is-infinite-spacetime-module-not-finite-circle-cut"
      ],
      "requiredPremiseIds": [
        "premise:trace-class-polarization-pair-with-restricted-unitary",
        "premise:smooth-matrix-clutch-on-original-negative-fourier-sea",
        "premise:actual-finite-ns-kernel-and-sampled-original-winding",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Prove the full relative pair-index class,connect actual original determinant class,and determine finite NS operator transport with valid determinant topology. Keep physical source identity separate.",
      "nextActionEN": "Reuse proof and controls. Do not demand an extra rank-one choice for the scalar factor,but prove same fields/time/reference and actual action on C_Sigma for the complete source.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:resolve-normal-index-line-and-full-source-pushforward-criterion",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Match normal index transport and full source response",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:close-pair-index-original-clutch-and-ns-limit-interface"
      ],
      "resolutionIds": [
        "finding:normal-spin-determinant-line-exactly-transports-whole-circle-in-given-product",
        "finding:normal-index-line-source-match-is-holonomy-condition-not-vertical-degree",
        "finding:full-normal-product-polarization-change-is-not-trace-class",
        "finding:massive-transverse-zero-index-retains-positive-determinant-response",
        "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel"
      ],
      "requiredPremiseIds": [
        "premise:given-normal-spin-line-and-genuine-circle-product",
        "premise:given-exact-reducing-indexline-with-horizontal-connection",
        "premise:positive-determinant-response-of-transverse-product-channels",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:typed-source-structures",
        "premise:closed-normal-fredholm-with-retained-complex-kernel-representation"
      ],
      "successCriterionEN": "Prove full circle map,domain,time and state in an explicit genuine product class;determine horizontal holonomy and boundary of the full ordinary determinant. Physical original identification remains separate.",
      "nextActionEN": "Reuse reducing transport,holonomy criterion and full trace-class/response boundaries;do not repeat Bott class or rank counts. Do not substitute original doublet multiplicity for a complex kernel line;a general closed normal operator suffices given the actual product and field map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compare-normal-connection-and-tetrahedral-cover-transport",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Compare normal connection fiber and tetrahedral cover transport",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:resolve-normal-index-line-and-full-source-pushforward-criterion"
      ],
      "resolutionIds": [
        "finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection",
        "finding:tetrahedral-quarter-face-phase-does-not-identify-original-quarter-marked-curve",
        "finding:existing-elliptic-cover-correspondence-has-exact-c6-image-and-retained-mixed-clock"
      ],
      "requiredPremiseIds": [
        "premise:smooth-matrix-circle-source-and-moving-projector-with-fixed-scalar-symbol",
        "premise:oriented-d3-tetrahedron-in-bloch-chart-versus-original-quarter-marks",
        "premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Determine the complete exact connection commutator in a named class,test first marked geometric identification,and calculate an existing broader cover correspondence with information loss and generator action. Do not infer physical source identity from equal phase.",
      "nextActionEN": "Reuse Kato criterion and existing elliptic correspondence;retain full C4 data and peripheral marks. Source must supply its own connection,fields and response.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:close-joint-lift-split-connection-and-native-clock-compatibility",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Match global joint lift,split connection and whole native clock",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:compare-normal-connection-and-tetrahedral-cover-transport"
      ],
      "resolutionIds": [
        "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
        "finding:global-split-joint-carrier-admits-parallel-native-c12-clock",
        "finding:pure-weak-clutch-clock-identification-fails-despite-quarter-matches",
        "finding:same-chern-clutch-native-compiler-does-not-select-physical-connection"
      ],
      "requiredPremiseIds": [
        "premise:natural-joint-spin-family-lift-with-given-split-connection",
        "premise:fixed-kappa-toral-third-centralizing-split-carrier",
        "premise:same-angle-evaluation-of-primitive-determinant-clutch-as-native-clock",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Reuse existing global lift,prove actual branch weights and common global connection and whole-clock action in a stated class. Test additional angle and marking identifications separately. Do not infer physical source identity from conjugacy.",
      "nextActionEN": "Reuse common parallel clock representative for every supplied split connection. Derive actual original connection,additional flavor transport,potential,domain and marked source intertwiner forward. Do not insert further free clutch optimization as P1 selection.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:identify-native-cartan-four-and-global-joint-mark-transport",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Resolve native four and global joint mark transport",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:close-joint-lift-split-connection-and-native-clock-compatibility"
      ],
      "resolutionIds": [
        "finding:native-gaussian-four-is-cartan-subspace-in-whole-sixtyfour",
        "finding:native-family-factor-is-not-gaussian-four-despite-symmetric-coincidences",
        "finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice",
        "finding:even-degree-pullback-removes-cartan-topology-without-selecting-clock-cover"
      ],
      "requiredPremiseIds": [
        "premise:native-cartan-four-in-full-clock-conjugate-source",
        "premise:primitive-normal-sphere-joint-k-bundle-class-two",
        "premise:given-same-normal-base-degree-pullback"
      ],
      "successCriterionEN": "Compare actual clock and tensor action,prove positive whole-source inclusion,and type global bundle transport and existing covers exactly.",
      "nextActionEN": "Reuse Cartan subspace and normalizer as scoped results. Only where whole Cartan-mark transport is actually needed,prove original punctures,covers and defects of the same source with connection. For scalar operator use explicit W8 completion.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:complete-native-octic-under-existing-source-zero-mode-symmetry",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Complete native octic under E8 in the same source",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:reconstruct-octic-directly-in-original-car-and-geometric-jet",
        "task:identify-native-cartan-four-and-global-joint-mark-transport"
      ],
      "resolutionIds": [
        "finding:global-cartan-choice-is-optional-for-original-scalar-source-fields",
        "finding:explicit-primary-e8-invariant-octic-completes-same-neutral-car-source",
        "finding:completed-octic-has-exact-old-root-ope-component-and-quarter-source-value"
      ],
      "requiredPremiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Test actual root and Virasoro actions;prove explicit positive operator completion and its connection to old source fields with exact scope.",
      "nextActionEN": "Reuse W8 and existing neutral CAR source. Resolve P1 connection through the same local-operator and Theta/Dcoll/Dref transport with domains;do not impose global Cartan choice first.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:compute-source-w8-twopoint-and-assess-original-local-p1-map",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Compute W8 source response and assess the original local P1 connection",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:complete-native-octic-under-existing-source-zero-mode-symmetry"
      ],
      "resolutionIds": [
        "finding:exact-separated-w8-twopoint-in-original-quarter-current-source",
        "finding:unshifted-vacuum-fails-same-w8-source-state-time-dictionary",
        "finding:local-current-phase-and-conditional-cyclic-p1-w8-image",
        "finding:all-neutral-w8-correlations-identify-the-two-original-quarter-charges",
        "finding:original-w8-response-has-infinite-same-time-spectral-support"
      ],
      "requiredPremiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Compute the complete separated source function exactly, retain the same original state/time, assess P1 operator status against reviewed originals and judge concrete candidates within scope. An unconstructed P1 map remains open.",
      "nextActionEN": "Reuse the function. Derive the actual local generating Weylsystem from the original admissible fermionic kernel; local phase, full state kernel, time, reflection and support must match. Then construct the actual P1 W8 image and separated target comparison.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:audit-older-seam-results-and-reconstruct-full-original-stress-cycle",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Review older seam results and reconstruct the complete original stress cycle",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:compute-source-w8-twopoint-and-assess-original-local-p1-map"
      ],
      "resolutionIds": [
        "finding:older-seam-equivalence-verifications-do-not-supply-marked-local-p1-map",
        "finding:full-original-c1-stress-cycle-reconstructs-neutral-w8-response",
        "finding:folded-c8-cycle-misses-intrinsic-w8-tangent-without-obstructing-original-stress",
        "finding:untransported-independent-quarter-stress-pair-is-not-current",
        "finding:current-public-paper-bytes-and-binding-source-gaps-recovered"
      ],
      "requiredPremiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Review old original claims and verifications in actual scope;retain all original modes at the first stress identification and reconstruct the actual W8 response. Keep local P1 identification separately open.",
      "nextActionEN": "Use the full original c1 stress and known geometric source variation for the local P1 insertion map. No new source branch or repeated folded-only exclusion.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:recover-original-winding-comparison-and-local-quarter-current-net",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Recover original winding comparison and local quarter current net",
      "kind": "construction",
      "status": "resolved",
      "dependsOn": [
        "task:audit-older-seam-results-and-reconstruct-full-original-stress-cycle"
      ],
      "resolutionIds": [
        "finding:old-cover-winding-reconstructs-local-quarter-current-net"
      ],
      "requiredPremiseIds": [
        "premise:existing-cut-cover-car-with-actual-winding-and-sea",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Use actual old factor transport with sea,Wick ordering and support;reconstruct the local current by complete operator equality and control direct independent subtraction.",
      "nextActionEN": "Reuse the proved transported current-net theorem. For P1 derive the original local field map with common state,time,Theta,collar,reference and full fold support. Do not treat the cut-cover comparison as missing again.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:assess-fixed-pin-descent-of-original-winding-conjugation",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Assess fixed Pin descent of original winding with charge conjugation",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:recover-original-winding-comparison-and-local-quarter-current-net"
      ],
      "resolutionIds": [
        "finding:winding-charge-conjugation-descends-fixed-pin-domain-but-not-full-dirac-sea"
      ],
      "requiredPremiseIds": [
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Retain the same actual domain and Pin/boundary marks;before further optimization check D action,state,same time and Fock type.",
      "nextActionEN": "Keep the positive domain arrow. Do not use A as an already compatible full P1 reflection or silently center D. For the actual P1 connection derive the original reflection and its source measure with boundary/reference data.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:resolve-full-pin-reflection-and-ns-cover-green-positivity",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Decide full Pin reflection and NS cover Green positivity",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:assess-fixed-pin-descent-of-original-winding-conjugation"
      ],
      "resolutionIds": [
        "finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea",
        "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity",
        "finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp",
        "finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum"
      ],
      "requiredPremiseIds": [
        "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover",
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Check same boundary domain,distinguish antiunitary sea symmetry from Green RP,use the smallest neutral witness,and test the existing whole cover with both charges and all transverse modes.",
      "nextActionEN": "Reuse the full positive cover Green kernel and scoped fixed-Pinminus exclusion. Now derive actual P1 field,support,state and time map. No second beta fit,no repeated zero-mode test,no relabeling of thermal H state as quarter Hardy vacuum.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:realize-existing-quarter-source-on-concrete-elliptic-moebius-cut",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Realize existing quarter source on the concrete elliptic Moebius cut",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower",
        "finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent",
        "finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms",
        "finding:finite-crosscap-cauchy-state-is-not-original-quarter-vacuum-by-normal-filtering"
      ],
      "requiredPremiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Test full real-form group rather than only kappa,compute spin central sign without phase fitting,and compare actual boundary tuple with domain,winding,state class and time. Deduplicate old verifications.",
      "nextActionEN": "Reuse concrete elliptic cut and its fixed KMS continuation. Now supply original equivariant P1 source map preserving genuine Spin/Pin structure,seam,Calderon projector,measure and time. Do not identify modulus1 test strip with modulus1/2 carrier or start a new fitted crosscap vacuum.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:complete-full-elliptic-real-slots-and-test-marked-seam-and-p2-pushforward",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Complete full elliptic Real slots and test actual seam and P2 pushforward",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:realize-existing-quarter-source-on-concrete-elliptic-moebius-cut"
      ],
      "resolutionIds": [
        "finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots",
        "finding:full-marked-equatorial-pullback-is-ramified-graph-not-smooth-seam-circle",
        "finding:same-elliptic-szego-green-functional-has-all-word-free-rp-and-calderon-marginal",
        "finding:elliptic-scalar-spin-pushforward-has-original-holomorphic-p2-anchor",
        "finding:natural-elliptic-anchor-connection-is-not-original-p2-cusp-connection"
      ],
      "requiredPremiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Lift missing already-present inversion,keep both original Real slots distinct,identify actual full seam pullback,test positive Gaussian source on same ellipse,and compare actual cusp classes before identifying anchors.",
      "nextActionEN": "Reuse full lifted group,seam graph and positive free elliptic source. Now derive original boundary trace/vertex or smooth-carrier selection with local field,state/time transport. Retain common P2 bundle anchor,but do not identify natural order-two connection with original order-three one;do not search for scalar-twist or free-vertex-scattering repairs.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:close-global-spin-kernel-and-test-modular-three-source-dictionary",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Close global spin kernel and compare modular three-source with originals",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:complete-full-elliptic-real-slots-and-test-marked-seam-and-p2-pushforward"
      ],
      "resolutionIds": [
        "finding:elliptic-ns-spin-trace-has-complete-global-quarter-kernel",
        "finding:source-induced-ramified-resolutions-do-not-select-quarter-circle-domain",
        "finding:fixed-native-and-fermat-c3-carriers-do-not-identify-marked-v117-pair",
        "finding:theta-square-modular-pair-reconstructs-v117-with-distinct-geometric-q",
        "finding:archived-d4-puncture-formula-fails-and-existing-v117-repairs-existence",
        "finding:geometric-square-clock-is-not-theta-v117-quarter-generator"
      ],
      "requiredPremiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:theta-square-modular-transport-with-distinct-geometric-clock",
        "premise:fixed-three-slot-permutation-and-original-compiler-comparison",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Determine actual full spin kernel,detours,operator and global meridians;test existing C3 carriers with marks and compare modular representation on both original generators.",
      "nextActionEN": "Reuse complete holomorphic kernel and exact modular intertwiner. Derive original real trace with positive CAR covariance and closed boundary domain,and actual level4 family/sewing map between spatial and moduli paths. Do not repeat local phase search or rename Q=S as T.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-real-equatorial-trace-and-recover-original-c4-monodromy-proof",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Determine real equatorial trace and restore older C4 proof",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [
        "task:close-global-spin-kernel-and-test-modular-three-source-dictionary"
      ],
      "resolutionIds": [
        "finding:actual-equatorial-half-form-trace-fixes-orthogonal-hardy-range",
        "finding:actual-holomorphic-quarter-cauchy-idempotents-are-not-positive-car-covariances",
        "finding:full-equatorial-checkerboard-free-algebra-fails-fixed-reflection-positivity",
        "finding:genuine-d4-orbifold-branch-has-unique-irreducible-v117-class",
        "finding:wall-weight-additivity-does-not-exclude-stable-v117-parabolic-bundle",
        "finding:recovered-september-c4-triangle-closes-original-a0star-monodromy",
        "finding:actual-a0star-connection-does-not-have-rational-base-inversion-lift",
        "finding:actual-v117-sign-lines-are-negative-weierstrass-triangle-two-torsion",
        "finding:antipodal-and-positive-sign-packets-fail-actual-marked-v117-ramification",
        "finding:common-cyclic-twelve-cover-does-not-trivialize-v117-unramified-sign-lines",
        "finding:negative-sign-packet-has-source-selected-quarter-clock-lift",
        "finding:original-root-and-sign-lines-have-minimal-degree48-common-cover"
      ],
      "requiredPremiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:actual-elliptic-half-form-l2-trace-on-full-marked-equator",
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:genuine-d4-unitary-stable-parabolic-orbifold-descent",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "successCriterionEN": "Check actual measure and analytic range, decide reflection positivity on named cut, compare original and older sources with actual clock marking.",
      "nextActionEN": "Reuse closed September analytic C4 identification and actual boundary range. No further free monodromy search. Supply original common source map for field,state,time and domains; retain signed line local system on recovered genus2 cover.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "task:derive-entire-charge-metric-from-joint-completion",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive entire charge metric from common completion",
      "kind": "assessment",
      "status": "resolved",
      "dependsOn": [],
      "resolutionIds": [
        "finding:puncture-meridians-have-one-glue-class-and-residue-duality-does-not-select-metric",
        "finding:joint-integral-unimodular-charge-closure-uniquely-selects-complete-invariant-metric"
      ],
      "requiredPremiseIds": [
        "premise:fixed-puncture-spinor-extension-with-integral-selfdual-pairing"
      ],
      "successCriterionEN": "Determine the complete invariant metric space and prove uniqueness over the entire positive class, retaining actual original glue actions.",
      "nextActionEN": "Resolved in the stated conditional scope. Separately derive the physical integral-selfdual completion and original common source map; do not repeat a metric parameter search.",
      "reviewState": "reviewed-authored"
    }
  ],
  "strategies": [
    {
      "id": "strategy:reuse-operational-future-quotient",
      "problemId": "problem:future-quotient-and-gns-reconstruction",
      "titleEN": "Reuse the operational future quotient",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:future-answer-functional"
      ],
      "findingIds": [
        "finding:future-equivalence-minimizes-declared-answer-process"
      ],
      "explanationEN": "Minimality is proved for fixed r and a fixed experiment alphabet.",
      "changesRequiredEN": "Do not infer a physical Hilbert space or TFPT source selector from it.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-conditional-positive-gns",
      "problemId": "problem:future-quotient-and-gns-reconstruction",
      "titleEN": "Reuse conditional positive GNS reconstruction",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:positive-word-kernel-null-stability"
      ],
      "findingIds": [
        "finding:positive-word-kernel-reconstructs-cyclic-gns"
      ],
      "explanationEN": "Cyclic GNS construction and uniqueness are reusable under explicit K conditions.",
      "changesRequiredEN": "It remains open which complete K the original source supplies.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:polynomial-degree-selects-source",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Polynomial degree as a physical source selector",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:operational-seed-is-input"
      ],
      "explanationEN": "The cited original seed definition assumes A_loc, tau_t, Theta, omega, [u_Sigma], and D_coll as data and shows only their collar completion. This cited evidence supplies no rule selecting the common physical source from a polynomial degree.",
      "changesRequiredEN": "Provide an explicit original-source rule mapping degree to source selection before assessing the strategy as a selector.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:source-time-character-closure-search",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Order-four markings from given time and full charge",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:full-normalized-charge-time-character-family",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:actual-chiral-opposite-quarter-domains"
      ],
      "findingIds": [
        "finding:source-generated-marking-classification"
      ],
      "explanationEN": "The whole family is completed by lattice saturation and exact classification, including an original-frame control.",
      "changesRequiredEN": "New knowledge requires a justified change to the original source operator or its field/sector map; further phases of the same family are already covered.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:internal-character-hit-selects-physical-source",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Use an internal character hit as physical source selection",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:full-normalized-charge-time-character-family",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:actual-chiral-opposite-quarter-domains"
      ],
      "findingIds": [
        "finding:source-marking-field-realization-boundary",
        "finding:source-generated-marking-classification"
      ],
      "explanationEN": "All candidates retain the missing original field/state identification. The composed marking does not prove that identification.",
      "changesRequiredEN": "Identify the actual original seam action on the same collar/field core, including domain, state and full time.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:minimal-defect-value-selects-unique-source",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Infer unique source from minimal defect",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:minimal-defect-uniqueness-not-proved"
      ],
      "explanationEN": "The proof does not classify the minimal operator fiber.",
      "changesRequiredEN": "Actually classify operator structures in the minimal fiber; do not relabel well-ordering or presentation invariance as uniqueness.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:source-hardy-representative-scan",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Scan further scalar Hardy isometries",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-scalar-quarter-hardy-source"
      ],
      "findingIds": [
        "finding:continuous-hardy-seam-classification"
      ],
      "explanationEN": "The whole continuous class is covered analytically; more Blaschke parameters provide no new selection.",
      "changesRequiredEN": "Supply a P1-grounded change of source class or actual operator action.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:same-source-energy-minimization",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Minimize seam energy within the same scalar source",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:charged-car-negative-sea-source"
      ],
      "findingIds": [
        "finding:same-source-seam-energy-selection"
      ],
      "explanationEN": "The entire H1 class is solved by E=alpha+Var(phi prime)/2; additional genotypes or GPU grids are unnecessary.",
      "changesRequiredEN": "Derive the physical source and least-excitation rule from P1; do not replace their selection with optimization inside a supplied source.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:master-functional-selects-original-source",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Use the downstream master functional as an original selector",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:master-functional-presupposes-source-selection",
        "finding:minimal-defect-uniqueness-not-proved"
      ],
      "explanationEN": "The allowed source is already named in the zero/infinity barrier. A minimum on that restricted branch does not prove this upstream selection.",
      "changesRequiredEN": "Supply a selection rule computable from original data without a presumed B_min and prove its relation to the actual field/state/time operator.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-geometric-deck-with-calderon-polarization",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Identify geometric deck lift with boundary polarization",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-geometric-dirac-deck-lift"
      ],
      "findingIds": [
        "finding:geometric-deck-not-calderon-polarization"
      ],
      "explanationEN": "The general implication from reflection regularity is disproved by a compact Dirac counterexample; carrier restrictions built on it need their actual operator map established again.",
      "changesRequiredEN": "Keep geometric lift, normal Clifford action and Calderon polarization distinct. For dynamics retain the full two-face relation and use the already verified inverse reader.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-mixed-carrier-from-positive-only-polarization",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Obtain mixed carrier by restriction to the positive-only space",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:literal-carrier-after-positive-compression"
      ],
      "findingIds": [
        "finding:positive-compression-erases-carrier-minus-sector"
      ],
      "explanationEN": "The actual restriction is identity; the negative sector has already been removed. Additional spectral tests cannot repair this type error.",
      "changesRequiredEN": "Retain field space and internal marking action before state projection. Check an actual embedding W with (2G−I)W=W epsilon if that polarization is intended; for a separate internal involution supply its source origin. Do not count an inserted 3+2 matrix as a derivation.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:primitive-invariant-selects-carrier-rank",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Invariant-ring primitiveness as rank selector",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:carrier-covariant-invariant-ring"
      ],
      "findingIds": [
        "finding:primitive-invariant-does-not-select-rank-three"
      ],
      "explanationEN": "The explicit minimum-degree primitive 5+2 tensor satisfies even fermion degrees and the same invariance. The local argument does not exclude it.",
      "changesRequiredEN": "Prove tensor support, a degree bound or global-minimality rule actually derived from the original source; do not again identify primitiveness with contraction surjectivity.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:determinant-section-count-selects-internal-rank",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Determinant section count as internal rank",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:higgs-determinant-does-not-discharge-carrier-map"
      ],
      "explanationEN": "The determinant line does not determine rank or kernel, and the archived argument already uses the marked branch.",
      "changesRequiredEN": "Provide the actual original bosonic operator, bundle and equivariant kernel-to-carrier map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:fixed-background-source-selects-mixed-vertex",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Fixed free background source as Yukawa selector",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:fixed-background-quarter-fermion-source"
      ],
      "findingIds": [
        "finding:fixed-background-source-does-not-fix-mixed-vertex"
      ],
      "explanationEN": "Identical complete fermionic background data have different supplied field derivatives; the actual field-dependent source contract is missing.",
      "changesRequiredEN": "Derive the original field-dependent source operator or complete interaction functional and its actual mixed responses.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:quarter-or-given-sm-inner-fluctuation-as-origin",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Inner fluctuation as original Higgs/3+2 selector",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:quarter-circle-coordinate-local-algebra",
        "premise:quarter-circle-nonlocal-cauchy-enlargement",
        "premise:given-finite-sm-triple-yukawa-inputs"
      ],
      "findingIds": [
        "finding:local-quarter-inner-variation-is-connection",
        "finding:calderon-enlargement-does-not-select-higgs",
        "finding:finite-sm-higgs-variation-retains-seed"
      ],
      "explanationEN": "The local circle source yields connections on its given module; nonlocal C enlargement allows arbitrary finite matrix directions; the given finite SM triple yields H times input Y. None of these investigated variants supplies the missing original noncommutative carrier and selected vertex.",
      "changesRequiredEN": "First derive from original principles the actual local insertion algebra and its offdiagonal Dirac action or mixed charged vertex with group action. Only then test fluctuation, state/time and specific carrier contractions; do not insert Y, a weak doublet or a3+2 module.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:full-operator-skeleton-selects-insertion-algebra",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Insertion algebra from full operator skeleton alone",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-domain-product-dirac-skeleton"
      ],
      "findingIds": [
        "finding:operator-skeleton-does-not-identify-insertion-algebra"
      ],
      "explanationEN": "Identical full operators admit scalar and matrix insertion algebras with different fiber actions.",
      "changesRequiredEN": "Derive actual local generators, products and sector representation or a proved unique minimal algebra/bimodule branch from the source.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:full-internal-car-as-spectral-coordinate-algebra",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Full internal CAR as spectral coordinate algebra",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:unmarked-hermitian-rank-five-exterior-carrier"
      ],
      "findingIds": [
        "finding:internal-even-car-hodge-is-not-coordinate-algebra"
      ],
      "explanationEN": "Full even internal algebra fails order zero with J_H; internal exterior parity is not a physical field identification.",
      "changesRequiredEN": "Supply a source-derived compatible left/right algebra and local field lift. Do not use global Hodge antiunitarity as a quaternionic factor of a different triple without a map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:minimum-rank-unique-primitive-yukawa-selects-32",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Smallest rank plus unique primitive trilinear channel as3+2 selector",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:minimum-rank-holomorphic-even-even-fundamental-class"
      ],
      "findingIds": [
        "finding:minimum-rank-unique-primitive-channel-does-not-select-32"
      ],
      "explanationEN": "Already at minimum rank5 several splits remain primitive and nonzero for the same canonical volume tensor; even channel uniqueness and the stated trace tests do not distinguish3+2 from4+1.",
      "changesRequiredEN": "Supply the actual original bosonic operator and sector action or an independently derived cross-identification of scalar response and carrier data. Do not repeat the same minimum-rank/primitivity comparison.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:downstream-singleton-selfconsistency-selects-upstream-algebra",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Downstream singleton self-consistency as upstream algebra selector",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:joint-selfconsistency-presupposes-minimal-algebra-fiber-selection"
      ],
      "explanationEN": "The chain presupposes the minimal discrete branch; its valid conditional rank decoders are proved in the source only after carrier selection.",
      "changesRequiredEN": "Classify the original minimal algebra/bimodule fiber or derive an evaluable separating occupancy/Bγ identification without presupposed carrier ranks.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:clock-symmetry-alone-selects-native-polar-transport",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Clock and native symmetries alone select polar transport",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark"
      ],
      "findingIds": [
        "finding:native-clock-compatible-polar-fibre-and-canonical-distance"
      ],
      "explanationEN": "The complete CP1/RP1 fibre satisfies these conditions; the original polar rule is an additional uniquely characterized point.",
      "changesRequiredEN": "Derive a distinguishing nonscalar response or actual polar-distance rule from original action.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-moment-parent-or-local-product-berry-as-quarter",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Moment parent or local-product code holonomy as quarter clock",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:original-native-fourth-moment-parent",
        "premise:local-product-code-orbit-geometric-parallel-transport"
      ],
      "findingIds": [
        "finding:native-moment-parent-and-product-path-selection-boundary"
      ],
      "explanationEN": "Parent vanishes on code, clock algebra is scalar on E+ and stated local geometric holonomy lies in phase-S6.",
      "changesRequiredEN": "Supply an actual original further interaction/collective operation and its permission; do not repeat the same parent or mere frame paths.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:literal-charged-c4-register-current-clock",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Charged C4 currents as unchanged native tensor registers",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:original-coupled-determinant-event-cover",
        "premise:literal-charged-current-native-register-dictionary"
      ],
      "findingIds": [
        "finding:literal-charged-current-register-dictionary-fails-quarter"
      ],
      "explanationEN": "Actual action fails at the intertwiner or complete stabilizer stated in the finding.",
      "changesRequiredEN": "Supply a different process derived from the original source or a genuinely different field map; no further pulse in the same excluded group.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:inner-e8-rotation-selects-native-cartan-code-quarter",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Inner E8 current rotations as native Cartan-code quarter clock",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:compact-inner-e8-zero-mode-operation-class"
      ],
      "findingIds": [
        "finding:native-cartan-code-inner-e8-stabilizer-excludes-marked-quarter"
      ],
      "explanationEN": "Actual action fails at the intertwiner or complete stabilizer stated in the finding.",
      "changesRequiredEN": "Supply a different process derived from the original source or a genuinely different field map; no further pulse in the same excluded group.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:neutral-weight-two-source-pulses-as-native-quarter",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Neutral weight-two source pulses as native quarter clock",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:existing-logical-clock-and-charge-marking",
        "premise:actual-clifford-identification-and-finite-overgroup-theorem",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:solely-neutral-local-weight-two-zero-mode-class"
      ],
      "findingIds": [
        "finding:native-code-neutral-weight-two-action-and-global-clock-exclusion"
      ],
      "explanationEN": "Full neutral class stays within U8 on mode1; endpoint code preservation restricts it to the already excluded logical stabilizer.",
      "changesRequiredEN": "Derive an actually mixed root/quadratic process, different mode history or source-grounded embedding. Do not try further solely neutral pulses in the same class.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:positive-adjoint-root-response-reweighting-as-common-clock-lift",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Positive reweighting of adjoint root responses as common lift",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:common-unnormalized-positive-return-erasure-test"
      ],
      "findingIds": [
        "finding:actual-mixed-return-fails-native-trimer-erasure-lift",
        "finding:strict-trace-gap-excludes-positive-mixed-return-reweighting"
      ],
      "explanationEN": "Trace gap is positive for every nonzero original channel and stays strict under every coherent positive profile.",
      "changesRequiredEN": "Derive another originally specified return field or longer source history with actual contraction; do not insert fitted weights or new relative normalization.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-original-positive-return-gram-as-full-code-operation",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Identify original positive return Gram with full code operation",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles"
      ],
      "findingIds": [
        "finding:uncompressed-original-mixed-return-does-not-preserve-code",
        "finding:original-root-response-sum-also-leaks-from-code"
      ],
      "explanationEN": "Exact neutral off-code witnesses refute full code closure of specific return and original sum; endpoint compression only removes this component mathematically.",
      "changesRequiredEN": "First derive the originally specified full source operation/history with code closure (I-Pi)U_source Pi=0 and actual erasure action. If protection/recovery is required, derive it from same source. Do not insert code projection, postselection, measurement/reset rule, free longer history or independent20/5 normalization. Prior rank5 matrix is endpoint compression only; individual return and original240 sum demonstrably fail code closure. Only after full-operation test passes infer clock, marking and3+2 from its action. General original higher processes remain open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:closed-five-state-realization-of-original-return-moments",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Closed five-state realization of original return moments",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-neutral-root-pair-moment-fields",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-positive-adjoint-two-insertion-response-profiles",
        "premise:specified-original-pair-ordered-response-composition"
      ],
      "findingIds": [
        "finding:original-return-requires-memory-in-every-code-direction"
      ],
      "explanationEN": "Hankel rank10 of first3 original matrix moments exceeds every5D factorization; full feedback Gram is strictly positive.",
      "changesRequiredEN": "Full feedback is derived for existing single pair: memory kernel B*D^kB, strict rank5 feedback Gram and Hankel rank lower bound10. Do not again use K^n as full history or build a freely chosen10D model. Next original-origin question: which actual P1-dependent field/boundary variation determines ordered insertion/history with4/5/20 readout and common time? Retain its complete source with charges, modes and memory. Code closure is required only for claimed closed code operations; do not impose it as a new P1 axiom. No clock/polar/3+2 origin claim without physical history selection; no fitted root weights, measurement/reset/projection rule or relative20/5 renormalization.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:pure-canonical-stress-history-as-marked-native-clock",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Pure canonical stress history as marked native clock",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:canonical-source-stress-all-mode-history",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "findingIds": [
        "finding:all-canonical-stress-histories-scalar-on-native-code"
      ],
      "explanationEN": "Exact Virasoro multiplicity factorization fixes logical labels for all words; new carry refutes global native-J/conformal-quarter identification despite seed agreement.",
      "changesRequiredEN": "Original canonical geometric route is now settled for ALL stress modes: common primary cycles on4/5/20, logically scalar action even with excursions/return, no R5/P2. Actual erasure Ward action additionally forces neutral weight5 twenty with fixed rho5 tensor bar rho4 action and norm78/85; no root/family branch required. Preserve this new source bridge. Next origin question within accepted native TFPT core: which actually original NONSTRESS field/boundary intervention and ordered insertion is allowed, and how does it act on full source with new carry, actual erasure and memory? Do not further vary pure conformal schedules, equate clocks from seed phases, or optimize freely combined carry/mode histories. Physical selection and polar/3+2 coupling remain open; assume no new measurement, projection, coupling or readout rule.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:pure-local-erasure-or-cartan-weyl-as-physical-clock",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Pure local erasure or Cartan-Weyl history as physical code clock",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:original-cartan-current-local-smearing-and-weyl-class",
        "premise:canonical-source-stress-all-mode-history",
        "premise:existing-logical-clock-and-charge-marking"
      ],
      "findingIds": [
        "finding:original-local-current-ope-forces-erasure-and-carry",
        "finding:all-real-local-cartan-profiles-erasure-third-bound",
        "finding:closed-cartan-weyl-histories-only-logical-phase"
      ],
      "explanationEN": "Actual erasure mode fails local commutation; full local field necessarily retains other modes. Ordered Cartan-Weyl products close only to scalar code endpoint. No originally selected non-Cartan insertion is replaced.",
      "changesRequiredEN": "Full original local Cartan-current OPE now connects native4/5 with singular erasure20 AND regular primary carry20. Pure erasure is global Fourier mode, not local insertion; every actual local Hermitian Cartan profile retains further source modes, erasure norm fraction<1/3. Finite Cartan-Weyl histories are fully fixed and have only phase at closed code endpoints. Preserve bridge; do not optimize Cartan profiles/pulses or pure stress schedules. First open physical map: which original P1 boundary variation induces a specified NON-Cartan/composite insertion in accepted E8 source net, and how is its A/A*-invariant physical sector action derived? Determine actual insertion map and full ordered response with charges/carry/memory before logical compression. Do not identify code with H_adm, contour-extracted mode with local intervention or given field with selected coupling. Preserve prior root-zero-mode and paired-process exclusions without an all-E8/P1 no-go union. Physical time/state and polar/3+2 selection remain open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:full-event-gram-positivity-as-physical-polar-selection",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Full event Gram positivity as physical polar selection",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:native-marked-simplex-clock-compatibility-without-fixed-polar-mark",
        "premise:original-native-event-difference-fields-and-state-controls"
      ],
      "findingIds": [
        "finding:original-full-field-event-gram-reconstructs-relative-polar-mark",
        "finding:raw-event-state-positivity-does-not-execute-polar-normalization"
      ],
      "explanationEN": "Source determinesG and positive relativeP2tensor, but physical execution/observable does not follow fromGNS. Rawresponses/fullstatecontrol distinguish metric fromprocessnormalization.",
      "changesRequiredEN": "Derive original boundary/eventvariation,state,record/readout map requiringexactpositive relative normalization; do notrelabel positivity as thatlaw.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:unique-rank-two-mark-from-unmarked-native-event-geometry",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Unique rank-two mark from unmarked event geometry",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock"
      ],
      "findingIds": [
        "finding:clock-free-event-geometry-fixes-clock-class-and-mark-orbit-not-member"
      ],
      "explanationEN": "UniquecovariantselectiononunmarkedsymmetricsourceobjectmustbeS6fixed;withonlyqS5fixed. Invariantranks0/5or0/1/4/5,never2. Positive resultiscanonicalclockclass/markingorbit.",
      "changesRequiredEN": "Deriveanadditionaloriginalinputdatumoractualstate/processsymmetrybreaking;donotrelabelfurtherinvariantproductsasautomaticuniqueselector.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:select-native-polar-flag-from-internal-quarter-vacuum-and-neutral-family-data",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Selectflagfrominternalquartercharacter,vacuum,neutralfamilydata",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector"
      ],
      "findingIds": [
        "finding:original-charged-seam-character-recovers-global-native-event-pair",
        "finding:internal-seam-vacuum-and-original-neutral-tensor-do-not-select-flag-root"
      ],
      "explanationEN": "Globalpairyes,butnofixedroot;explicitfullsourceisometryswapsoldflagwithdifferentpolaroperator.",
      "changesRequiredEN": "Mapactualoriginalstate/fieldresponse;donotreplaceitsseam/shiftwithinternalcharacter/vacuum.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:select-native-polar-flag-by-fold-shift-fixed-point-condition",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Selectflagbyoriginalfoldshiftfixedpointcondition",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector"
      ],
      "findingIds": [
        "finding:actual-quarter-fold-shift-removes-native-symmetry-obstruction-without-flag-selector",
        "finding:fold-shift-equivariance-needs-actual-source-response-map-not-another-symmetry-no-go"
      ],
      "explanationEN": "Actualdstabilizer1:all60fixed,covariancealonenotunique;oldno-gogone.",
      "changesRequiredEN": "Deriveactualoriginalsourcefield/stateresponseselector,donotinventselectionfunction.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:select-native-flag-by-original-fold-quartic-mean-or-spectral-response",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Selectnativeflagbyoriginalquarticmeanorspectralresponse",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport"
      ],
      "findingIds": [
        "finding:original-fold-quartic-mean-and-spectral-responses-do-not-match-sixty-flags"
      ],
      "explanationEN": "Actualmean/kernelraysoutside6simplexrays;no60PcommuteswithcompleteB4orD1.",
      "changesRequiredEN": "DeriveanotheractualORIGINALobservable/interventionoutput,nospectrum/profilefit/newphysicalcommutationaxiom.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-source-time-winding-history-normal-form",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Global source time/winding as internal marking selection",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:charged-car-negative-sea-source",
        "premise:fixed-scalar-quarter-hardy-source"
      ],
      "findingIds": [
        "finding:original-source-global-time-winding-history-factorization"
      ],
      "explanationEN": "Given Ward increments are c_n(q)=Falpha(q+n)-Falpha(q), Falpha(q)=q(q-1)/16+alpha q/8. Thus K-Falpha(Q) is winding invariant and alpha independent. Actual CAR space factors via W_n as ell2(Z) tensor H_Q0, not an assumed rotor. Every finite ordered time/winding word has the stated exact normal form; all n=8z+r checked symbolically. On a fixed neutral R_b,k field mode the input multiplicity is unchanged. Charge-return acts scalarly in actual B_k metric, retaining all intermediate charges/modes. W1 lies in original odd vector sector; W2 is smallest even winding and ends at an actual E8 root.",
      "changesRequiredEN": "17Oct original density/geometric bridge: all global time/winding words reduced, no more waiting-time/power scan. Original local c1 density folds to correlated non-Cartan root currents with fixed coefficients; full actual CAR state response, erasure20, all32 energy modes and original c1 stress Wards computed. Do not identify twisted folded Yd(T)/original Lcal+-1 with old unshifted stress/primary-vacuum theorem. Density/geometric Riesz response pair irreducible M5; mode30 rank2 matches no60polarflags, no Coxeter dictionary from number30. Next connect full local products/ordered responses of THESE originally fixed c1 density/geometric fields to existing intrinsic six-ray event geometry and original seam character/admissible output. No free root weights/selected profiles/new clock/measurement/filter/eigenvalue grouping. Retain every charge/carry/mode/correlation path and conditional physical reference; global pair retained, physicalq/S/P1/3+2 open. No abstract reset or closed-C5 axiom.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-density-geometric-response-common-spectral-32",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Common spectral mark of original density/geometric response",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "findingIds": [
        "finding:original-current-geometric-response-pair-has-no-common-polar-sector"
      ],
      "explanationEN": "Both quarters: B4^-1G_J and B4^-1G_L are B4 selfadjoint with common commutant dimension1 overQ(i), hence generated complex response *-algebra M5 on input labels. No common reducing rank2/3 decomposition of these actual response forms. Density response has five distinct generalized eigenvalues. In COMPLETE mode family J30 response rank2, but rank3 kernel matches none of60 original polar flags; Adjacent rank3 J29 response is not ORTHOGONALLY complementary in B4 metric, but joint rank5 gives an oblique algebraic direct sum. Positive relative normalization for this supplied mode pair remains possible; neither its original selection nor a literal normalized polar comparison is claimed. Mode30 lowers source energy by30, not a derived unitary Coxeter30 action.",
      "changesRequiredEN": "17Oct original density/geometric bridge: all global time/winding words reduced, no more waiting-time/power scan. Original local c1 density folds to correlated non-Cartan root currents with fixed coefficients; full actual CAR state response, erasure20, all32 energy modes and original c1 stress Wards computed. Do not identify twisted folded Yd(T)/original Lcal+-1 with old unshifted stress/primary-vacuum theorem. Density/geometric Riesz response pair irreducible M5; mode30 rank2 matches no60polarflags, no Coxeter dictionary from number30. Next connect full local products/ordered responses of THESE originally fixed c1 density/geometric fields to existing intrinsic six-ray event geometry and original seam character/admissible output. No free root weights/selected profiles/new clock/measurement/filter/eigenvalue grouping. Retain every charge/carry/mode/correlation path and conditional physical reference; global pair retained, physicalq/S/P1/3+2 open. No abstract reset or closed-C5 axiom.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-current-geometric-seam-graded-full-correlations",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Full original current correlations and seam order",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "findingIds": [
        "finding:original-current-ordered-hall-kernel-and-actual-folded-field-products",
        "finding:original-seam-grades-full-density-geometric-products-and-energy-response",
        "finding:original-density-all-profile-mean-work-scalar-on-native-packet"
      ],
      "explanationEN": "Actual five neutral sourceE32 states map exactly by original Maya occupations to Schur states. All32 lowering-current VECTORS independently match Young ribbons, stress1/2 matches fixed Sugawara and full CCR, both quarters. All state coefficients saved. Kij(u,v)=<Pi,exp(sum um pm)Pj(pm+mvm)>Hall gives all mixed current correlations; Weyl response additionally retains Gaussian sum over ALL profile modes, not only1..32. Every finite smooth density/source-time history follows with original BCH phase. Actual folded quartic fields remain on eight original preimages: A_a=Ualpha diag(Vka)Ualpha*, scalar source operation gives Gphi(x+)dagger A_a Gphi(x-). Entire existing point splitting/reference subtraction conjugated, no second b shift. Separated Heisenberg field products follow from finite Wick Pfaffians using same ordered Calpha/1-Calpha.",
      "changesRequiredEN": "17Oct full original current/field response available: exact Maya/Hall state intertwiner with all32 CAR vectors, closed multi-profile/time history kernel retaining ALL Gaussian tails, actual folded-field products on eight original preimages with same ordered Calpha/1-Calpha point splitting. No weight32 point-field identification. Internal seam grades products mod4; all four full energy classes strictly fullrank, commutant1, no sharp3+2 input reading. Mean density work scalar on wholeK4 packet; full coherence nonscalar. Next test ORIGINAL P1 boundary action and its claimed admissible physical variations/output data against THIS explicit full-field path: does it supply a selected source family/response functional or intrinsic event relation with fixed reference/admissibility? Name first underived dotD/dotB/dotQ or output functional and work there. Reuse existing P1-INSERTION-TANGENT/action-response-sewing results, no generic inverseKMS/composition replay. No free profile weights/modes29/30/newclock/measurement/positiveprocessing/mark-commutation axiom. Retain global pair/sixrays/60flags/E8 whole; physicalq/S/3+2/P1 open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-seam-full-density-energy-sharp-32-reading",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Sharp3+2 reading of full seam-graded density energy",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress"
      ],
      "findingIds": [
        "finding:original-seam-complete-density-grading-not-sharp-32-input-sectors"
      ],
      "explanationEN": "All four complete Grho are EXACTLY positive definite rank5 in BOTH quarters, sum32B4. Hence Erho=(32B4)^-1/2 Grho(32B4)^-1/2 lies strictly between0 andI, as does every proper nonempty coarsening. Deck-even/odd responses both rank5. Exact common commutant of(32B4)^-1Grho has dimension1 overQ(i). No sharp deterministic character/deck classification of five input directions or common reducing3+2 spectrum of these forms.",
      "changesRequiredEN": "17Oct full original current/field response available: exact Maya/Hall state intertwiner with all32 CAR vectors, closed multi-profile/time history kernel retaining ALL Gaussian tails, actual folded-field products on eight original preimages with same ordered Calpha/1-Calpha point splitting. No weight32 point-field identification. Internal seam grades products mod4; all four full energy classes strictly fullrank, commutant1, no sharp3+2 input reading. Mean density work scalar on wholeK4 packet; full coherence nonscalar. Next test ORIGINAL P1 boundary action and its claimed admissible physical variations/output data against THIS explicit full-field path: does it supply a selected source family/response functional or intrinsic event relation with fixed reference/admissibility? Name first underived dotD/dotB/dotQ or output functional and work there. Reuse existing P1-INSERTION-TANGENT/action-response-sewing results, no generic inverseKMS/composition replay. No free profile weights/modes29/30/newclock/measurement/positiveprocessing/mark-commutation axiom. Retain global pair/sixrays/60flags/E8 whole; physicalq/S/3+2/P1 open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-p1-gap-normalized-action-cotangent-to-native-event-selector",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Original P1 gap differential and source-family interface",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress",
        "premise:declared-p1-p2",
        "premise:typed-source-structures",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:charged-car-negative-sea-source",
        "premise:original-gap-normalized-primitive-relative-action"
      ],
      "findingIds": [
        "finding:original-p1-gap-normalized-action-covector-and-scalar-holonomy-class"
      ],
      "explanationEN": "chi=1/lambda forces delta(D/chi)=lambda deltaD+deltaLambda D. For isolated simple signed gap branch deltaLambda=sgn(E0)<u0,deltaB u0>; entire corresponding term in relative action differential derived without commutativity. Clusters, constant nullity, moving R/domain/reference/eta correctly scoped. In actual scalar quarter circle, EVERY smooth real v gives Balpha+v unitarily equivalent to Balpha+mean(v). On fixed holonomy branch mean(v)=0, gap/chi unchanged exactly while Pgap moves. This supplies a source covector, not a selected physical source variation/event functional; scalar gauge orbit is not inequivalent-minimal-P1 model theorem.",
      "changesRequiredEN": "17Oct originalP1 action source-audited including chi=1/lambda and full gap-scale term. It is a covector on GIVEN source variations; physical tangent/event not derived. Whole scalar-potential class of actual quarter source gauge equivalent to mean; fixedholonomy fixesgap/chi, not field response. Original canonical gapCAR projector(mode0/-1) tested on fullnative inputs: gap/complement rank5 each, nonprojective response, exterior rank5; NO sharp3+2 identification or local insertion. Do NOT replay this test/profile scan/KMSinverse/knownmasterbarrier/defectwellordering. Needed is first actual ORIGINAL family/connection from native local field/event arguments toD+,B_Sigma,bulk/domain/state, or actual minimal operator-fiber classification supplying it. Existing Higgsrank2/branchYukawa/d_disc* assumptions cannot replace this map. No arbitrary matrixpotential or linearj.F coupling. Two physical tasks remainopen; retain whole original E8/fields/correlations/sixrays/60flags/globalpair.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-gap-projector-canonical-car-sector-response",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Read original gap mode as sharp native3+2 mark",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:original-single-circle-local-density-and-geometric-stress",
        "premise:declared-p1-p2",
        "premise:typed-source-structures",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:charged-car-negative-sea-source",
        "premise:original-gap-normalized-primitive-relative-action"
      ],
      "findingIds": [
        "finding:original-p1-gap-car-component-not-native-sharp-32-event"
      ],
      "explanationEN": "Actual original gap definition selects mode0 foralpha1/4 and mode-1 foralpha3/4, gap1/4 each. Within same stipulated CAR, Qgap=sgn(E0):a_r*a_r: is full particle/hole projector without rank fitting. On complete actual R_b4 inputs, B=I*I,H=I*QgapI obey EXACTLY H>0 and B-H>0, both rank5. Correct metric response strictly between0 andI, nonscalar/nonidempotent; exterior H-HB^-1H strictly positive rank5, bothquarters. This direct spectral bridge from original scale function is not a sharp3+2 input mark. Qgap is global spectral mode, not insertion localized in proper interval.",
      "changesRequiredEN": "17Oct originalP1 action source-audited including chi=1/lambda and full gap-scale term. It is a covector on GIVEN source variations; physical tangent/event not derived. Whole scalar-potential class of actual quarter source gauge equivalent to mean; fixedholonomy fixesgap/chi, not field response. Original canonical gapCAR projector(mode0/-1) tested on fullnative inputs: gap/complement rank5 each, nonprojective response, exterior rank5; NO sharp3+2 identification or local insertion. Do NOT replay this test/profile scan/KMSinverse/knownmasterbarrier/defectwellordering. Needed is first actual ORIGINAL family/connection from native local field/event arguments toD+,B_Sigma,bulk/domain/state, or actual minimal operator-fiber classification supplying it. Existing Higgsrank2/branchYukawa/d_disc* assumptions cannot replace this map. No arbitrary matrixpotential or linearj.F coupling. Two physical tasks remainopen; retain whole original E8/fields/correlations/sixrays/60flags/globalpair.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:classify-full-scalar-first-order-seam-time-operator-fiber",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Whole scalar first-order time-seam fiber",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures",
        "premise:positive-scalar-first-order-source-comparison-class",
        "premise:given-original-fixed-one-particle-time-winding-ward"
      ],
      "findingIds": [
        "finding:complete-positive-scalar-first-order-circle-source-normal-form",
        "finding:fixed-source-time-seam-ward-rigidifies-scalar-principal-symbol-with-carry"
      ],
      "explanationEN": "Every operator in declared class has B=-i(a d+a_prime/2)+c,a>0,c real. T=integral1/a,omega=2pi/T,beta=integral c/a/(2pi),x_prime=omega/a,eta_prime=(omega beta-c)/a yield unitaryUf=sqrt(omega/a)exp(ieta)f(x),BU=Uomega(-i dx+beta) on fullH1 domains. Whole spectrum omega(Z+beta), no mode cutoff. SameB determines unique-up-to-phase uniform wind1 representative u_B=exp(ix),[B,u_B]=omega u_B andQ_B=exp(iTB/4),Q_B^4=exp(2pi i beta)I: spacing,proper-timecoordinate/chargedquarterreturn fromoneoperator,not newclock/interventionselection. Original fixedquarter holonomy andgap1/4 giveomega1; unmarked one-particle source sameBalpha up to coordinate/phase transport. Four fixed marks require all arc travel times/possible endpoint phases, not dimension/species identification.",
      "changesRequiredEN": "17Oct whole smooth positive scalar LOCAL firstorderfiber classified includinga(theta),state/marktransport/globalNcarry. No more scalar speed/profile scan. UnitSF+gap+quarterholonomy+fourmarks/quartercovariance do NOT force fixedtime-seamWard; exactk4control. SameactualgivenWard[B,Z]=Z forcesa1; continuousmarkedresidualfiber onlygaugetransport,globalNmod4timequarterphase/4Zseacarryexplicit. Sourcefiberresult,notWardorigin. Nextoriginalproof must supply physical localoperator/representation map and thisstrongerjointtimeseamrelation fromP1,or actualoriginalnon-scalar/nonlocaldirection withlocalization. Nochosenmatrixpotential/Yukawa/measurementrule. Do not promoteoneparticleunitarity tounchangedFocksea/Schwarzian/relativeaction. RetainwholeE8/products/sixrays/60flags/globalpair andtwoopenphysicaltasks;3+2notderived.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:unit-flow-gap-fourmarks-imply-constant-time-seam-ward",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Unitflow/marks as constant time-seam Ward",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures",
        "premise:positive-scalar-first-order-source-comparison-class"
      ],
      "findingIds": [
        "finding:unit-spectral-flow-gap-and-four-marks-do-not-imply-fixed-source-ward"
      ],
      "explanationEN": "For arbitrarya>0,Z*BZ=B+a,pathB_s=B+s a has eigenvaluesomega(n+beta+s):0<beta<1 gives exactlyone upwardcrossing independentofa. UnitSF is not constantunitWard. Exact controls a=(1+epsilon cos(ktheta))^-1,c=alpha,abs(epsilon)<1,k1/4 have samegap1/4,holonomy,SF1;k4 additionally preservesall4marks,equalarctimes/geometricquartercovariance. Yet[B,Z]=aZ differsfromZ forepsilon!=0. Controls not claimed completeP1models; under fullcovariantdatatransport they represent sameunmarkedsource.",
      "changesRequiredEN": "17Oct whole smooth positive scalar LOCAL firstorderfiber classified includinga(theta),state/marktransport/globalNcarry. No more scalar speed/profile scan. UnitSF+gap+quarterholonomy+fourmarks/quartercovariance do NOT force fixedtime-seamWard; exactk4control. SameactualgivenWard[B,Z]=Z forcesa1; continuousmarkedresidualfiber onlygaugetransport,globalNmod4timequarterphase/4Zseacarryexplicit. Sourcefiberresult,notWardorigin. Nextoriginalproof must supply physical localoperator/representation map and thisstrongerjointtimeseamrelation fromP1,or actualoriginalnon-scalar/nonlocaldirection withlocalization. Nochosenmatrixpotential/Yukawa/measurementrule. Do not promoteoneparticleunitarity tounchangedFocksea/Schwarzian/relativeaction. RetainwholeE8/products/sixrays/60flags/globalpair andtwoopenphysicaltasks;3+2notderived.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-four-native-starts-as-fixed-fold-state-gauge-redundancy",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Four native marks as fixed-source-state gauge redundancy",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:four-starts-fixed-state-versus-whole-datum-comparison"
      ],
      "findingIds": [
        "finding:four-native-polar-marks-not-fixed-source-state-gauge-equivalent"
      ],
      "explanationEN": "Excluded is identifying the four marks as all-response-preserving symmetries of the FIXED original fold state within the specified actual quartic space. Universal central OPE metric forces such action unitary and preservation of tr(Pq D1), whose four exact values are pairwise distinct per quarter. Not a universal classification of physical P1 gauge equivalences or exclusion of passive whole-presentation transports.",
      "changesRequiredEN": "18Oct: The four starts and polar planes have pairwise distinct correlation invariants in the SAME original fold/NS field dictionary. Whole E8 datum transport is covariance, not fixed-state symmetry or physical gauge proof; odd-CAR only separately transported passively. Do not maximize c1 or polar trace or repeat fixed-point/profile tests. Check the actual original preparation, event or output datum for which already distinguishable relation is instantiated. No fitted coupling, invented detector or four P1 theories. Retain full E8/erasure/time/carry response; physical source and q/S/3+2 remain open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:compare-four-native-starts-by-full-state-relative-kernels-and-data-transport",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Compare four marks via full state-relative kernels",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:four-starts-fixed-state-versus-whole-datum-comparison"
      ],
      "findingIds": [
        "finding:four-native-starts-have-distinct-original-fold-state-correlations",
        "finding:four-starts-full-joint-kernel-and-charged-covariant-transport"
      ],
      "explanationEN": "Actual unitquarticrayswq=sqrt(6/5)nq,q2..5,S01 in same originalFCαF* fixedconformalNS/M/Odictionary give phase-invariant connectedc1=wq*D1wq. Common denominator1006632960,numeratorsα1/4=(1200580,1300621,982285,1446340),α3/4=(1308100,1521805,1089805,1338820);all6pairs distinct perquarter. c2=4335/131072,c3=85/256,c4=1 equal; firstdifference alongtheserays sixthorderinb. Alsotr(P(q,01)D1) givesfour pairwisedistinctQ(sqrt6)values perquarter. Therefore noall-response-preserving fixed-state*-equivalence transporting actualquarticspace andtheseplanes; universalOPE-I metric forcesunitarity. Obstruction doesNOTrelyonlyontrivialG31stabilizer andplane-onlytestneedsnoextra distinguished-raypreservation.",
      "changesRequiredEN": "18Oct: The four starts and polar planes have pairwise distinct correlation invariants in the SAME original fold/NS field dictionary. Whole E8 datum transport is covariance, not fixed-state symmetry or physical gauge proof; odd-CAR only separately transported passively. Do not maximize c1 or polar trace or repeat fixed-point/profile tests. Check the actual original preparation, event or output datum for which already distinguishable relation is instantiated. No fitted coupling, invented detector or four P1 theories. Retain full E8/erasure/time/carry response; physical source and q/S/3+2 remain open.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:classify-four-polar-pointer-contexts-and-original-multilocal-support",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Original pointer template, four-context algebra and full CAR support",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:local-e8-current-response-realization",
        "premise:native-g31-concrete-event-representation",
        "premise:native-symmetric-quartic-and-erasure-constructors",
        "premise:literal-native-positive-cartan-quartic-fock-embedding",
        "premise:original-displayed-j-equivariant-cartan-root-isometry",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:intrinsic-native-event-geometry-without-marked-clock",
        "premise:original-seam-state-data-on-native-flags-without-fitted-selector",
        "premise:fixed-conformal-current-reference-for-original-fold-state-transport",
        "premise:four-starts-fixed-state-versus-whole-datum-comparison",
        "premise:original-single-circle-local-density-and-geometric-stress",
        "premise:original-stable-pointer-instrument-and-given-context",
        "premise:same-full-positive-energy-separating-local-car-source"
      ],
      "findingIds": [
        "finding:original-pointer-template-requires-source-context-identification",
        "finding:four-polar-context-algebra-and-source-crosscoupling",
        "finding:every-native-quartic-has-all-eight-original-car-supports",
        "finding:bounded-proper-local-source-operation-cannot-exactly-prepare-positive-eigenpacket",
        "finding:full-original-erasure20-and-joint25-have-all-eight-source-supports"
      ],
      "explanationEN": "Complete exact classification of given four-mark algebra and every nonzero quartic field support; positive-energy preparation lemma with explicit local separation. No new physical source or selection follows. Complete original joint25 field space now classified by degree8/6 injectivity.",
      "changesRequiredEN": "19Oct: Original conditional pointer template found; four native polar planes are incompatible potential contexts, not outcomes of one joint sharp measurement. Mark algebra C+M4 is coupled to full M5 by original D1. Every nonzero native quartic has all eight original support locations under same M/O pullback. In positive separating CAR net, exact E32 preparation from same sea by bounded proper-local A is excluded; approximation, other states and unbounded insertions are not. Connect ONE actual original P1 context/preparation/record datum, real support, reference, time and A/A* admissibility to this field dictionary. Do not impose exact eigenpacket preparation, code closure or pointer commutation with every response. No fitted coupling, q maximization, profile scan or eight independent arc vacua. Physical source/q/S/3+2 and common clock lift remain open. Addendum: same exact support theorem now covers original normalized erasure20 and all25 joint fields; no field combination removes a source arc. No separate E24 preparation claim.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-full-dirac-cauchy-vector-current-with-original-chiral-phase",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Identify complete Dirac Cauchy vector current with original chiral phase",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:charged-car-pure-two-face-cauchy-graph-state",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures",
        "premise:complete-lagrangian-dirac-cauchy-car-quantization"
      ],
      "findingIds": [
        "finding:full-dirac-cauchy-vector-cocycle-cancels-and-endpoint-domain-distinction"
      ],
      "explanationEN": "Under the complete Lagrangian/CAR/implementability premises, the normal-commuting central cocycle vanishes. A scalar chiral level1 current is therefore not automatically the full P1 Dirac vector current.",
      "changesRequiredEN": "First identify the original physical chiral-scalar measure/line connection or actual inflow, including reference/domain/OS Padm, with the existing CAR/E8 dictionary. Gamma already supplies the differential block; no new component, freely chosen projector or profile scan. Further 1D boundary research does not require prior 4D closure.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:squeeze-unitary-neutral-pair-return-at-fixed-compact-time",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Squeeze unitary neutral pair return at fixed source time",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:smooth-unitary-pair-return-fixed-compact-source-time",
        "premise:fixed-scalar-quarter-hardy-source",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:smooth-unitary-endpoint-removal-diverges-at-fixed-source-time"
      ],
      "explanationEN": "DeltaK>=2pi/eps excludes bounded-energy normalized UNITARY state limit in this entire class.",
      "changesRequiredEN": "Construct nonunitary charged field intertwiner with actual microscopic sector/reference map; do not scan another profile or exclude standard sectors wholesale.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:nonunitary-endpoint-limit-with-unchanged-full-source-time-and-observables",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Nonunitary endpoint limit with unchanged full source/time/observable action",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:unchanged-full-source-observable-map-and-continuous-time-insertion-limit",
        "premise:retained-local-register-with-one-common-original-vacuum-reference",
        "premise:unchanged-quarter-qwz-full-excitation-source",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:continuous-original-time-nonunitary-limits-stay-in-old-source-folium",
        "finding:common-register-vacuum-reference-uniform-and-local-grade-reduction"
      ],
      "explanationEN": "Finite nonzero norm and continuous actual time kernel imply tightness; full spectral windows/fixedoperator action keep word states inoldfolium. LocalZ/uniform common reference reducegrade mixtures. No bounded meanenergy required.",
      "changesRequiredEN": "Derive ACTUAL original charged sector/reference/time/observable comparison or originally selected different localGaussnet rule. Do not exclude standard sectors,choose freeHamiltonian as solution,or run anotherprofile/renormalization underidenticalglobal contract. OldoddPhi specifically changesoperator comparison andretainsseparate scope.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:holomorphic-kms-uniqueness-as-microscopic-charged-generator",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Use holomorphic KMS uniqueness as microscopic charged generator",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:given-holomorphic-kms-inclusion-and-local-global-modular-domains",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:holomorphic-kms-extension-assumes-charged-net-and-not-microscopic-generator",
        "finding:fixed-interval-rotation-modular-chain-fails-local-state-takesaki-repairs"
      ],
      "explanationEN": "CitedtheoremalreadyassumesB/definesomegaasitsrestriction.GroupaverageandlocallyrepairedTakesakistepdonotgeneratemissingfields.",
      "changesRequiredEN": "Firstderiveactualchargedlocalalgebra/fielddictionaryfromoriginaloperations;thenapplyKMS/modulartransport.Donotuseglobalrotationonfixedintervalaslocalmodulartime.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:repair-global-odd-spinor-phi-by-kms-or-global-parity",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Locally repair global odd-spinor Phi by KMS or global parity",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:canonical-source-gibbs-and-parity-probe-with-retained-winding",
        "premise:given-eightfold-source-odd-refielding-dictionary",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:source-winding-cartan-four-word-and-two-edge-kms-gso-discriminator"
      ],
      "explanationEN": "FullSOURCE-W1/Cartanfourword+I/-Iandthermaltwo-edgeresponsedistinguishunchangedoperators.Total-evenretainsodd/odd;LEFT-evenremovesSOURCE-W1.",
      "changesRequiredEN": "ConstructoriginallyjustifiedchangedCartan/statistics/netmapwithchargedfieldcarrier,fullwords,timeandprimitivewindingcomparison.Nospectral/KMSclaimasasubstitute.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-existing-parity-gauss-rule-from-original-p1-definitions",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Derive existing parity-Gauss rule only from original P1 definitions",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:conditional-local-parity-gauss-completion-with-common-H",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:p1-parity-gauss-net-selection-undecidable-without-original-localization-map"
      ],
      "explanationEN": "Forward source comparison identifies a concrete insertion/localization definition gap. The seed already takes the local net as input; no inverse selection of the gauge net or full P1 compatibility of both models is proved.",
      "changesRequiredEN": "Build no further extension. A later decision needs the originally defined local insertion/sector map with Padm/Gx, state, time, reflection and primitive winding identification. State this gap and stop.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-source-minimality-and-domain-audit",
      "problemId": "problem:common-source-state-event-selection",
      "titleEN": "Reuse original minimality and domain audit",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:literal-boundary-minimality-and-first-order-domain-statements",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions"
      ],
      "findingIds": [
        "finding:original-minimality-does-not-reconstruct-operational-source",
        "finding:generic-first-order-relative-bound-zero-counterexample-and-correct-domain-repair"
      ],
      "explanationEN": "The specific proof steps are audited; generic bound0 is refuted and replaced by correct conditional hypotheses. The source inverse still needs an actual defined local reconstruction.",
      "changesRequiredEN": "Continue only with a precise source map, complete correlators or newly proved symbol/domain bounds. A freely chosen helper model does not replace these conditions.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:parallelity-as-axiom",
      "problemId": "problem:seam-family-connection-compatibility",
      "titleEN": "Parallelity as a silent axiom",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:parallel-irreducible-family-connection"
      ],
      "findingIds": [
        "finding:parallelity-excludes-2plus2-only-conditionally"
      ],
      "explanationEN": "The 2+2/3+1 comparison excludes only under explicit common parallelity and irreducibility. These are additional premises, not accepted TFPT axioms.",
      "changesRequiredEN": "Derive an original common covariance/transport rule before rejecting a packet.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-sign-only-obstruction",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Reuse the sign-only dynamics obstruction",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:sign-covariance-only"
      ],
      "findingIds": [
        "finding:sign-projector-does-not-determine-time-magnitude"
      ],
      "explanationEN": "The fixed sign projector loses |H|; a=2 and a=3 yield the same rho_0 and C.",
      "changesRequiredEN": "Proceed only with complete transfer or faithful KMS covariance.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-full-transfer-kms-reconstruction",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Reuse full-transfer/KMS reconstruction",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:known-faithful-kms-or-full-transfer"
      ],
      "findingIds": [
        "finding:full-faithful-kms-or-transfer-recovers-magnitudes"
      ],
      "explanationEN": "Injectivity holds exactly under the named faithfulness and completeness conditions.",
      "changesRequiredEN": "Still supply physical identification of the TFPT channel.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:full-two-boundary-calderon-graph-reconstruction",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Use complete two-face reconstruction",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:actual-product-collar-two-face-data"
      ],
      "findingIds": [
        "finding:full-two-face-collar-recovers-signed-operator"
      ],
      "explanationEN": "This inverse is analytically settled; do not repeat Hamiltonian search when complete G is supplied.",
      "changesRequiredEN": "For source selection supply the actual original graph kernel, fiber comparison and normal length; G generated from a guessed B is not a provenance derivation.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-shared-register-gkls-q-classification",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Reuse the existing GKLS q interval",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:specified-shared-s3-register-channel-family"
      ],
      "findingIds": [
        "finding:shared-register-gkls-embedding-exact-q-interval"
      ],
      "explanationEN": "The specified source proof is available and need not be searched for again as a missing derivation.",
      "changesRequiredEN": "A different starting equation or physical realization requires its own justification.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:exclude-fixed-m4-homogeneous-gksl-logarithm",
      "problemId": "problem:physical-time-projector-transfer",
      "titleEN": "Do not repeat homogeneous GKSL time search for the fixed M4 channel",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:specified-marked-m4-clifford-channel"
      ],
      "findingIds": [
        "finding:marked-m4-channel-all-powers-homogeneous-gksl-excluded"
      ],
      "explanationEN": "The all-branch proof also excludes every positive integer power.",
      "changesRequiredEN": "Time-dependent execution or a larger justified source is a different comparison class, not a repair of the same homogeneous M4 generator.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-ratio-not-absolute-anchor",
      "problemId": "problem:flavor-ratio-amplitude-readout",
      "titleEN": "Reuse the ratio, keep the absolute anchor open",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:declared-p1-p2"
      ],
      "findingIds": [
        "finding:flavor-ratio-closed-absolute-anchor-open"
      ],
      "explanationEN": "The discrete ratio is closed, while U_f* remains a separate open source-selection task.",
      "changesRequiredEN": "Continue only with the absolute scale.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:numerical-root-as-origin-proof",
      "problemId": "problem:alpha-fixed-input-root",
      "titleEN": "Numerical root as origin proof",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:fixed-input-models-scoped"
      ],
      "findingIds": [
        "finding:alpha-equation-is-fixed-input-closure"
      ],
      "explanationEN": "An exact root confirms only the chosen equation and inputs; it does not select them.",
      "changesRequiredEN": "Derive the missing input and readout selector independently.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-alpha-convexity-proof",
      "problemId": "problem:alpha-fixed-input-root",
      "titleEN": "Reuse the existing convexity proof",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-em-seam-function"
      ],
      "findingIds": [
        "finding:alpha-global-positive-root-unique"
      ],
      "explanationEN": "Positive root uniqueness is already analytically closed; another numerical scan would not be a new derivation.",
      "changesRequiredEN": "Specify a genuinely different function or a violated convexity premise.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:add-free-geometric-cocycle",
      "problemId": "problem:gravity-flow-normalization",
      "titleEN": "Use a free geometric cocycle as a TFPT counter-source",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures",
        "premise:fixed-input-models-scoped"
      ],
      "findingIds": [
        "finding:matter-observations-do-not-fix-geometric-response"
      ],
      "explanationEN": "The cited observation result shows ambiguity in the larger matter-only observation class and explicitly says W→W+lambda Q[g] is not thereby an admissible change to the fixed original functional. It therefore does not establish a TFPT source cocycle.",
      "changesRequiredEN": "Derive an admissible change to the fixed original functional from original principles; matter-only ambiguity alone is insufficient.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-clock-jordan-response-inverse",
      "problemId": "problem:clock-linked-neutral-response-reconstruction",
      "titleEN": "Reuse clock-Jordan response inverse",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:native-current-clock-ope-access"
      ],
      "findingIds": [
        "finding:four-clock-fields-complete-quadratic-response"
      ],
      "explanationEN": "The complete neutral matrix is reconstructed in this class. Self-correlators alone remain insufficient.",
      "changesRequiredEN": "A different state, clock action or nonquadratic fields require a new matching contract.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-j-covariant-source-lift",
      "problemId": "problem:clock-source-covariant-transport",
      "titleEN": "Use covariant J source lift",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:stipulated-e8-clock-tuple"
      ],
      "findingIds": [
        "finding:actual-j-covariant-source-transport"
      ],
      "explanationEN": "Existence in the given Fock space is analytically proved and123 groups checked.",
      "changesRequiredEN": "A different representation, cocycle or physical sector requires matching new premises.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:fixed-affine-j-as-source-time-symmetry",
      "problemId": "problem:clock-source-covariant-transport",
      "titleEN": "Affine J as a symmetry of the same fixed time",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:stipulated-e8-clock-tuple"
      ],
      "findingIds": [
        "finding:fixed-source-affine-j-obstruction"
      ],
      "explanationEN": "2δ is not in the original E8 lattice.",
      "changesRequiredEN": "Explicitly justify background transport or a genuinely different operator action; do not claim the same fixed K.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:more-neutral-vacuum-moments-select-twist",
      "problemId": "problem:charged-twist-response-identifiability",
      "titleEN": "Select twist with additional neutral vacuum moments",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:neutral-current-vacuum-insertions"
      ],
      "findingIds": [
        "finding:neutral-vacuum-allword-twist-blindness"
      ],
      "explanationEN": "All such words are exactly twist-blind; more GPU samples cannot recover the absent information.",
      "changesRequiredEN": "Derive charged intermediate fields or an explicitly different state/probe source.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-eight-charge-twist-inverse",
      "problemId": "problem:charged-twist-response-identifiability",
      "titleEN": "Use charged eight-direction response inverse",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:normalized-charged-primary-time-access"
      ],
      "findingIds": [
        "finding:eight-charged-responses-reconstruct-twist"
      ],
      "explanationEN": "The exact linear inverse is available and23 check groups confirm its implementation.",
      "changesRequiredEN": "Check availability and identical physical meaning of the charged preparations.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:native-invariant-start-matches-single-twist",
      "problemId": "problem:native-charged-seam-selection",
      "titleEN": "Read unchanged native response as a single twist",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:native-full-charge-field-source",
        "premise:native-c-invariant-start",
        "premise:fixed-nonzero-quarter-twist-comparison"
      ],
      "findingIds": [
        "finding:native-invariant-response-not-fixed-chiral-twist"
      ],
      "explanationEN": "Equal plus/minus ratio contradicts the nonzero fixed twist.",
      "changesRequiredEN": "Justify an actual change of state, source operator or marked field map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:fixed-quarter-hopping-phase-selects-chiral-time",
      "problemId": "problem:native-charged-seam-selection",
      "titleEN": "Add a quarter phase only to hopping",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:native-full-charge-field-source",
        "premise:native-fixed-link-phase-a-invariance",
        "premise:fixed-nonzero-quarter-twist-comparison"
      ],
      "findingIds": [
        "finding:fixed-hopping-quarter-phases-retain-antiunitary-discriminator"
      ],
      "explanationEN": "A=CK survives; the discriminating Euclidean response remains symmetric.",
      "changesRequiredEN": "A seam-derived A-breaking operator or initial state changes the premise.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-native-charged-corner-ratio",
      "problemId": "problem:native-charged-seam-selection",
      "titleEN": "Reuse native charged-corner ratio",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:native-full-charge-field-source",
        "premise:native-zero-sector-chemical-comparison"
      ],
      "findingIds": [
        "finding:native-chemical-mark-visible-in-charged-corners"
      ],
      "explanationEN": "The exact ratio formula is available; C0 must include the charged corners for this purpose.",
      "changesRequiredEN": "A different charge action or nonuniform marking requires a new calculation.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:repeat-closed-seam-phase-search",
      "problemId": "problem:constructive-seam-lift-state",
      "titleEN": "Repeat the same phase class",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-car-crossed-half-charge-search"
      ],
      "findingIds": [
        "finding:constructive-phase-class-and-full-winding"
      ],
      "explanationEN": "The whole class is classified; genetic repeats supply no new source information.",
      "changesRequiredEN": "Supply a new original-source-derived variable or representation and a decisive acceptance criterion.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:shift-functional-selects-physical-state",
      "problemId": "problem:constructive-seam-lift-state",
      "titleEN": "Unique shift functional as physical state selection",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:fixed-car-crossed-half-charge-search",
        "premise:fixed-positive-crossed-state"
      ],
      "findingIds": [
        "finding:constructive-positive-state-extension",
        "finding:constructive-state-algebra-resolution-and-source-test"
      ],
      "explanationEN": "Different ground densities induce the same functional; actual Cartan observables distinguish them.",
      "changesRequiredEN": "Retain the full original observable/Cartan restriction; do not infer Rc invariance from [K,Rc]=0.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:crossed-phase-hit-as-unchanged-source",
      "problemId": "problem:constructive-seam-lift-state",
      "titleEN": "Phase hit as unchanged source realization",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:fixed-car-crossed-half-charge-search",
        "premise:unchanged-quarter-car-qwz-source-comparison"
      ],
      "findingIds": [
        "finding:constructive-all-phases-fail-unchanged-source"
      ],
      "explanationEN": "Every hit adds half-Cartan sectors and the same second K-zero vector; both are absent from the unchanged source.",
      "changesRequiredEN": "Derive a changed source representation with the neutral partner or a different common time/operator dictionary from original principles.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:root-coordinate-equality-as-physical-partner",
      "problemId": "problem:seam-partner-charge-state-time",
      "titleEN": "Equal root as equal physical partner",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:oriented-p2-exterior-carrier",
        "premise:fixed-e8-fold-quarter-dictionary"
      ],
      "findingIds": [
        "finding:partner-carrier-charges-and-state-types",
        "finding:partner-fixed-quarter-time-splits-sm-multiplet"
      ],
      "explanationEN": "M r0=e1+e4 does not define a state map; source charge is not Y and K splits the multiplet.",
      "changesRequiredEN": "Derive the actual field representation with all charges, boundary conjugation, state and time from the same source.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:fixed-time-weyl-repair-quarter-conjugation",
      "problemId": "problem:seam-partner-charge-state-time",
      "titleEN": "Restore fixed marking after quarter conjugation by Weyl correction",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:actual-chiral-opposite-quarter-domains",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:given-first-marked-quarter-character"
      ],
      "findingIds": [
        "finding:joint-fixed-time-marking-repair-excluded"
      ],
      "explanationEN": "Unequal projection norms exclude the whole orthogonal correction class at fixed d_beta.",
      "changesRequiredEN": "Use the actually transported marking or supply a different source action derived from P1/P2; a larger phase scan does not change the invariant.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:repeat-known-car-synthesis-calibration",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Repeat unchanged known CAR synthesis calibration",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:declared-finite-operator-synthesis-inputs"
      ],
      "findingIds": [
        "finding:typed-operator-search-calibrated"
      ],
      "explanationEN": "The declared control domain was exhausted. Its result calibrates the search software.",
      "changesRequiredEN": "For new research extend the actual operator contract or structural grammar, rather than only changing seed or runtime.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:repeat-finite-positive-kernel-calibration",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Repeat unchanged finite kernel calibration",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:finite-positive-kernel-search-class"
      ],
      "findingIds": [
        "finding:positive-kernel-construction-with-exact-discriminator"
      ],
      "explanationEN": "Exact finite completions and shortest degree5 separation are available; the campaign persists reusable results.",
      "changesRequiredEN": "A source-grounded new operator/composite-field relation, another justified representation, or full OS/seam data. Seed, runtime or a numerical gap alone do not close an original contract.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:trace-and-joint-ward-select-fixed-fields",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Select the field map from traces and the joint Ward identity alone",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:fixed-field-four-mode-inverse-data-control"
      ],
      "findingIds": [
        "finding:joint-ward-two-field-data-miss-fixed-four-field-response"
      ],
      "explanationEN": "These data do not determine the fixed pair response in the tested inverse contract. The joint identity remains a valid consistency check.",
      "changesRequiredEN": "Derive the actual local field map and source insertions from the original action; test the multifield response or full appropriate Schwinger-Dyson identity. Do not impose a free creator equation on the interacting action.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:complete-kernel-to-nongaussian-functional",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Reconstruct the complete kernel rather than separate action and measure",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:complete-labeled-even-car-kernel"
      ],
      "findingIds": [
        "finding:complete-car-kernel-fixes-nongaussian-link-functional"
      ],
      "explanationEN": "The full link action follows without a Gaussian assumption in the given dictionary.",
      "changesRequiredEN": "Derive the original field dictionary and T[Φ].",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:repair-ns-vector-matter-by-local-composites",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Generate spinor matter from local composites of the unchanged NS vector fermionization",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:fermionized-ns-vector-algebra-fixed-d5"
      ],
      "findingIds": [
        "finding:unchanged-ns-vector-generators-cannot-create-d5-spinor-fields"
      ],
      "explanationEN": "The central kernel element acts trivially on the entire unchanged generator algebra, and local products cannot generate spinorial character.",
      "changesRequiredEN": "A source-grounded sector/field extension with actual charged intertwiners or another demonstrated group/source map. New coefficients or longer composite searches do not change this premise.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:repeat-given-quarter-gns-feedback-control",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Repeat the unchanged given thermal query-feedback control",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:finite-faithful-car-gns-source-completion"
      ],
      "findingIds": [
        "finding:faithful-gns-completion-closes-automated-source-query-feedback"
      ],
      "explanationEN": "Compatible mixed-state completion and automatic one-transfer query are validated in the existing entry point. The control does not derive its source from P1.",
      "changesRequiredEN": "For progress on the original goal supply the actual local P1 insertion or a newly source-derived multifield response. Do not feed candidate predictions back as source facts, change only seed/runtime, or substitute a new pure/free source.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:exact-kernel-and-common-insertion-identification",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Exact kernel and common original insertion contract",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-local-quarter-channel-in-constant-odd-source",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:actual-diagonal-lepton8-common-insertion-contract"
      ],
      "findingIds": [
        "finding:whole-quarter-channels-identified-by-exact-internal-kernel",
        "finding:actual-joint-insertion-hull-resolves-eight-coefficient-directions"
      ],
      "explanationEN": "New concrete source tests are executed, including a minimal operator counterexample. General synthesis software and Universalraum/GNS results already existed.",
      "changesRequiredEN": "For origin progress use independently original insertion images or a newly derived common response; do not repeat the same controls.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:repeat-e8-single-anchor-weyl-polynomial-search",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Continue searching E8 single-anchor Weyl polynomials",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:one-e8-bracket-weyl-pairing-with-single-anchor-dressing"
      ],
      "findingIds": [
        "finding:e8-bare-trilinear-and-single-anchor-weyl-class-insufficient"
      ],
      "explanationEN": "The entire polynomial class reduces analytically to I,X and is excluded; random/genetic search cannot find a missing triplet coupling in it.",
      "changesRequiredEN": "An additional originally derived family-distinguishing operation, different field type or actual higher-product process changes the class and must be tested separately.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:repeat-sm-preserving-family-four-cycle-native-clock-search",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Reuse the complete family-four-cycle clock classification",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:spin10-su4-family-four-cycle-quarter-lift-class",
        "premise:family-four-cycle-lift-commutes-with-original-sm",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "findingIds": [
        "finding:complete-family-four-cycle-class-separates-native-clock-from-sm-preservation"
      ],
      "explanationEN": "The entire restricted and larger1024 class are exactly classified and independently confirmed analytically; changing genetic seeds cannot repair the character conflict.",
      "changesRequiredEN": "A different originally grounded family action or jointly transported SM/field marking changes the class. Reuse solved native glue/C12 conjugacy rather than treating existence as open. Physical progress requires actual original coupled insertion images.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-whole-coupled-source-and-test-first-original-oneform",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Retain whole coupled source and test first original one-form action",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:native-third-clock-current-word-pairing-class"
      ],
      "findingIds": [
        "finding:native-clock-word-transpose-has-static-rank-four-counterexample",
        "finding:whole-constant-coupled-source-is-implementable-despite-isolated-insertion-domain"
      ],
      "explanationEN": "Affine word source exists but alone creates no physical time. Do not assume pure insertion generator on old vacuum domain; whole coupled source works in stated setting. Identify actual q=I neutrino transition in independently original source variation.",
      "changesRequiredEN": "For origin progress derive same mixed insertion value from original reader rather than defining it from target chart.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-fixed-scalar-quarter-beta-with-original-pfaffian-source",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Read unchanged scalar quarter pairing as original Pfaffian source",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:fixed-scalar-quarter-full-jloc-pfaffian-candidate",
        "premise:typed-source-structures",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing"
      ],
      "findingIds": [
        "finding:fixed-quarter-jloc-pfaffian-closure-fails-local-skew-test"
      ],
      "explanationEN": "Specific old beta_Dalpha form already fails skewness locally. Whole source remains positive but claimed identical Pfaffian form does not follow.",
      "changesRequiredEN": "A different originally justified whole source space or actual J-odd charge connection must be identified with same source. Paired sectors must carry whole field/state/R/time and reference map; log profile needs original scale rule. No eta-only repair.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:rescan-constant-whole-clutch-for-selected-protected-three-modes",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Rescan constant whole clutch for selected protected three modes",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:whole-constant-odd-coefficient-on-scalar-unit-clutch-domain"
      ],
      "findingIds": [
        "finding:whole-constant-coupled-clutch-defects-are-exact-internal-kernels"
      ],
      "explanationEN": "Entire constant class is analytically decided by actual internal kernel. More runtime or genetic parameter choice does not supply original coefficient rule.",
      "changesRequiredEN": "An originally derived variable Φ/connection,noncentral clutch or different common closed source operation retaining whole fields/time changes premise. Do not simply choose rank defect to fit3.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:rescan-common-leading-distance-clutch-for-original-flavor",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Rescan common leading clutch distances for original flavor lengths",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:common-leading-distance-flavor-readers"
      ],
      "findingIds": [
        "finding:all-common-leading-distance-clutches-fail-original-flavor-lengths"
      ],
      "explanationEN": "Entire real class decided analytically; no further genetic kappa scan.",
      "changesRequiredEN": "Actual original different spectra/weights, full source sums or C6 operator histories with the real consumer.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:d5-zero-mode-commutator-as-odd-hardy-background-generator",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "D5 current commutators as odd Hardy background generator",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:oriented-p2-exterior-carrier",
        "premise:original-d5-base-current-action-on-given-p2-e8-source"
      ],
      "findingIds": [
        "finding:actual-hardy-response-has-weak-clifford-odd-and-ko-real-completion"
      ],
      "explanationEN": "All actual D5 Clifford bilinears and their words commute with the even Hardy projection; no parameter search in this class.",
      "changesRequiredEN": "An actual original odd weak Clifford/product operation or whole mixed E8 field consumer with family leg, not a fitted matrix unit.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:infer-yukawa-hierarchy-and-ckm-from-two-directed-hardy-entries",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Infer Yukawa hierarchy and CKM from two directed Hardy entries",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:oriented-p2-exterior-carrier",
        "premise:declared-q-column-to-v252-chiral-slot-comparison",
        "premise:actual-full-v252-unimodular-p2-gauge-lift"
      ],
      "findingIds": [
        "finding:two-entry-hardy-adjoint-hierarchy-fails-full-ko-and-su2"
      ],
      "explanationEN": "FullKO6 symmetrizesM; complete two-edgeclass has degenerate nonzero singularvalues; differentbare components violatefixedSU2.",
      "changesRequiredEN": "Actualoriginal sector-specificreaders/intertwiners or complete sourceleg with derivedcoefficients,not another scan of sameclass.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:compensate-hardypair-quarter-character-with-native-clock-adjoint",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Compensate Hardy quarter character by native adjoint clock",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:oriented-p2-exterior-carrier",
        "premise:declared-q-column-to-v252-chiral-slot-comparison",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:native-clock-adjoint-compensation-for-hardypair"
      ],
      "findingIds": [
        "finding:native-adjoint-quarter-clock-cannot-compensate-hardypair-odd-character"
      ],
      "explanationEN": "Endomorphism has two endpoint actions; vectorphase cancels and weaklift has sign-1.",
      "changesRequiredEN": "Actual differently transforming originalHom endpoints or another sourceconsumer; use the existingfour openpaths, do not rescan the sameclockclass.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:replace-whole-marked-hardy-reader-by-linear-spectral-centralization",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Replace whole marked Hardy reader by linear spectral centralization",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:whole-six-original-induced-inputs-at-fixed-kinetic-ns-reader",
        "premise:original-closed-real-delta-transport-action"
      ],
      "findingIds": [
        "finding:linear-spectral-centralization-does-not-replace-full-marked-hardy-source"
      ],
      "explanationEN": "Centralization preserves linear scalar traces but loses actual marked quadratic/higher terms and the full adjoint relation.",
      "changesRequiredEN": "Retain whole original insertions with both P0 endpoint legs or derive a genuinely new complete original source map including products and adjoints. Do not repeat the same scalar replacement.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:enumerate-finite-compatibility-as-unique-physical-source-selector",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Enumerate finite compatibility as a unique physical selector",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:actual-v252-entire-yukawa-majorana-family-with-compatibility-only"
      ],
      "findingIds": [
        "finding:actual-v252-entire-compatibility-family-has-generic31-dimensional-quotient"
      ],
      "explanationEN": "The entire v252 family passes these equations, leaving generic31 parameters. More tests of the same predicate do not select a source.",
      "changesRequiredEN": "Execute an independent original HolK/S_adm/T_V/K_car source rule and establish its actual restriction. Then solve that changed space with existing exact methods.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:infer-original-locality-from-bare-native-code-weyl-commutators",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Read original spatial locality from bare5codeWeylcommutators",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:actual-proper-local-current-weyls-and-bare-native-code-compression",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:actual-disjoint-local-weyls-acquire-spurious-commutator-under-bare-native-compression"
      ],
      "explanationEN": "For every disjointproperintervalpair the statedtwo-strengthclass gives nonzero5codecommutators although wholelocalWeyls commute. Globalcompression withordinarymatrixcomposition fails this original spatialrelation.",
      "changesRequiredEN": "Use actual local subalgebras or losslesswordreadout with Qintermediates andoriginalstate/time/reflection/support map;do not optimize anothergraph of same barecompression.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-actual-quarter-local-modular-time-with-geometric-current-point-flow",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Identify actual quarter modular time with geometric current point-flow",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:actual-elliptic-quarter-supported-current-and-interval-car-modular-test",
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:actual-quarter-current-state-excludes-nontrivial-geometric-local-point-time"
      ],
      "explanationEN": "Wholeconnectedshortdistancekernel forcesv0 in statedC5class;actualsupportedWeylprobeshowsMobiusfailure directly.",
      "changesRequiredEN": "Use actualstate-dependentlocalsourcetime andderiveoriginalfield/carrier/sewingdictionary. No morepointflowvariants ofsameclass.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-proper-opposite-face-alone-as-canonical-local-purification-partner",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Use proper opposite-face region alone as canonical local partner",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:actual-elliptic-two-face-projection-with-genuine-regional-support",
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks"
      ],
      "findingIds": [
        "finding:actual-proper-two-face-regions-do-not-contain-pure-local-source-double"
      ],
      "explanationEN": "OriginalanalyticXforcesstrictoutsidecontributionforeveryproperregionpair/nonzerorightprofile. Actualregionaltwofacecovarianceisnotprojection.",
      "changesRequiredEN": "Useactualwholeenvironment/polarpartner;derivephysicalP1/chargedinsertionmapseparately. Forinteractingnonquasifreenessretainwholewordsratherthanlinearprojectionreplacement.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:complete-original-higgs-color-source-from-two-and-four-words-only",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Complete original Higgs color source using only two and four field words",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture"
      ],
      "findingIds": [
        "finding:two-and-four-field-words-do-not-complete-original-color-triplet-source"
      ],
      "explanationEN": "Exactpositiveoriginalrange counterexamplehassamealltwo/fourdataanddifferentsixfieldresponse.",
      "changesRequiredEN": "Produceactualwholenumberinsertionor d3;noGaussianization/Wicksubstitution.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reconstruct-common-radial-higgs-law-from-entire-original-quarter-occupation-tower",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Reconstruct common radial Higgs law from entire original quarter occupation tower",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-common-positive-constant-higgs-law-over-whole-quarter-tower",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source",
        "premise:given-o1-mode-isometry-and-weak-invariant-positive-higgs-covariance-marginal"
      ],
      "findingIds": [
        "finding:whole-original-quarter-occupation-tower-uniquely-reconstructs-common-radial-higgs-law",
        "finding:finite-original-tower-reader-and-existing-weak-symmetry-fix-shared-matter-responses"
      ],
      "explanationEN": "Actualarithmeticptowerisdeterminingbypositive-realanalyticityanddivergentBlaschkesum;Stieltjeswithoriginalthermaltriangularreductionyieldswholeradiallaw.",
      "changesRequiredEN": "Deriveactualoriginalforwardanswers/commonclasspremiseatcarriersourceproducerinsteadoffurtherdistributionsearch.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-unchanged-primitive-free-quarter-covariance-with-integrated-nontrivial-higgs-source",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Use unchanged primitive free quarter covariance as nontrivial integrated Higgs source",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:original-common-positive-constant-higgs-law-over-whole-quarter-tower",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:actual-original-rightup-triplet-fixed-family-and-even-color-source"
      ],
      "findingIds": [
        "finding:unchanged-free-quarter-source-cannot-be-nontrivial-integrated-higgs-mixture"
      ],
      "explanationEN": "ExactmaximalfreeoccupationforcespositiveradialsourceatH0alreadyatonesinglep.",
      "changesRequiredEN": "Retainprimitivepreintegrationsourceandexecutegenuineoriginalfielddependentcarrier/sourcecall;nodefinitionalphysicalidentity.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-original-record-action-on-doily-and-ordered-source-response",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Derive original record action on Doily and ordered source response",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables",
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:actual-single-source-event-coherent-stinespring-record"
      ],
      "findingIds": [
        "finding:actual-e8-record-doily-action-is-signed-p-plus-compatible-point-with-typed-sym2-lift",
        "finding:actual-e8-record-words-distinguish-order-and-retain-phase-beyond-fifteen-labels",
        "finding:actual-doily-context-record-characters-have-ranks-four-two-two-two"
      ],
      "explanationEN": "Executedavailableoriginalsource:unsignedgraphhidesphasesandorderedresponse;actualSym²wordwitnessreplacestoymodel.",
      "changesRequiredEN": "Deriveactualphysicalrecord/carrier/insertionandlocalalgebrainoriginalprocess;nonewgraphscan.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-doily-compatible-point-with-unitary-record-output-and-causal-event",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Identify compatible Doily point as unitary record output and causal event",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables",
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words"
      ],
      "findingIds": [
        "finding:literal-doily-incidence-output-and-strict-causal-order-on-fifteen-source-labels-excluded"
      ],
      "explanationEN": "Actualoutputp+qnotq;unsignedinvolutionspermitbothdirections.",
      "changesRequiredEN": "Derivefulloriginalrecord/history/state/localitycontractinsteadof15labels,preserveorderedresponse.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:canonical-split-localization-of-original-source-records-with-state-and-region-audit",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Canonical split localization with original state and region audit",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:given-e8-current-vacuum-net-and-original-grade-two-descendant-with-standard-split",
        "premise:typed-source-structures",
        "premise:local-e8-current-response-realization",
        "premise:original-sixty-e8-unrefined-record-source-and-typed-doily-observables"
      ],
      "findingIds": [
        "finding:canonical-standard-split-localizes-original-source-record-words-with-full-descendant-companion",
        "finding:unchanged-global-sixty-event-source-fails-local-exterior-current-test",
        "finding:canonical-source-localization-changes-exterior-state-and-does-not-select-event-origin"
      ],
      "explanationEN": "Canonicallocalinstrumentexistsingivennet;directexteriortestseparatesencodingfromoriginalsourceprocess.",
      "changesRequiredEN": "Executegenuineoriginalsupportedinsertionwithstate/effect/inside-outsidewords,nofurtherimplementationconstruction.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:actual-elliptic-source-equilibrium-versus-causal-current-response",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original elliptic source variation and causal response together",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion",
        "premise:typed-source-structures",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra"
      ],
      "findingIds": [
        "finding:original-elliptic-fixed-holonomy-insertion-gives-local-operation-on-unchanged-source",
        "finding:original-quarter-pair-fixes-square-charge-law-half-response-and-real-quillen-norm",
        "finding:actual-elliptic-source-determines-all-path-normalized-causal-current-response"
      ],
      "explanationEN": "Wholegivensmoothclasssolvedforwardwithoriginalinside/outside/timedistinctionandexactQuillenconnection.",
      "changesRequiredEN": "Proceedonlywithactualnewmarked/nonabelianorinteractingmixedoriginalproducer,noscalarrepetition.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-coupled-higgs-color-holonomy-response-versus-free-quillen",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Test original coupled Higgs color group response against free Quillen response",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-quark-particle-color-group-counting-on-whole-constant-quarter-source",
        "premise:typed-source-structures",
        "premise:actual-original-quark-higgs-family-and-positive-conditional-source-mixture",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:given-original-elliptic-quarter-source-and-supported-scalar-current-insertion"
      ],
      "findingIds": [
        "finding:original-higgs-quark-source-has-exact-whole-su3-counting-response",
        "finding:single-original-color-parity-separates-free-quillen-from-positive-higgs-integrated-source"
      ],
      "explanationEN": "WholegivenSU3responseclassevaluated;oneexactboundedprobe separatesfreeandpositiveH-integratedcalls.",
      "changesRequiredEN": "Continuewithactualoriginalsource/ref/fieldinsertionorexplicitlychangedconditionalclass,notanotherHscan.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:whole-source-color-selection-versus-one-face-postselection",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute whole source color lift before one-face postselection",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:given-whole-quarter-graph-and-canonical-diagonal-original-color-lift",
        "premise:typed-source-structures",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:original-quark-particle-color-group-counting-on-whole-constant-quarter-source",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:stipulated-e8-h8-with-original-color-center-selector"
      ],
      "findingIds": [
        "finding:whole-original-quarter-graph-color-response-is-relative-and-diagonal-singlet",
        "finding:original-center-selector-requires-typed-state-field-and-face-transport"
      ],
      "explanationEN": "Wholegivenliftandjointcorrelationsresolved;actualtypedmappingmustnowbesupplied.",
      "changesRequiredEN": "Continuewithactualoriginalintertwiner/insertion,notanotherfreeprojectionorHscan.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-color-center-fixed-source-and-charged-ward-words",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original color center on whole field words instead of charged state slots",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-marked-color-center-on-whole-e8-lattice-current-source",
        "premise:typed-source-structures",
        "premise:stipulated-e8-h8-with-original-color-center-selector",
        "premise:local-e8-current-response-realization",
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:native-even-e8-gaussian-clock-and-sign-extension"
      ],
      "findingIds": [
        "finding:original-color-center-fixes-whole-e6-a2-source-and-charged-ward-word-action",
        "finding:original-color-neutral-lattice-class-cannot-supply-odd-fields-by-inherited-superlattice-extension"
      ],
      "explanationEN": "WholecolorfixedsourceandoriginalWardwordactionresolved;entireinheritedodd-latticeextensionshortcutexcluded.",
      "changesRequiredEN": "Executeactualoriginalgradedfield/support/covermap,notanotherColor/E6/lattice/projectorscan.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-unchanged-folded-ns-source-as-whole-original-color-current-net",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Infer full color interface of unchanged folded NS source from center compatibility alone",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:original-fixed-color-and-folded-ns-cartan-interface"
      ],
      "findingIds": [
        "finding:original-color-center-extends-to-folded-ns-but-full-current-action-needs-spin-sector-transport"
      ],
      "explanationEN": "Four original color roots change spin sector and are not internal fields of unchanged NS CAR algebra. Z3 action alone is insufficient.",
      "changesRequiredEN": "Derive actual original spin/defect/support and source/sewing transport on complete charged words;retain existing four-module parent without fitted frame alignment or renaming E8/CAR.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-full-marked-spin-source-from-unmarked-heat-partition-alone",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Identify full marked spin source from unmarked partition alone",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:actual-thermal-quarter-source-and-retained-spin-parent-mixed-word"
      ],
      "findingIds": [
        "finding:actual-color-spin-car-mixed-word-has-complete-thermal-source-and-cyclic-sewing",
        "finding:exact-original-ns-ramond-heat-equality-does-not-identify-fixed-color-restricted-source"
      ],
      "explanationEN": "Equal whole heat sums coexist with different original color/spin trace blocks and mixed answers. Actual entire source call is decisive.",
      "changesRequiredEN": "Derive original source and insertion producer with support/state/time/reference/spin seam. Do not repair using new free KMS/Gaussian/sector weights.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:replace-actual-spin-cartan-insertion-with-original-scalar-cover-phase",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Replace actual color Cartan insertion by scalar cover phase",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:actual-eightfold-arc-residue-source-and-fixed-spin-cartan-insertion"
      ],
      "findingIds": [
        "finding:original-scalar-cover-profile-cannot-implement-fixed-spin-cartan-loop",
        "finding:actual-spin-cartan-composite-source-retains-multi-arc-support-and-fails-additive-even-locality"
      ],
      "explanationEN": "Original scalar Gphi remains arc-diagonal while actual smooth q operation requires offdiagonal entries. Shared charge neutrality does not remove this operator mismatch.",
      "changesRequiredEN": "Derive existing composite current/field source with actual multi-arc support and original physical net insertion. No additional scalar profile or common-frame fit.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:execute-original-color-density-and-coordinate-region-descent",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original color admissibility on whole density variations and coordinate regions",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:actual-original-ns-color-center-continuous-density-and-coordinate-net",
        "premise:original-fixed-color-and-folded-ns-cartan-interface",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:actual-color-selector-admits-exactly-eighth-periodic-original-density-variations",
        "finding:actual-color-is-internal-exactly-on-eightfold-coordinate-source-regions"
      ],
      "explanationEN": "Entire scalar-variation and coordinate-support decision completed from fixed original center. Unchanged finer cover locality does not make this color center internal.",
      "changesRequiredEN": "Derive actual P1 image of whole color-neutral source algebra with seam/determinant/gap and full state/time/RP. No renewed scalar profile/color/number search or forced second composite vertex.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:execute-original-calderon-operation-and-full-source-response",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Test original Cauchy reduction against implementable whole source change",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:actual-original-full-two-face-graph-and-local-matrix-operations",
        "premise:actual-product-collar-two-face-data",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:original-whole-two-face-multiplier-reduction-is-only-constant-residue-diagonal",
        "finding:original-two-face-local-fock-implementation-and-exact-source-variation-differ-from-reduction"
      ],
      "explanationEN": "Entire given matrix multiplication class decided. PreservingG is not physical execution rule.",
      "changesRequiredEN": "Continue F1 after R074 at actual original field/source insertion. Reuse R073 color test and R074 entire Cauchy multiplication/HS classes and exact two-face response:preserving oldG differs from implementable source change and physicalPadm admissibility. Execute supported field correspondence in original Z_adm/S_prim/C_Sigma with whole2/4/higher words,actual face labels,K_F/reflection/time/domain;then original seam/determinant/gap action on those actualOS images. Original Psing is center projector,not an added fullSU3 singlet. No G_Cauchy=Padm_OS,Gamma(G),universal whole-Fock intertwiner,Dadm=L0 orQTheta=CARparity. Reuse original Green/HS partner/boundedRP. Retain fullRef/Eta/H0/Z0,charged intermediate histories,R035/R037/R043/R054/R063/R067/R068/R069/R071,memory,E8/clocks,Y/flavor/alpha,H before/after integration. No renewed decided multiplier/profile/color/heat/Y/scale/gap search. Physical3+1 and universalSpin2 remain F1 goal.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:close-original-marked-source-from-undecorated-transfer-and-finite-injectivity",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Close marked source and uniform gap from undecorated transfer alone",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:original-blocked-transfer-algebra-and-marked-source-uniformity-audit",
        "premise:given-original-two-stage-admissibility-complex-and-blocked-weight-caller",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:whole-undecorated-transfer-does-not-determine-original-marked-field-source",
        "finding:volume-wise-injective-positive-transfer-does-not-prove-uniform-parent-gap"
      ],
      "explanationEN": "E_I does not fix marked response,and finite injectivity lacks uniform parent-gap control for varying tensors. Countertests concern inference,not wholeTFPTmaster.",
      "changesRequiredEN": "Continue F1 after R075 at original field-dependent source call. Execute actual C6 Green plus transport-count/carrier/selector weights to T_V[J] or decorated E_O from the same S_adm/sewing rule;first obtain real source derivative with support,reflection,time,domain and Ref/Eta/H0/Z0. Undecorated transfer/Perron data do not select E_O;do not rescan decided implication class. MPS is this named original route,not a universal requirement;another original complete field law is valid. Given an original common tensor,compare marked2/4/higher histories with existing K_F/Green/HS and prove fixed-tensor or quantitative uniform parent control,never PF gap=parent gap. R074 preserving G is not physical execution. Reuse solved full moments/cumulants and penalty-weight results. No free Kraus rotation,new weights,Gaussian,geometry,coupling or generic gap/profile/Y/scale/multiplier search. Keep center selector,actual QTheta/Dadm,typed OS/Cauchy/Fock spaces,no universal whole-Fock intertwiner. Preserve charged intermediates,whole source,Z0/Ref/Eta/H0,R035/R037/R043/R054/R063/R067/R068/R069/R071,memory,State/Time/RP,E8/clocks,Y/flavor/alpha,H before/after integration. Physical local3+1 and universal spin2 from same source remain goal.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-original-c6-entire-word-expansion-before-marked-field-coupling",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Reuse entire original C6 words before marked field coupling",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-bare-c6-fixed-analytic-half-power-and-literal-word-alphabet",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:original-c6-half-power-has-exact-entire-positive-ordered-word-expansion",
        "finding:original-c6-whole-word-sewing-retains-source-amplitude-and-controlled-infinite-tail"
      ],
      "explanationEN": "Whole word class and original homogeneousdelta response decided;no2^nscan or new physical probability choice.",
      "changesRequiredEN": "Continue F1 after R076 at actual original marked field/coupling call. Reuse decided whole canonical word expansion of bareC6 Q^-1/2 and GreenQ^-1:all lengths,intermediate labels,Vandermonde concatenation,absolute normalization,homogeneous originaldelta response. Execute original map of a marked transport word with actual counts,carrier,Hol and selector weights to T_V[J]/E_O from same S_adm/seam rule;compare first actual word/source derivative with support,reflection,time,domain,Ref/Eta/H0/Z0. Distinguish Pf(Q)P from f(PQP);no stepwise P insertion. Preserve actual HolK Yukawa and Green consumers,no Y fit. Canonical positive expansion is not selected primitive physical probability law. No repeat generic length,gap,profile,Y,scale,measure,Kraus search or newGaussian. R075 E_I does not determineE_O;actual MPS requires original common tensors/uniform parent control,not universal MPS mandate. Preserve whole source,charged histories,R035/R037/R043/R054/R063/R067/R068/R069/R071,memory,State/Time/RP,E8/clocks,Y/flavor/alpha,H before/after integration. Physical local3+1/universal spin2 remain goal.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-recovered-historical-source-and-native-timed-consumer-before-primitive-matching",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Reuse recoveredparent and actualtimedconsumer before primitive matching",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:actual-original-finite-v990-source-and-historical-parent-recovery",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:historical-parent-and-actual-field-time-bridges-must-be-reused-before-new-source-models",
        "finding:actual-native-v990-full-timed-words-recover-kubo-response-distinct-from-instantaneous-variance"
      ],
      "explanationEN": "Originalformalparentandconcretefieldbridgesexistinstatedscope;donotrebuild. Compareactualtimednativeconsumer,not96/Z6namematching.",
      "changesRequiredEN": "ContinueF1 afterR077 at actual original common field/source call. Reuse older originalcircle/domain/Ward,microscopic CAR-to-neutralF8 field/time chain,formal originalv42Wk with ALLhigherSadmvertices,whole96H/two-face source,R076wholeC6words. Do not reopen these or solvedYukawas. Actualv990 now provides full timed reference words and nativeKubo normalization,not physical target orQFT004TV. v486 is spectrum-to-rates,not origin selection. Next map actual collectivefield/insertion and weights from SAME Sadm/Wk or originalCSigma->PFCSigmaPF to existing coupledmatter/Hsource;execute first actual mixed timedfield response,retaining support,state/time/reflection,domains,norm,boundRef/Eta/H0/Z0,allvertices. No newHintegral/rates/C6scan. Givenoriginalstate needs no second chosenstate. Formaldefinition/modelagreement cannot replace original map or constructedmeasure. TV/C6 is optionaloriginalroute,not universalMPS/v990mandate. No newY/profile/scale/weight/Kraus/projector/Gaussian search. Preserve allwhole sources,chargedhistories,memory,State/Time/RP,E8/clocks,Y/flavor/alpha. Physicalcommon3+1/spin2 remainsgoal;38scopedsubtasksretained.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-collective-higgs-force-source-before-any-new-classical-measure",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original collective force source before new classical measure",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-original-finite-car-higgs-force-and-faithful-collective-source"
      ],
      "findingIds": [
        "finding:actual-original-higgs-force-has-complete-ordered-fermionic-determinant-source",
        "finding:finite-covariant-higgs-composites-have-no-nontrivial-positive-instantaneous-classical-law",
        "finding:actual-original-collective-mean-has-exact-ball-domain-and-relative-entropy-action"
      ],
      "explanationEN": "Given source has complete collective quantum/mean reader;literal fixedfiniteclassicalreplacementfailsinthegivenscope.",
      "changesRequiredEN": "Physicalcontinuationrequiresoriginalfield/support/weightmaporactuallyderivedlimit/quantumbridge,notmerechoiceofmeasure.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:whole-original-circle-force-actual-time-before-classical-higgs-identification",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Test whole original force against actual time first",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-whole-circle-product-car-force-and-original-time-smearing"
      ],
      "findingIds": [
        "finding:original-uniform-allmode-force-clt-is-nonzero-only-before-fixed-time-smearing",
        "finding:original-unscaled-time-smeared-force-has-selfadjoint-whole-ordered-source"
      ],
      "explanationEN": "Uniform same-time limit is no dynamic smeared completion;original unscaled temporal quantum source fully constructed.",
      "changesRequiredEN": "Original supported field/insertion and weight map instead of another normalization/mode round.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:original-supported-force-source-before-new-geometric-measure",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Execute original supported force source before new geometric measure",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-constant-circle-local-higgs-force-and-hilbert-schmidt-time-source",
        "premise:literal-archived-global-positive-kernel-finite-measure-map"
      ],
      "findingIds": [
        "finding:original-local-higgs-force-has-whole-centered-hilbert-schmidt-determinant-source",
        "finding:given-original-circle-force-source-generates-an-exact-causal-local-net",
        "finding:literal-archived-global-rg-kernel-does-not-preserve-finite-measures"
      ],
      "explanationEN": "Givenlocalforcesourceandcausalliftfullyconstructed;literalarchivedglobalkernelcallfailsbeforefinitefixedpoint.",
      "changesRequiredEN": "Actualoriginalkernel/support/basemeasureandjointblockedsourcewithwholemarginalidentity,norepeatcircle/profileround.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:einstein-noether-four-origin-hypotheses-first-structural-tests",
      "problemId": "problem:automated-operator-source-synthesis",
      "titleEN": "Test four Einstein Noether origin routes at first structural identification",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-constant-circle-local-higgs-force-and-hilbert-schmidt-time-source",
        "premise:given-native-quasifree-higgs-source-and-actual-graded-restriction"
      ],
      "findingIds": [
        "finding:native-higgs-marginal-retains-induced-vertex-and-noether-response",
        "finding:isospectral-noether-orbit-does-not-supply-original-metric-higgs-variation"
      ],
      "explanationEN": "Constructive induced source response on actual matter block; specified isospectral/entropy/dimension shortcuts rejected. Whole common source remains goal.",
      "changesRequiredEN": "Execute actual original measure/restriction and true mixed metric/field insertion with whole Z and PQ memory; no repeated identical reader/profile/dimension round.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-e8-complete-separated-current-response",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "titleEN": "Reuse the existing exact boundary-current dictionary",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:local-e8-current-response-realization"
      ],
      "findingIds": [
        "finding:e8-current-dictionary-all-separated-responses"
      ],
      "explanationEN": "No need to rebuild generic CAR matrices or approximate nonabelian current fields as Gaussian.",
      "changesRequiredEN": "A different physical field net, changed state, contact terms or physical time require a separately source-derived map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:replace-microscopic-charged-map-by-abstract-fock-refinement",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "titleEN": "Use abstract boson refinement as microscopic field derivation",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:literal-microscopic-charged-scaling-and-v988-slater-data",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:charged-scaling-microscopic-map-still-unspecified",
        "finding:original-slater-proxy-fitted-bound-fails-actual-norm",
        "finding:periodic-microscopic-zero-modes-distinguish-source-state"
      ],
      "explanationEN": "A correct abstract lattice Fock operator does not identify the original QWZ state or charged sector. The earlier proxy fit also does not provide the required energy estimate.",
      "changesRequiredEN": "Construct actual B_N and local charged field from the microscopic algebra, then check refinement and actual energy norms. Do not substitute a freely chosen new coupling for the origin.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-proved-fourmark-three-five-views",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "titleEN": "Reuse proven three and five views of the same four-mark system",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:known-fourmark-system-has-three-and-five-canonical-views"
      ],
      "explanationEN": "The question is resolved. Broad retrieval or an open downstream map does not justify reopening it.",
      "changesRequiredEN": "Revisit only with an actually changed base object or premises, stating the change.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-unbounded-pascal-carrier-proof",
      "problemId": "problem:carrier-pascal-glue-formal-scope",
      "titleEN": "Reuse the existing unbounded Pascal theorem",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:pascal-carrier-exhaustion-equation"
      ],
      "findingIds": [
        "finding:pascal-carrier-rank-unique-unbounded-source-proof"
      ],
      "explanationEN": "The specified source proof is available and need not be searched for again as a missing derivation.",
      "changesRequiredEN": "A different starting equation or physical realization requires its own justification.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-explicit-finite-glue-classification",
      "problemId": "problem:carrier-pascal-glue-formal-scope",
      "titleEN": "Reuse the explicit finite glue declarations",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:specified-finite-carrier-discriminant-form"
      ],
      "findingIds": [
        "finding:finite-carrier-glue-elements-orbits-and-halfway"
      ],
      "explanationEN": "The specified source proof is available and need not be searched for again as a missing derivation.",
      "changesRequiredEN": "A different starting equation or physical realization requires its own justification.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-complete-quarter-clock-monodromy-normal-forms",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reuse proved quarter-clock normal forms",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:native-even-e8-gaussian-clock-and-sign-extension",
        "premise:ordered-four-punctures-fixed-quarter-projection"
      ],
      "findingIds": [
        "finding:quarter-clock-sign-lift-complete-four-puncture-classification",
        "finding:quarter-lift-central-quotient-class-and-all-subgroup-restrictions"
      ],
      "explanationEN": "Complete existence/orbit/stabilizer classification proved; extra groups/markings are different explicitly defined problems.",
      "changesRequiredEN": "For extensions state exact group, peripheral classes, coefficients and equivalence.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-original62-clock-obstruction-classification",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reuse complete G31obstruction classification",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:marked-seam-pure-mathematical-program",
        "premise:original-g31-central-determinant-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "findingIds": [
        "finding:orbifold-lift-criterion-and-determinant-eight-divisibility",
        "finding:original-g31-reflection-census-and-all-integral-cohomology",
        "finding:all62-original-clock-obstructions-and-central-variants",
        "finding:actual-sign-lift-g31-group-comparison",
        "finding:complete-g31-lift-invariants-and-explicit-collisions"
      ],
      "explanationEN": "All62strict cases and defined central variants are decided.",
      "changesRequiredEN": "Different problems require explicit different punctures,coefficients,markings or equivalence.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-global-g31-character-lift-decision",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reuse G31lattice-lift decision",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:ordered-original-g31-reflection-and-clock-markings"
      ],
      "findingIds": [
        "finding:global-original-g31-character-lift-nonsplitting",
        "finding:all62-original-character-clock-lifts-complete",
        "finding:all17-original-character-monodromy-lifts-complete"
      ],
      "explanationEN": "Global nonsplitting and complete monodromy lift quotients are proved.",
      "changesRequiredEN": "Specify a new question and changed groups, markings or equivalences.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-complete-e-series-compiler-closure",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reuse complete E-series compiler dictionary",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:existing-marked-cyclic-cover-and-burau-model",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension"
      ],
      "findingIds": [
        "finding:e7-pair-full-lattice-field-character-torsor",
        "finding:e-series-complete-native-compiler-cut-dictionary",
        "finding:common-cover-clock-and-maximal-integral-phi12-intertwiner",
        "finding:native-four-cut-projectors-unify48-fourthirds-fivequarters"
      ],
      "explanationEN": "All four requested follow-ups are decided by complete field lifts, cut classification, maximal actual clock transport and shared projector identities.",
      "changesRequiredEN": "Open new cases only with explicitly changed object class or marking; retain the established P1/P2 derivation and global nonsplitting.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-complete-covariant-compiler-cover-source",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reuse complete covariant compiler-cover source",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:existing-marked-cyclic-cover-and-burau-model",
        "premise:original-full-g31-action-and-inherited-lattice-sign-extension",
        "premise:joint-native-compiler-cover-covariance-category"
      ],
      "findingIds": [
        "finding:complete-covariant-compiler-voa-source-and-weyl-closure",
        "finding:complete-fixed-jhat-cyclic-field-lift-and-associated-clock",
        "finding:relative-native-burau-clock-hom-faithful12-transport",
        "finding:e6-vertex-nonselection-survives-full-field-clock-phases"
      ],
      "explanationEN": "Joint associated object, exact transition composition, minimal Weyl closure, one cyclic lift class and relative12 transport are determined; full field phases do not remove the selection obstruction.",
      "changesRequiredEN": "For stronger or different goals specify the changed object class or an actually supplied new marking. No freely correcting line twist or silent freezing of every field vector.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-marked-c4-vacuum-source-reconstruction",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reuse canonical local C4 reconstruction",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:marked-c4-unitary-local-extension-reconstruction-class"
      ],
      "findingIds": [
        "finding:marked-c4-glue-unique-local-e8-vacuum-source",
        "finding:canonical-vacuum-clock-preserves-e6-nonselection"
      ],
      "explanationEN": "All products and conformal vacuum data follow within the exact extension class; the internal clock remains distinct from conformal rotation.",
      "changesRequiredEN": "A stronger origin theorem requires an actual local identification of the primitive source with this class, not another freely constructed field model.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-generator-forced-local-e8-completion",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reuse generator-forced local E8 completion",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:connected-local-same-conformal-compiler-extension-with-generator"
      ],
      "findingIds": [
        "finding:marked-generator-forces-e8-without-support-multiplicity-or-minimality-input"
      ],
      "explanationEN": "One supplied generator forces the entire Lagrangian support once; separate sector selection and minimality are eliminated.",
      "changesRequiredEN": "New hypotheses or maps are required only outside this local conformal class or for primitive source identification.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-lossless-e6-tetrahedron-incidence",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reuse complete finite cut algebra and tetrahedron reconstruction",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:standard-e8-root-cut-full-flag-incidence-category"
      ],
      "findingIds": [
        "finding:e8-cut-five-orbital-incidence-algebra-complete",
        "finding:compiler-d8-frame-requires-full-d5-a3-flag",
        "finding:tetrahedron-incidence-lossless-e6-reconstruction"
      ],
      "explanationEN": "The full five orbitals are classified. MMt=NNt+24I directly proves lossless reconstruction from tetrahedron sums and locates the rank loss of the E7 view.",
      "changesRequiredEN": "Other cut classes or a distinguished input require explicit new premises; do not replace the proved incidence algebra by numerical coincidences.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-native-glue-cyclic-inner-conjugacy",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reuse common glue-clock and C12 conjugacy class",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "findingIds": [
        "finding:native-quarter-glue-inner-conjugacy-and-oriented-tetrahedron-flags",
        "finding:native-cyclic-compiler-inner-conjugacy"
      ],
      "explanationEN": "Complete finite orbits classify the quarter class and entire cyclic compiler family; their7560 unoriented flags are the existing tetrahedra.",
      "changesRequiredEN": "A preferred conjugator or frozen Cartan/Y/V4 marks require additional verified intertwining conditions.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-uniform-scalar-quarter-with-native-clock-over-fixed-d8",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Identify scalar quarter character over fixed D8 with native clock",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:scalar-eight-channel-twist-and-explicit-compiler-charge-chart",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "findingIds": [
        "finding:scalar-quarter-two-involutive-e8-extensions"
      ],
      "explanationEN": "Both and all compatible extensions are involutions with actual field spectra different from Jhat.",
      "changesRequiredEN": "A different original microscopic operation or restriction map must be explicitly derived. An added phase in the same fixed contract is insufficient.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-reviewed-e-series-field-roles-and-completed-e6-cubic",
      "problemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "titleEN": "Reuse complete E-series field roles and solved E6 source correlator",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:fixed-native-d5-a3-compiler-split-and-seed",
        "premise:marked-c4-unitary-local-extension-reconstruction-class",
        "premise:four-d8-sectors-with-fixed-affine-source-time"
      ],
      "findingIds": [
        "finding:recovered-e6-closed-81-current-module-and-unique-source-cubic",
        "finding:e-series-operational-role-review-and-source-time-centralizer"
      ],
      "explanationEN": "Do not rederive the completed E6 closure or cubic source product. The source bridge must compare actual joint insertions, charges and H8 action. Tetrahedral incidence and bare projectors do not replace that map.",
      "changesRequiredEN": "A new physical interpretation requires a derived common insertion and time map from the original operations.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-primitive-b-u-reconstruction-and-full-os-repair",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse operator reconstruction and corrected full OS moments",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:strong-seam-covariance-and-same-pair-index",
        "premise:original-seam-pair-and-full-moment-os-statements"
      ],
      "findingIds": [
        "finding:original-winding-theorem-does-not-select-seam-ray",
        "finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel",
        "finding:original-os-step-needs-full-moments-not-connected-cumulants",
        "finding:graded-field-image-precedes-physical-observable-restriction"
      ],
      "explanationEN": "Complete operator proof, exact countercontrols and OS moment repair are available. The decisive new step is deriving their hypotheses from the actual original pair/functional.",
      "changesRequiredEN": "Do not choose a matching source and present it as an original derivation; identify actual original operators, time, monodromy, locality and full functional.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-recovered-original-circle-and-controlled-heat-ir",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse recovered original circle and controlled heat limit",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:given-quarter-circle-full-heat-transfer-comparison"
      ],
      "findingIds": [
        "finding:older-original-circle-representative-already-realizes-ward-and-index",
        "finding:old-quarter-heat-transfer-has-controlled-rank-one-limit-and-odd-product",
        "finding:historical-em-rank-one-and-full-heat-traces-have-different-contracts",
        "finding:older-frg-functional-already-supplies-formal-full-moment-parent",
        "finding:earliest-c3-route-quantizes-level-but-needs-physical-kinetic-normalization"
      ],
      "explanationEN": "Concrete older one-particle data, full-moment generator and mathematical IR limit are available. The remaining task is their actual common admissible source identification.",
      "changesRequiredEN": "Do not treat older representatives as missing, heat as physical time, full finite transfer as rank one, or source notation as an obstruction.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-direct-old-seam-defect-and-relative-weight",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse direct old seam defect and relative weight contract",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:full-graded-car-with-original-positive-time",
        "premise:historical-sf-sector-action-and-relative-normalization",
        "premise:original-admissibility-and-graded-source-interfaces"
      ],
      "findingIds": [
        "finding:old-seam-shift-canonically-gives-relative-car-line-and-fredholm-factor",
        "finding:old-index-coupling-removes-heat-map-and-has-sharp-residual-ward-test",
        "finding:original-admissibility-requires-image-membership-not-positive-half-or-commutation",
        "finding:old-closure-already-assumes-car-but-does-not-map-the-geometric-circle"
      ],
      "explanationEN": "Direct defect fixes the line without heat limit and old index coupling fixes the weight under its relative contract. A freely chosen mode or heat-parameter fit would bypass the existing connection.",
      "changesRequiredEN": "Prove actual local source and response map plus residual-ratio condition; do not demand a second CAR state choice after time identification.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-historical-uv-profile-map-exclusion",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse historical UV-profile map exclusion",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:literal-positive-rg-map-on-finite-halfline-measures"
      ],
      "findingIds": [
        "finding:historical-uv-map-infinite-mass-exclusion-already-proved-and-recovered"
      ],
      "explanationEN": "The first map already leaves the declared finite-measure cone. Exclusion is proved in the older original audit and confirmed on the registered paper.",
      "changesRequiredEN": "Provide an actual original integrable kernel or justified finite reference with actual moment preservation; only then examine the fixed point.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-original-pin-and-actual-four-sector-defect",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse original Pin lift and actual four-sector defect",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-a4-same-moebius-order-four-pin-lift",
        "premise:fixed-marked-glue-and-retained-source-d8-frame",
        "premise:standard-four-d8-module-parent-with-retained-subtheories",
        "premise:full-graded-car-with-original-positive-time",
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "findingIds": [
        "finding:a4-spin-lift-fixes-local-ns-and-unordered-quarter-pair",
        "finding:cover-winding-exchanges-quarter-sectors-before-its-square",
        "finding:retained-winding-preserves-local-support-and-neutral-time",
        "finding:marked-glue-square-is-the-e8-fermionization-character",
        "finding:fixed-canonical-d8-is-not-transported-source-d8",
        "finding:actual-winding-has-four-module-e8-defect-extension",
        "finding:ramond-lift-sign-is-common-intertwiner-basis-gauge"
      ],
      "explanationEN": "Geometric spin consequence and mathematical affine bridge are explicit; basis gauge and alternate D8 markings must not create extra artificial origin problems.",
      "changesRequiredEN": "Prove original physical source/OS/response map rather than repeat group or spectrum comparisons.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-fixed-canonical-and-source-d8-by-identity",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify fixed compiler and source D8 by identity",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:fixed-marked-glue-and-retained-source-d8-frame"
      ],
      "findingIds": [
        "finding:fixed-canonical-d8-is-not-transported-source-d8"
      ],
      "explanationEN": "Exact root sets and actual time phases contradict fixed identity.",
      "changesRequiredEN": "Use actual D8_F or provide originally justified changed relative marking. Not a TFPT exclusion or necessity of identity.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:extend-original-seam-relative-determinant-through-faithful-kms-and-actual-carrier-compression",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use faithful KMS continuation and full carrier Schur transport",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:same-original-circle-trace-class-covariance",
        "premise:existing-finite-orthogonal-carrier-on-same-source"
      ],
      "findingIds": [
        "finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class",
        "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor",
        "finding:schur-carrier-plus-complement-preserves-original-relative-determinant"
      ],
      "explanationEN": "Exact factor persists in the same polarization class and across carrier plus complement.",
      "changesRequiredEN": "For physical application derive the actual original source and local maps.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:replace-full-thermal-winding-response-by-naive-finite-compression",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Replace full thermal winding response by naive finite compression",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:same-original-circle-trace-class-covariance",
        "premise:existing-finite-orthogonal-carrier-on-same-source"
      ],
      "findingIds": [
        "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor"
      ],
      "explanationEN": "Positive defect trace remains outside every finite circle subspace; derivative at0 contradicts1-z.",
      "changesRequiredEN": "Retain Schur term and QQ response or justify an originally different infinite-rank factor map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-seam-source-by-inverting-given-v258-dirac",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive seam source by inverting supplied v258 Dirac",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:original-admissibility-and-graded-source-interfaces",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:v258-forward-source-gap-is-reused-not-solved-by-inversion"
      ],
      "explanationEN": "Inverse functional calculus constructs neither P_F nor C_Sigma; the September audit remains applicable.",
      "changesRequiredEN": "Supply actual kernel and carrier map computed forward from original seam data.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:replace-rank-one-ray-selection-by-trace-class-pair-index-relative-determinant",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Determine relative factor by pair index and actual matrix clutch",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:trace-class-polarization-pair-with-restricted-unitary",
        "premise:smooth-matrix-clutch-on-original-negative-fourier-sea",
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "findingIds": [
        "finding:trace-class-pair-index-fixes-relative-factor-without-primitive-ray",
        "finding:matrix-clutch-degree-connects-weak-determinant-class-without-ray-selector"
      ],
      "explanationEN": "Trace class and determinant winding determine scalar response. No primitive ray needed; original physical source map is not thereby replaced.",
      "changesRequiredEN": "Recompute only after changing pair/source/trace-class premises. For EM supply actual original Ward variation.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:obtain-infinite-winding-factor-as-ordinary-finite-ns-determinant-limit",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Obtain infinite winding factor as ordinary finite NS determinant limit",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:actual-finite-ns-kernel-and-sampled-original-winding",
        "premise:historical-original-circle-and-transfer-source-passages"
      ],
      "findingIds": [
        "finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index"
      ],
      "explanationEN": "Cyclic UV partner keeps ordinary finite indexzero. Strong convergence does not control Fredholm determinants.",
      "changesRequiredEN": "Prove an original relative or UV normalization. Do not assert a numerical limit by deleting one partner.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:normal-dirac-index-pushforward-to-original-circle-source",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Transport normal spin index to the complete original circle source",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:given-normal-spin-line-and-genuine-circle-product",
        "premise:given-exact-reducing-indexline-with-horizontal-connection",
        "premise:historical-original-circle-and-transfer-source-passages",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:normal-spin-determinant-line-exactly-transports-whole-circle-in-given-product",
        "finding:normal-index-line-source-match-is-holonomy-condition-not-vertical-degree",
        "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel",
        "finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection"
      ],
      "explanationEN": "Sufficient exact transport on reducing product image is proved,without literally identifying normal equator and tangential circle. Original identification and horizontal connection remain to derive. More generally a closed normal Fredholm operator with its true adjoint suffices;original doublet multiplicity does not replace complex kernel rank.",
      "changesRequiredEN": "Supply actual original kernel family with connection and closed domains. A moving fiber requires the proved offdiagonal term;vertical degree or face phase does not select diagonal holonomy.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:extend-one-dimensional-ordinary-fredholm-factor-to-full-normal-product",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Extend ordinary one-dimensional Fredholm factor to full normal product",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:given-normal-spin-line-and-genuine-circle-product"
      ],
      "findingIds": [
        "finding:full-normal-product-polarization-change-is-not-trace-class"
      ],
      "explanationEN": "Full projection change fails L1 already at one circle index;thermal tails do not repair it. Circle theorem remains valid on reducing image.",
      "changesRequiredEN": "Supply an originally justified relative regularization and whole response including complement;index transport alone is insufficient.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:use-bosonic-callias-doublet-count-as-rank-one-source-index",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use bosonic doublet multiplicity as a single complex circle index",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:closed-normal-fredholm-with-retained-complex-kernel-representation",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel"
      ],
      "explanationEN": "For a retained complex SU2 doublet and scalaru I_M,r=2,index2 and factor(1-z)^2. Species countone does not change this ordinary trace.",
      "changesRequiredEN": "Prove actual source representation and trace,or an original different clutch or exterior-power map;do not delete a component without group and field map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-tetrahedral-bloch-quartet-with-original-quarter-by-mobius",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Directly identify tetrahedral Bloch quartet with original quarter marks by Mobius",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:oriented-d3-tetrahedron-in-bloch-chart-versus-original-quarter-marks"
      ],
      "findingIds": [
        "finding:tetrahedral-quarter-face-phase-does-not-identify-original-quarter-marked-curve"
      ],
      "explanationEN": "Disjoint complete cross-ratio orbits exclude this identification;equal normalized three-point phase is insufficient.",
      "changesRequiredEN": "Supply another explicit correspondence,family or semilinearity with actual mark and operator transport.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-existing-elliptic-cover-correspondence-with-full-c4-data",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse existing elliptic cover correspondence retaining full C4 data",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images",
        "premise:oriented-d3-tetrahedron-in-bloch-chart-versus-original-quarter-marks"
      ],
      "findingIds": [
        "finding:existing-elliptic-cover-correspondence-has-exact-c6-image-and-retained-mixed-clock"
      ],
      "explanationEN": "Concrete maps connect j0 and j1728 through the same existing curve;paired images are exactly C6 and retain mixed clock12.",
      "changesRequiredEN": "For complete source additionally transport C4 sign,peripheral data,spin and actual fields/connection;do not substitute clock order for cover information.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-global-joint-lift-with-native-clock-in-split-connection-centralizer",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Connect whole native clock in centralizer of existing split connection",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:natural-joint-spin-family-lift-with-given-split-connection",
        "premise:fixed-kappa-toral-third-centralizing-split-carrier",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "findingIds": [
        "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
        "finding:global-split-joint-carrier-admits-parallel-native-c12-clock"
      ],
      "explanationEN": "Global lift already existed;intersection with whole native clock class and connection centralizer is constructively nonempty and torally completely12of243.",
      "changesRequiredEN": "For actual original source jointly transport connection,marks,potential,domain and any extra family connection;do not rebuild mathematical existence.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-pure-weak-primitive-clutch-angle-with-native-full-compiler",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Directly use pure weak clutch angle as whole native clock",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:natural-joint-spin-family-lift-with-given-split-connection",
        "premise:same-angle-evaluation-of-primitive-determinant-clutch-as-native-clock",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks"
      ],
      "findingIds": [
        "finding:pure-weak-clutch-clock-identification-fails-despite-quarter-matches"
      ],
      "explanationEN": "Fixed dimension at least32 versus22 excludes the pure loop for every m;quarter or square comparison is insufficient.",
      "changesRequiredEN": "Prove a different original angle/connection map or use the already compatible separate clock automorphism. Do not extend exclusion to all representatives of the same topology.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-native-cartan-subspace-as-whole-source-little-weyl-dictionary",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use Cartan subspace as common source dictionary",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:native-cartan-four-in-full-clock-conjugate-source"
      ],
      "findingIds": [
        "finding:native-gaussian-four-is-cartan-subspace-in-whole-sixtyfour"
      ],
      "explanationEN": "Existing full conjugacy and torus isogeny prove actual G31 action.",
      "changesRequiredEN": "Derive global source connection retaining class2 and curvature.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-native-gaussian-four-directly-with-family-factor",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use Gaussian four directly as family factor",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:native-cartan-four-in-full-clock-conjugate-source"
      ],
      "findingIds": [
        "finding:native-family-factor-is-not-gaussian-four-despite-symmetric-coincidences"
      ],
      "explanationEN": "Third character(2,1,1) versus(0,2,2);Sym2 andSym3 hide the difference.",
      "changesRequiredEN": "Use correct Cartan subspace inside whole64.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:global-smooth-cartan-selection-on-primitive-normal-sphere",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Choose smooth whole Cartan field on primitive normal sphere",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:native-cartan-four-in-full-clock-conjugate-source",
        "premise:primitive-normal-sphere-joint-k-bundle-class-two"
      ],
      "findingIds": [
        "finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice"
      ],
      "explanationEN": "Finite normalizer reduction contradicts class2 in Z4.",
      "changesRequiredEN": "Only for stronger whole Cartan-mark question derive original punctures,defects or proved same-base even cover pullback. This addition is not mandatory for internally invariant source operators;reuse explicit W8.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-bare-native-octic-with-full-e8-invariant-operator",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify bare octic with whole E8 invariant operator",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:bare-native-octic-is-not-whole-e8-zero-mode-singlet"
      ],
      "explanationEN": "Actual root zero-mode alpha(-7) component is nonzero.",
      "changesRequiredEN": "Retain existing current and derivative terms of explicit W8 completion;bare F8 responses remain valid.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-screened-primary-octic-in-same-original-car-source",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use screened primary octic completion in the same original source",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:global-cartan-choice-is-optional-for-original-scalar-source-fields",
        "finding:explicit-primary-e8-invariant-octic-completes-same-neutral-car-source",
        "finding:completed-octic-has-exact-old-root-ope-component-and-quarter-source-value"
      ],
      "explanationEN": "Explicit unique solution in17 dimensional ansatz with full norm and original-source connection exists.",
      "changesRequiredEN": "For physical fundamental solution prove actual local P1 map and common reflection/collar/reference transport;no further freely chosen source branch.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:replace-original-quarter-w8-source-by-unshifted-e8-vacuum",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Replace original W8 quarter source by unshifted E8 vacuum",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:unshifted-vacuum-fails-same-w8-source-state-time-dictionary"
      ],
      "explanationEN": "The first W8 spectral norm is positive versus0 at the same N; the complete functions differ.",
      "changesRequiredEN": "Retain the actual original shifted state or explicitly prove a different contract derived from P1.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:use-local-cyclic-current-image-for-original-p1-w8",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use a local cyclic current image for original P1 W8",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:exact-separated-w8-twopoint-in-original-quarter-current-source",
        "finding:local-current-phase-and-conditional-cyclic-p1-w8-image",
        "finding:all-neutral-w8-correlations-identify-the-two-original-quarter-charges",
        "finding:original-w8-response-has-infinite-same-time-spectral-support"
      ],
      "explanationEN": "A sufficient conditional route and complete source function exist. The actual generating P1 current embedding is not constructed in the reviewed original passages.",
      "changesRequiredEN": "Actually construct the original local kernel and Weyl operators with state,time,reflection and support; only then identify P1 W8 and target response.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:use-only-folded-c8-stress-cycle-for-complete-w8-response",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use only folded c8 stress modes for the entire W8 response",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:folded-c8-cycle-misses-intrinsic-w8-tangent-without-obstructing-original-stress"
      ],
      "explanationEN": "The first response has an exactly nonzero tangential component outside the one-dimensional folded level1.",
      "changesRequiredEN": "Use the already existing full original c1 stress modes and all neutral intermediate states. The response then belongs to the existing source cycle;no extra generator is thereby needed.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-full-original-c1-stress-cycle-for-neutral-w8-states",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use the full original c1 stress cycle for neutral W8 states",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:older-seam-equivalence-verifications-do-not-supply-marked-local-p1-map",
        "finding:full-original-c1-stress-cycle-reconstructs-neutral-w8-response",
        "finding:folded-c8-cycle-misses-intrinsic-w8-tangent-without-obstructing-original-stress"
      ],
      "explanationEN": "All grade components of the neutral W8 response are in the original stress span;the first has an exact22-word CAR construction. Prior microscopic and net-extension results retain their scope.",
      "changesRequiredEN": "For actual physical P1 identification still connect local fields,support,reflection and original collar/reference domains. Cyclicity or character equality is not a local operator map.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-actual-cover-winding-for-local-quarter-current",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse actual old cover winding for the local quarter current",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:existing-cut-cover-car-with-actual-winding-and-sea",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:old-cover-winding-reconstructs-local-quarter-current-net",
        "finding:untransported-independent-quarter-stress-pair-is-not-current"
      ],
      "explanationEN": "The old winding arrow supplies the common CAR comparison within the existing cover source and generates exactly the local current net with both stress families.",
      "changesRequiredEN": "For complete physical P1 identification still connect source net,support,Theta,time,collar and reference from the originals;do not insert a newly fitted comparison matrix.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:subtract-independent-quarter-stress-factors-without-winding",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Subtract independent quarter stress factors without winding",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:existing-cut-cover-car-with-actual-winding-and-sea",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:untransported-independent-quarter-stress-pair-is-not-current"
      ],
      "explanationEN": "Independent factors retain the cubic Virasoro commutator term and do not yield a Heisenberg current algebra.",
      "changesRequiredEN": "Use the existing actual winding transport;then the positive local current theorem applies.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:use-winding-charge-conjugation-as-reflection-of-full-flat-dirac-sea",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use winding times C as reflection of the full flat D sea",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:winding-charge-conjugation-descends-fixed-pin-domain-but-not-full-dirac-sea"
      ],
      "explanationEN": "A fixed-domain involution is proved,but the explicit pi sigma1 term and divergent full PH polarization mismatch prevent the requested same-state/time identification in this class.",
      "changesRequiredEN": "Check the actual original P1 reflection and polarization type;do not present an additional flat connection or new sea as a derivation.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:use-fixed-pin-green-covariance-as-original-positive-p1-kernel",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use single fixed Pin Green covariance as positive P1 kernel",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity"
      ],
      "explanationEN": "Neutral zero-branch word has complex OS norm. Repairing a single charged block by phase is insufficient.",
      "changesRequiredEN": "Use the existing whole NS cover or another originally derived positive kernel;then check its actual P1 identification.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:retain-full-original-ns-cover-for-free-dirac-green-positivity",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Retain full original NS cover for free Dirac Green positivity",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea",
        "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity",
        "finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp",
        "finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum"
      ],
      "explanationEN": "Both charges and all transverse modes are proved with correct source-order sign. Deck exchange explains the failing isolated sector.",
      "changesRequiredEN": "Supply P1 map and actual W8 state/time transport;do not introduce a new free kernel or fitted beta.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-concrete-elliptic-moebius-quarter-source-bridge",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse concrete elliptic Moebius and quarter source bridge",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower",
        "finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent",
        "finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms"
      ],
      "explanationEN": "Reuse previous proof in its named h,Q,kappa subgroup stratum. Full original D4 Real group has an additional equatorial pair. Actual seam pullback is ramified;boundary-tuple identity does not supply an unchecked physical seam morphism.",
      "changesRequiredEN": "Supply original P1 source morphism;do not search again for arbitrary free kernels or quarter phases.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:replace-quarter-hardy-source-by-finite-normal-crosscap-preparation",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Replace quarter Hardy source by finite normal crosscap preparation",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:finite-crosscap-cauchy-state-is-not-original-quarter-vacuum-by-normal-filtering"
      ],
      "explanationEN": "Finite crosscap state is nonstationary under signed B;its filtering limit loses the loop quarter mark.",
      "changesRequiredEN": "Prove actual channel and state/time transport from original source,instead of renaming tree filtered vacuum.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reconstruct-neutral-native-transfers-in-connected-original-current-net",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reconstruct neutral native transfers in connected original current net",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures",
        "premise:full-existing-local-e8-field-hull-observer-code"
      ],
      "findingIds": [
        "finding:original-neutral-interarc-fields-have-exact-connected-current-vertex-reconstruction"
      ],
      "explanationEN": "Exact original bosonization with quarter factor and separate connected-net theorem supplies existing neutral composites. Their existence requires no newly chosen elementary coupling.",
      "changesRequiredEN": "For physical derivation supply actual original P1 current image with state,time,Theta,regional admissibility and invariant admissible subspaces. Do not relabel larger connected net or dual commutant as additive eight-arc net.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-original-half-cover-cauchy-projection-and-source-response",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Test actual Cauchy/zero-branch source and geometric return",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:typed-source-structures",
        "premise:given-pin-source-conformal-normal-geometry-probes",
        "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover"
      ],
      "findingIds": [
        "finding:actual-pin-zero-branch-retains-quarter-car-state-time-but-no-uniform-scale-return",
        "finding:conformal-pin-source-geometry-fixes-exterior-return-and-unitary-memory",
        "finding:geometric-exterior-schur-response-transfers-proper-native-arc-charge-but-is-compact",
        "finding:actual-ns-half-cover-cauchy-graph-purifies-green-state-with-neutral-ground-time-obstruction"
      ],
      "explanationEN": "Source-derived geometric return and canonical state construction are closed in stated scopes;physical P1 profile/history remains open.",
      "changesRequiredEN": "Supply actual original action/reference/intervention map and full native field interface.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-full-marked-equator-pullback-with-single-smooth-quarter-circle",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify full marked equator pullback with single smooth quarter circle",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:full-marked-equatorial-pullback-is-ramified-graph-not-smooth-seam-circle"
      ],
      "explanationEN": "Four-valent ramification crossings and b1=5 obstruct literal marked circle/collar homeomorphism.",
      "changesRequiredEN": "Derive original pushforward,field trace or smooth carrier readout with actual domain.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-same-elliptic-free-gaussian-rp-and-labelled-calderon-state",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse positive free Gaussian source and labelled Calderon state on same ellipse",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:same-elliptic-szego-green-functional-has-all-word-free-rp-and-calderon-marginal"
      ],
      "explanationEN": "All-mode charged factorization and Wick word proof belong to actual NS NS E;state marginal agrees with same collar.",
      "changesRequiredEN": "Supply primitive P1 source measure and local field/time-slice map,rather than searching again for free positivity.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-original-p2-connection-from-natural-c2-scalar-spin-pushforward",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Replace original P2 connection by natural C2 scalar spin pushforward",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:elliptic-scalar-spin-pushforward-has-original-holomorphic-p2-anchor",
        "finding:natural-elliptic-anchor-connection-is-not-original-p2-cusp-connection"
      ],
      "explanationEN": "Holomorphic anchor agrees,but actual local eigenvalues,traces and orders differ;scalar twist retains wrong multiplicity.",
      "changesRequiredEN": "Derive original irreducible order-three connection on common bundle from seam data;do not hide a change of existing P2 target.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-full-current-functional-of-existing-elliptic-gaussian-source",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse full current functional of existing elliptic Gaussian source",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:actual-elliptic-gaussian-source-determines-full-quarter-current-functional",
        "finding:elliptic-current-state-differs-from-hardy-on-every-proper-current-interval"
      ],
      "explanationEN": "The free kernel supplies current operators,state,all Weyl words and neutral native field correlations. The local neutral state witness prevents silently replacing Hardy.",
      "changesRequiredEN": "Derive original P1 source measure and local insertion map. Free candidate fixes four-point functions by Wick;primitive interactions must be checked against it. Do not identify source interventions with spectral-action variations.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-coupled-primitive-geometric-response",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive coupled original geometry response",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:primitive-reflection-split-and-controlled-geometric-variation",
        "premise:finite-positive-heat-channel-endpoint-selection-test",
        "premise:typed-source-structures",
        "premise:original-admissibility-and-graded-source-interfaces",
        "premise:historical-sf-sector-action-and-relative-normalization"
      ],
      "findingIds": [
        "finding:primitive-geometric-force-retains-coupled-reference-and-parity-variation",
        "finding:equal-finite-positive-heat-channel-values-do-not-fix-geometric-force"
      ],
      "explanationEN": "Coupled differential contract derived and endpoint self-consistency excluded as sufficient selection. This does not determine the full physical history.",
      "changesRequiredEN": "Identify actual original P1 geometry/field insertion with its first response;for the fixed seam transfer retain delta g->delta q and residual/reference terms instead of choosing new free spectral profiles.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-complete-elliptic-spin-quarter-kernel",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse complete elliptic quarter spin kernel",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:elliptic-ns-spin-trace-has-complete-global-quarter-kernel"
      ],
      "explanationEN": "Full normalized kernel and global quarter meridians are analytically proved.",
      "changesRequiredEN": "Supply real positive source trace and original closed domain,not a new holomorphic phase choice.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:automatic-ramified-flat-transport-selects-single-quarter-circle",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Obtain single quarter circle automatically from ramified flat transport",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:source-induced-ramified-resolutions-do-not-select-quarter-circle-domain"
      ],
      "explanationEN": "Actual resolutions and pole operator do not supply that circle domain.",
      "changesRequiredEN": "Prove original real trace selection and self-adjoint boundary domain.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-fixed-native-three-cycle-with-v117-at-fixed-compiler",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify fixed native three-cycle with v117 at fixed compiler",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:fixed-three-slot-permutation-and-original-compiler-comparison",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:fixed-native-and-fermat-c3-carriers-do-not-identify-marked-v117-pair"
      ],
      "explanationEN": "Both simultaneous intertwiner spaces of the tested fixed ansatz are zero.",
      "changesRequiredEN": "Supply complete marked tuple transported from originals.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-v117-from-theta-family-with-unchanged-geometric-q",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive v117 from theta family with unchanged geometric Q",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:theta-square-modular-transport-with-distinct-geometric-clock",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:theta-square-modular-pair-reconstructs-v117-with-distinct-geometric-q",
        "finding:geometric-square-clock-is-not-theta-v117-quarter-generator"
      ],
      "explanationEN": "Joint pair dictionary exists but sendsT toU;Q=S has different eigenvalue ratios.",
      "changesRequiredEN": "Derive original level4 family/sewing map with distinct spatial/moduli paths and phase section.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-conformal-boundary-trace-before-geometric-fourpoint-mixture",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive conformal boundary trace before geometric four-point mixing",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures",
        "premise:same-marked-elliptic-annulus-massless-conformal-metric-family"
      ],
      "findingIds": [
        "finding:canonical-conformal-boundary-trace-fixes-existing-elliptic-cauchy-state",
        "finding:conformal-factor-averaging-preserves-given-free-boundary-wick-words"
      ],
      "explanationEN": "The positive boundary transport follows from the Dirac law and boundary density without a free trace fit. It preserves the complete Cauchy projection and existing free boundary source. Conformal factors alone produce no non-Wick correction under this identification.",
      "changesRequiredEN": "For the primitive P1 four-field comparison identify an original variation changing the transported covariance or an original higher fermion vertex. Preserve the unresolved full marked graph real trace/domain and the free conditional quantization premise; do not replace them by arbitrary couplings.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-retarded-geometric-response-of-retained-seam-defect",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive causal geometric response of the retained seam defect",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:retained-zero-branch-defect-on-common-pin-geometric-history",
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:given-pin-source-conformal-normal-geometry-probes",
        "premise:typed-source-structures",
        "premise:historical-sf-sector-action-and-relative-normalization"
      ],
      "findingIds": [
        "finding:retained-seam-defect-has-derived-causal-geometric-response-with-contact",
        "finding:same-final-pin-geometry-retains-history-while-relative-index-factor-is-fixed"
      ],
      "explanationEN": "Relative source response with contact/memory and protection of the scalar factor are calculated. An originally selected geometry history does not yet follow.",
      "changesRequiredEN": "Compare actual admissible P1 geometry/field insertion and original residual sector variationR with measure,reference,state,time and domains to the explicit response kernel. Do not replace the complete native field action by q_min alone or this single bilinear response.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-positive-full-projector-source-before-independent-fourpoint-fit",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive the positive full projection source before an additional four-point fit",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:positive-joint-car-source-tested-against-full-geometric-projector",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:full-projector-covariance-and-positivity-force-all-car-words",
        "finding:actual-two-face-projector-reduces-free-source-test-to-cross-coherence"
      ],
      "explanationEN": "Full positive CAR projection covariance forces every word without an extra Gaussian assumption. The existing joint Cauchy graph supplies the precise target including X_A;the single mixed face marginal does not.",
      "changesRequiredEN": "Derive the actual original joint CAR insertion map and covariance including cross kernel from the real marked carrier. Do not infer it from a chosen purification. If the actual kernel differs from the projection target,retain it and its higher vertices.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:generate-fermion-fourfield-by-retained-quarter-geometric-averaging",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Generate a four-field term by geometry averaging in the retained quarter compiler",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:same-marked-elliptic-annulus-massless-conformal-metric-family",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:retained-marked-quarter-compiler-has-no-local-geometric-wick-correction"
      ],
      "explanationEN": "Marked Q rigidity removes the complex modulus;canonical conformal trace removes the remaining free boundary-state variation.",
      "changesRequiredEN": "Supply an actual additional original field insertion,connection variation,higher vertex or derived change of marked admission;do not optimize further conformal profiles.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-real-elliptic-modulus-boundary-and-fourfield-response",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive boundary and four-field response of the explicitly changed elliptic modulus family",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:real-marked-elliptic-complex-structure-family-with-transported-spin",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:changed-elliptic-modulus-has-derived-cauchy-response-and-neutral-fourfield-variance"
      ],
      "explanationEN": "Concrete modulus-to-state map and exact variance identity are determined. The fixed original compiler excludes the changed parameter;primitive law and source map are not replaced.",
      "changesRequiredEN": "First derive original measure support and actual marked source/sewing transport. Do not insert a chosen rho variance as the solution.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-recovered-original-c4-triangle-monodromy-proof",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse recovered original C4 triangle proof",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:recovered-september-c4-triangle-closes-original-a0star-monodromy",
        "finding:wall-weight-additivity-does-not-exclude-stable-v117-parabolic-bundle"
      ],
      "explanationEN": "Original A0* equation is already analytically solved; older synthesis and current independent replay close group identification.",
      "changesRequiredEN": "Check full field/state/time source map reusing closed signed C4 line action. No new ODE fit.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:use-oblique-quarter-cauchy-idempotent-as-positive-car-state",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use oblique quarter Cauchy idempotent as positive CAR state",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:full-original-four-mark-inversion-and-equatorial-real-slots",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:actual-elliptic-half-form-l2-trace-on-full-marked-equator",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:actual-holomorphic-quarter-cauchy-idempotents-are-not-positive-car-covariances"
      ],
      "explanationEN": "Exact range-kernel overlap excludes self-adjointness in actual measure.",
      "changesRequiredEN": "Retain orthogonal analytic range and actual state map; do not choose fitted channel metric.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-actual-a0star-c4-connection-with-genuine-d4-base-inversion",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify actual A0* connection with genuine D4 base inversion",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:genuine-d4-unitary-stable-parabolic-orbifold-descent",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:actual-a0star-connection-does-not-have-rational-base-inversion-lift"
      ],
      "explanationEN": "Rational lift is zero; actual isotropy orders4 and2 distinguish orbit points.",
      "changesRequiredEN": "Use actual C4 triangle identification or explicitly derive another original connection with marking.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-actual-negative-triangle-sign-line-cover",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse actual negative triangle sign lift",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-p2-order-three-cusp-and-stable-anchor-target",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:actual-v117-sign-lines-are-negative-weierstrass-triangle-two-torsion",
        "finding:negative-sign-packet-has-source-selected-quarter-clock-lift"
      ],
      "explanationEN": "Kummer function field,actual4,3,2 passport and fiber product identify lines with given v117 connection.",
      "changesRequiredEN": "Supply actual joint field/state/time source map; flat coefficient comparison is closed.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:complete-sign-fields-by-bare-common-cyclic-twelve-root-cover",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Complete sign fields by bare common cyclic twelve root cover",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:ramified-holomorphic-half-form-trace-of-existing-c2-spin",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:common-cyclic-twelve-cover-does-not-trivialize-v117-unramified-sign-lines"
      ],
      "explanationEN": "Unique quadratic intermediate is ramified;actual sign lines are nontrivial unramified.",
      "changesRequiredEN": "Reuse minimal degree48 root/sign compositum and transport full primitive field/state data.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:construct-given-elliptic-flat-quillen-family-before-physical-insertion-comparison",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Construct given elliptic Quillen family before physical insertion comparison",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:given-square-nsns-elliptic-unit-charge-flat-connection-family",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:given-elliptic-flat-connection-family-has-explicit-quillen-norm-and-two-holonomies"
      ],
      "explanationEN": "Norm,operator,domain,null divisor,connection,both holonomies and local response are concrete. Common original P1 source map and actual Berry comparison remain open.",
      "changesRequiredEN": "Derive actual common P1 insertion/field transport with source reference against these concrete quantities;equal Chern integer is not a metric/connection proof.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-bare-flat-large-gauge-quotient-with-minimal-em-counting-transfer",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify bare flat gauge ratio with minimal EM counting transfer",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:given-square-nsns-elliptic-unit-charge-flat-connection-family",
        "premise:same-original-circle-trace-class-covariance",
        "premise:historical-sf-sector-action-and-relative-normalization",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:bare-large-gauge-quillen-norm-does-not-equal-original-winding-counting-factor"
      ],
      "explanationEN": "Actual ratios are1 and1-q;the zero-twist derivative additionally excludes the expressly described ansatz.",
      "changesRequiredEN": "Supply original operator/field insertion map instead of renaming parameters. Do not fitz(alpha),response exponent or reference to the target value.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-actual-half-period-graded-gns-and-source-saturation",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive actual half period and graded GNS connection with source saturation",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:normal-even-sea-car-source-and-canonical-graded-hs-double",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:existing-elliptic-half-period-has-canonical-graded-gns-intertwiner",
        "finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law"
      ],
      "explanationEN": "The existing free Green kernel already containsX;canonical parity-GNS partner realizes all modes. General standard doubling instead gives source-dependent affinityM. Its maximal saturation characterizes linear modular half action in the stated classes.",
      "changesRequiredEN": "Derive half-modular action on odd fields and the marked real sewing/carrier map from the actual original source. Do not merely rename geometric reflection as TomitaJ. For nonlinear action determine actual operator vertices;for established linear action the free source follows in the stated class.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-source-selected-spin-and-correct-pauli-translation-target",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse source-selected spin and correct Pauli target",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:source-cubic-and-quarter-select-even-theta-and-spin-half-turn-lift",
        "finding:source-cubic-matches-native-pauli-translations-after-context-target-correction",
        "finding:joint-source-clock-relations-have-one-native-clifford-gauge-class",
        "finding:marked-negative-point-norm-restores-required-spin-central-character",
        "finding:source-spin-relative-poincare-normalization-closes-point-norm-family",
        "finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package"
      ],
      "explanationEN": "c,Q determine S0,beta. Spin-relative norm family and full complex N64/clock intertwiner for Wq are proved. Original source must still select one inverse point norm.",
      "changesRequiredEN": "Reuse proved S0-relative point-norm family. Source must select one inverse point norm in actual boundary operator. Do not repeat free spin selection,code/context search,or finite matrix census.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-native-central-quarter-from-ordinary-theta-determinant",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive native central quarter from ordinary theta determinant",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:ordinary-rigidified-genus-two-theta-determinant-functor",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:ordinary-theta-determinant-erases-selected-spin-central-character"
      ],
      "explanationEN": "chi=0 erases spin character before projectivization;alpha_D⁴=+I contradicts required alpha_native⁴=−I.",
      "changesRequiredEN": "Requires explicitly phase-preserving refinement or an additional line justified by existing markings. Repeating same matrix census or dimension matching does not change functor.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:promote-fixed-point-spin-phase-via-direct-theta-evaluation-family",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Transfer point phase by direct theta evaluation family",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:ordinary-rigidified-genus-two-theta-determinant-functor",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:point-normalized-theta-family-correction-fails-original-cubic-action"
      ],
      "explanationEN": "Only q0-normalized family has non-c-invariant flat factor P_delta;source-selected S0 normalization removes it. Prior squaring still loses quarter phase.",
      "changesRequiredEN": "Reuse proved S0-relative family. Then derive selection of exactly one inverse point norm from actual boundary functor.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-complete-tfpt-origin-investigation-state",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse complete stored E6/E7/E8 through W8 and theta investigation",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:tfpt-origin-investigation-full-source-coverage-and-current-frontier"
      ],
      "explanationEN": "197 existing findings are linked by topic. Historical reports and subsequent corrections are retained. Full complex module bridge is solved;first remaining origin question is one inverse point norm in actual boundary operator.",
      "changesRequiredEN": "Reuse full finding and current source contract before repeating a calculation. Name any changed premise. Do not infer physical derivation from persistence status.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-original-winding-relative-three-cable-hardy-norm",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse original three-cable unit-winding inverse norm",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class"
      ],
      "findingIds": [
        "finding:original-unit-winding-selects-one-inverse-norm-in-three-cabled-hardy-pair",
        "finding:full-clock-norm-power-class-and-canonical-eighth-period"
      ],
      "explanationEN": "Integer winding and relative jet determinant close power selection in named Hardy functor. Physical coefficient identification remains separate.",
      "changesRequiredEN": "For physical continuation identify actual operator pair and relative action; do not fit another power or freely chosen reference.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-same-spin-seam-reference-and-retain-fermionic-grading",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse same-spin seam reference and retain fermion grading",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:same-spin-hardy-shift-against-identity-with-grading-retained"
      ],
      "findingIds": [
        "finding:same-spin-unit-shift-gives-native-module-class-with-odd-determinant-line",
        "finding:original-even-odd-operator-split-is-compatible-with-same-spin-seam-reference"
      ],
      "explanationEN": "Unspun reference unnecessary for ungraded module class; actual source map must retain odd defect line.",
      "changesRequiredEN": "Derive actual Cauchy/Hardy intertwiner and graded action; no new norm power, O_C reference or matrix census.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-cubic-cauchy-range-and-oriented-car-dual-before-physical-source-map",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse cubic Cauchy range and oriented CAR dual before physical source map",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:standard-chiral-spin-trace-on-original-cubic-disk-pullback",
        "premise:same-spin-hardy-shift-against-identity-with-grading-retained",
        "premise:conditional-three-sheet-negative-sea-car-source"
      ],
      "findingIds": [
        "finding:cubic-spin-cauchy-range-is-three-hardy-with-strong-domain-distinction",
        "finding:original-negative-sea-three-mode-ket-is-dual-to-required-hardy-line"
      ],
      "explanationEN": "Analytic threefold Hardy space and duality of charged defect/Fredholm line are closed under explicit source conditions. They do not replace actual P1 operator and directed boundary amplitude map.",
      "changesRequiredEN": "Transport actual bulk Dirac/Cauchy datum, relevant closed domains and graded amplitude; tangential spectra, state correlations or elliptic Weyl scaling alone do not suffice.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:construct-theta-frame-e8-lattice-pair-with-retained-odd-spin-lift",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reconstruct completed theta frame as E8 lattice pair retaining spin and field action",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:fixed-native-pauli-translation-target-and-gaussian-phase-class",
        "premise:marked-theta-frame-with-explicit-primitive-gaussian-root-normalization",
        "premise:two-theta-lattice-voas-with-given-geometric-faithful-c12-lift"
      ],
      "findingIds": [
        "finding:primitive-gaussian-theta-frame-constructs-e8-pair-with-retained-spin-action",
        "finding:existing-c12-lift-induces-coherent-two-object-e8-vertex-groupoid"
      ],
      "explanationEN": "Normalized lattice and actual spin exchange are exactly connected. Given C12 and one isometry lift yield full two-object field transport; no additional full G31 splitting required.",
      "changesRequiredEN": "Physical origin requires original local P1 field map and selection of arithmetic normalization. A new common embedding or different frozen field marking is a different contract.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:generate-source-spinor-by-winding-functional-calculus",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Generate spinor field by actual winding functional calculus",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:standard-four-d8-module-parent-with-retained-subtheories"
      ],
      "findingIds": [
        "finding:actual-winding-functional-calculus-preserves-ns-ramond-split"
      ],
      "explanationEN": "P_R reduces W_ext and every spectral function. NS vacuum side is not left.",
      "changesRequiredEN": "An independently source-derived s-charge intertwiner with local field, state and time. Global E_s already exists; do not reconstruct W_ext again.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:select-local-e8-extension-by-chiral-vacuum-cycle-exchange",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Select local E8 extension by actually transported chiral vacuum line",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:connected-local-same-conformal-compiler-extension-unselected-support"
      ],
      "findingIds": [
        "finding:single-chiral-cycle-exchange-selects-e8-in-four-extension-class"
      ],
      "explanationEN": "Exact S Fourier connects the old holomorphy route to the four extensions. The condition selects both E8 markings.",
      "changesRequiredEN": "Physical origin requires charge-resolved P1 block functor and actual cycle exchange with background/time; fixed h marking for plus. Do not infer it from scalar determinant or CAR purity.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-full-local-marked-e8-with-unchanged-clustering-source-time",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify full marked local E8 completion with unchanged clustering source time",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:marked-local-e8-completion-with-original-source-time-and-euclidean-clustering",
        "premise:four-d8-sectors-with-fixed-affine-source-time",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:marked-local-e8-with-unchanged-source-time-fails-euclidean-clustering"
      ],
      "explanationEN": "Local zero-energy transition prevents C4 in Ls;Lc violates q/2 marking. Global sector penalty is not a continuous local time in the fixed net.",
      "changesRequiredEN": "Derive actual P1 OS transfer and admissible local field map. A source-derived different time or smaller observable algebra is a changed premise. Do not repeat identical spectra or Ward ground-state selection.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-affine-source-spectrum-and-local-operator-discriminator",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse affine spectral identity and concrete current discriminator",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:four-d8-sectors-with-fixed-affine-source-time",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:affine-source-involution-pairs-full-d8-sector-spectra"
      ],
      "explanationEN": "Exact complete H,Q equality is analytically explained. Individual Cartan charges refute the stronger fixed-D8 field dictionary.",
      "changesRequiredEN": "Proceed only with an actual compatible local operator and statistics map; no further thermal fit.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-original-parity-before-local-spinor-extension",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse original parity rule before local spinor extension",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:original-parity-audit-does-not-supply-local-spinor-gauging"
      ],
      "explanationEN": "Parity projection is established in the tested finite setting;Ramond gauging and local extension are different steps.",
      "changesRequiredEN": "Construct actual local G1 to G4 field or common spin amplitudes with relative phase from P1. Simultaneously satisfy time and observable test.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-full-recursion-and-signed-petersen-double-cover",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse full recursion and signed Petersen double transport",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:specified-petersen-shell-and-full-family-finite-recursions",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:hypergraph-local-update-repaired-with-full-family-clock",
        "finding:petersen-polar-step-has-exact-double-cover-family-intertwiner"
      ],
      "explanationEN": "Actual local function repaired,all three family modes and all even times explained. Moving frame carries K=Z Delta and nonzero charge transfer.",
      "changesRequiredEN": "Test original field operation with charge compensation and marked compression. No further spectral fitting or sixth power as physical identification.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:replace-hodge-amplitude-by-positive-petersen-via-phase-gauge",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reinterpret Hodge amplitude as positive Petersen action by phase gauge",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:specified-petersen-shell-and-full-family-finite-recursions",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:petersen-source-current-and-hodge-candidates-fail-physical-identification"
      ],
      "explanationEN": "Spectrum and negative pentagon flux prevent linear gauge identification. Single original bilocal also has wrong support.",
      "changesRequiredEN": "Born event rule is a different claim and must come from existing instrument;derive actual quartic,compensating charge,marking and time.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-calderon-and-perron-by-natural-face-compression",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify Calderon and Perron by natural face compression",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:natural-single-face-inclusion-in-given-family-calderon-graph",
        "premise:specified-petersen-shell-and-full-family-finite-recursions",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:calderon-single-face-compression-is-not-perron-projector"
      ],
      "explanationEN": "Compression has three eigenvalues strictly between0 and1,not rank1 Perron projector.",
      "changesRequiredEN": "New inclusion must come from original source and transport invariance,inner product,charge and field action. Freely chosen mixing or similar reflection formula does not suffice.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-e8-a4-hodge-and-record-resolved-petersen-response",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse direct E8 A4 Hodge channel and resolved phase record",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:given-full-e8-current-source-with-fixed-carrier-su5",
        "premise:specified-inclusive-current-response-with-invariant-metric",
        "premise:specified-old-j20-instrument-in-fixed-six-mark-duad-chart",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:five-complement-amplitudes-form-full-petersen-quantum-channel",
        "finding:original-twenty-events-factor-through-hodge-and-conditional-phase-record",
        "finding:actual-e8-mixed-current-response-is-full-clifford-channel",
        "finding:carrier-su5-centralizer-gives-direct-e8-petersen-response"
      ],
      "explanationEN": "Hodge field operator found in given E8 algebra;rates and actual old phase averaging established. No renewed Hamiltonian or edge-filter search needed.",
      "changesRequiredEN": "Next origin comparison is full P1 two-boundary/event kernel with coherent reference:test actual50-sector insertion,invariant weight,record/readout,state and time. Old20 share effects but have known different coherences;population or further spectral fit is insufficient.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-full-covariant-quantum-rigidity",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse full covariant quantum rigidity",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:specified-conjugate-su5-covariant-petersen-channel",
        "premise:fixed-three-plus-two-mark-and-typed-original-degree-clock"
      ],
      "findingIds": [
        "finding:su5-covariance-and-petersen-support-fix-complete-quantum-response",
        "finding:neutral-pair-witness-separates-old-events-and-hodge-response"
      ],
      "explanationEN": "Full response classified within SU5 covariant class;Petersen support selects one vertex.",
      "changesRequiredEN": "Derive full covariance at actual same P1 event object or direct epsilon sewing law;no further fitted model.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:exclude-central-clock-and-mark-transport-as-complete-phase-selector",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Exclude central clock and mark transport as complete phase selector",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-five-slot-exterior-source-with-retained-complement-index",
        "premise:specified-conjugate-su5-covariant-petersen-channel",
        "premise:fixed-three-plus-two-mark-and-typed-original-degree-clock"
      ],
      "findingIds": [
        "finding:original-degree-clock-is-not-carrier-slot-cycle-at-fixed-source",
        "finding:full-mark-transport-and-isospectrality-do-not-select-hodge-channel",
        "finding:original-pair-source-fixes-state-but-not-selected-epsilon-process"
      ],
      "explanationEN": "OriginalU5 scalar;natural non-Hodge families persist with same effects,real selfadjointness and response spectrum.",
      "changesRequiredEN": "New load-bearing premise must supply more than family covariance or central phases at same source object. Prove actual epsilon amplitude/record law from source. Do not infer complete classification from one phase combination.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-single-source-epsilon-process-saturation",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive single positive epsilon process identity from original source",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:specified-cptp-source-process-with-p5-saturation",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:single-positive-process-saturation-selects-full-hodge-channel"
      ],
      "explanationEN": "Mathematical selection theorem solved. Source closure needs no new fullSU5 symmetry premise if actual event amplitudes lie in epsilon fourform space.",
      "changesRequiredEN": "ProveTr((I-P5)J_source)=0 or equivalent amplitude/sewing identity at original local source/insertion path. MereP_A state expectation,marktransport,centralclock or equal spectra insufficient. TP/dualinputoutput/reference/register must be actual original data.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:recover-native-f20-spin5-carrier-before-event-selection",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Recover native F20 and Spin5 carrier before selecting events",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:two-actual-source-events-with-coherent-record-access",
        "premise:stipulated-e8-h8-with-original-color-center-selector",
        "premise:actual-single-source-event-coherent-stinespring-record"
      ],
      "findingIds": [
        "finding:native-pauli-f20-metric-and-quarter-bridge",
        "finding:marked-symplectic-functor-fixes-native-hodge-kraus-space",
        "finding:canonical-native-spin5-hodge-is-already-one-source-record-subchannel",
        "finding:irreducible-f20-four-cannot-host-original-independent-native-family-clock",
        "finding:native-hodge-is-exact-collective-five-current-action",
        "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
        "finding:six-hodge-responses-have-exact-full-current-barycenter",
        "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts",
        "finding:spin5-hodge-five-is-plucker-kernel-not-original-quartic-hessian",
        "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
        "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
        "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
        "finding:old-ward-root-generates-exact-charged-fifty-module",
        "finding:tp-charged-bracket-support-forces-entire-carrier-marginal"
      ],
      "explanationEN": "Marked native Spin5 bridge is closed; six ovoid fibers avoid extra common-fixed-form requirement. Neutral current theorem remains A3 and does not identify P2 charges. Continue physical origin at charged E8 line.",
      "changesRequiredEN": "ActualoldnoncentralF20 isconnectedbyactualPauliwordsandmetric. CanonicalSpin5transportwithcompactrealformandBellnormalization ischecked,Phi_nativealreadyin60record. Donotrepeat. Jointphysicalcarrier/familyclockcannotbeidentifiedinsameirreduciblefour;donotphysicallyequateoldrank8modulewithoutdictionary.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:coherent-two-event-record-search-exact-support-and-loewner",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Solve coherent two-step search exactly by span and CP order",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:two-actual-source-events-with-coherent-record-access",
        "premise:stipulated-e8-h8-with-original-color-center-selector",
        "premise:actual-single-source-event-coherent-stinespring-record"
      ],
      "findingIds": [
        "finding:two-actual-coherent-events-herald-hodge-at-one-over-twenty-five",
        "finding:canonical-native-spin5-hodge-is-already-one-source-record-subchannel",
        "finding:native-hodge-record-selector-is-image-projector-not-kraus-kernel",
        "finding:native-hodge-is-exact-collective-five-current-action",
        "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
        "finding:six-hodge-responses-have-exact-full-current-barycenter",
        "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts",
        "finding:spin5-hodge-five-is-plucker-kernel-not-original-quartic-hessian",
        "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
        "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
        "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
        "finding:old-ward-root-generates-exact-charged-fifty-module",
        "finding:tp-charged-bracket-support-forces-entire-carrier-marginal"
      ],
      "explanationEN": "Record search is closed for stated resources. Physical record execution is an additional condition only for that implementation. New current/OPE route needs no measured records. Do not genetically search effects already exactly determined.",
      "changesRequiredEN": "Completeexactrecordsearchisclosed. Earlycharttargets:one stepimpossible,two steps1/25. CorrectnativeSpin5channel:one step1/15,two steps4/75. Nogeneticfitneeded. RemainingoriginiscoherentrecordaccessandexecutionofthealreadydeterminedeffectE.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:test-original-color-selector-before-repeating-e8-ground-no-go",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Apply original color selector before repeating double-ground exclusion",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-native-pauli-and-v419-f20-source-words",
        "premise:two-actual-source-events-with-coherent-record-access",
        "premise:stipulated-e8-h8-with-original-color-center-selector",
        "premise:actual-single-source-event-coherent-stinespring-record"
      ],
      "findingIds": [
        "finding:original-color-center-removes-only-extra-h8-ground-state",
        "finding:full-admissibility-vacuum-test-needs-source-image-and-transfer-reduction"
      ],
      "explanationEN": "Center-neutral H8 ground state is already unique and gapped. Do not reuse full-field objection to exclude observables. Next original test isWΩ inPprim/PTheta andH8 reduction,not another root census.",
      "changesRequiredEN": "Center-neutral H8 ground state is already unique and gapped. Do not reuse full-field objection to exclude observables. Next original test isWΩ inPprim/PTheta andH8 reduction,not another root census.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:replace-fixed-clock-four-by-full-native-six-ovoid-bundle",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Full native six-fiber family instead of fixed clock form",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:native-pauli-clock-family-with-marked-f20-inclusion",
        "premise:local-e8-current-response-realization"
      ],
      "findingIds": [
        "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
        "finding:six-hodge-responses-have-exact-full-current-barycenter",
        "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts"
      ],
      "explanationEN": "Finite common clock family and current barycenter are exact. Next issue is original F20/field marking, not another larger auxiliary carrier.",
      "changesRequiredEN": "Finite common clock family and current barycenter are exact. Next issue is original F20/field marking, not another larger auxiliary carrier.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-source-selected-charged-e8-sewing-line",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive source-selected charged E8 sewing line",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:native-pauli-clock-family-with-marked-f20-inclusion",
        "premise:local-e8-current-response-realization"
      ],
      "findingIds": [
        "finding:native-hodge-is-exact-collective-five-current-action",
        "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
        "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
        "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
        "finding:old-ward-root-generates-exact-charged-fifty-module",
        "finding:tp-charged-bracket-support-forces-entire-carrier-marginal",
        "finding:original-ward-and-p2-grading-select-smaller-creation-thirty",
        "finding:charged-source-quarter-recovers-inverse-internal-glue",
        "finding:state-independent-creation-branch-removes-whole-process-hodge-demand",
        "finding:given-source-current-constructs-half-kink-spinor-transport",
        "finding:neutral-ward-response-needs-no-spinor-observable-membership",
        "finding:actual-source-sector-transport-distinguishes-identical-hodge-marginals"
      ],
      "explanationEN": "Smooth neutral spinor transport follows from original current on given quotient. Test P1 locality and marked joint observable response; neither individual-field observability nor larger extension is automatically necessary.",
      "changesRequiredEN": "CURRENT: local_source_origin_20261028/STAND-EINFACH-DE.txt. Algebraic rho_s on given evenCAR quotient and smooth closed half-kink line are closed: originalJ_tot,n=J_cover,8n,level8,W(-b oF),Weyl/Hall/Pfaffian histories,K_alpha time. Do not seek spin sum/missingrho_s again on this given net; individual field need not be observable. Priority is actual P1 locality map iota_I:one quotient interval has eight cover arcs. Jointly transport support,state,Theta,source charge,physicalP2 action and actualOS time with marked neutral Ward response. Neutral correlation/observable response can useDHR net action,boundedL_gamma andunitality; demand neither full localE8 observable extension nor added measurement apparatus. Sharp closable point limit required only for corresponding point-field claim,not smooth transporters. ActualNS14 comparison shows identical fullPhi marginal does not identify joint source/spinor transport. Do not genetically fit weights toPhi; test joint-source gauge/locality. Preserve original30 Ward/P2/charged-quarter bridge. Pprim/PTheta,admissibleA/A* net,actualOS,EM readout andspacetime evolution remain within full origin goal.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:use-charge-compensated-quarter-and-smaller-original-ward-component",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Read retained source charge and smaller Ward component jointly",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-e8-fold-matrix-with-retained-source-charge-and-p2-grading",
        "premise:local-e8-current-response-realization"
      ],
      "findingIds": [
        "finding:original-ward-and-p2-grading-select-smaller-creation-thirty",
        "finding:charged-source-quarter-recovers-inverse-internal-glue",
        "finding:state-independent-creation-branch-removes-whole-process-hodge-demand"
      ],
      "explanationEN": "Complete exact root checks and all-lattice proof replace heuristic weight search here. No GA refit of already unique operators. Test open P1 field map against actual local sources.",
      "changesRequiredEN": "CURRENT: bracket_process_origin_20261028/STAND-EINFACH-DE.md. Smallest positive route: original D5+A3 Ward creation30, joint P2 U5 residue3 and exactly derived charge-compensated source quarter. Identity g_alpha²=exp(2pi i alpha Qsource/4) Cint^-1 is closed on entire given E8 module; retain charge phase. Demand neither refitted clocks nor larger A4 family. Old full60 process has creation3/5 and actualLambda1 output2/5; normalized creation branch is direct30 Hodge response. Unconditional purePhi whole-process demand and uniform30-event policy are unnecessary for sector-resolved response. Priority: test local Xi_loc from actual P1 seam fields to marked E8 Ward insertion Y(e^(q/2),f), jointly for smearing/domain,source charge,U5,g_alpha,adjoint,reflection,state and OPE residue. Prove actual selected source branch and scalar effect; operator-valued marginal rigidity then forces entire carrier response even with entangled families. Do not equate state projector with process,geometric gamma_n with internal Majorana,neutral A3 Bell10 with charged P2 carrier or winding with NS/R twist. Preserve narrow unchangedH8 full-local exclusion and positive center-neutral source. WΩ inPprim/PTheta,admissible A/A* net,actualOS reduction,EM readout and spacetime evolution remain within full origin goal.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-neutral-observable-source-through-half-kink-transport",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reconstruct neutral source through existing smooth half-kink transport",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-eightfold-even-car-quotient-with-marked-charge-and-source-time"
      ],
      "findingIds": [
        "finding:given-source-current-constructs-half-kink-spinor-transport",
        "finding:neutral-ward-response-needs-no-spinor-observable-membership",
        "finding:actual-source-sector-transport-distinguishes-identical-hodge-marginals"
      ],
      "explanationEN": "Smooth neutral spinor transport follows from original current on given quotient. Test P1 locality and marked joint observable response; neither individual-field observability nor larger extension is automatically necessary.",
      "changesRequiredEN": "CURRENT: local_source_origin_20261028/STAND-EINFACH-DE.txt. Algebraic rho_s on given evenCAR quotient and smooth closed half-kink line are closed: originalJ_tot,n=J_cover,8n,level8,W(-b oF),Weyl/Hall/Pfaffian histories,K_alpha time. Do not seek spin sum/missingrho_s again on this given net; individual field need not be observable. Priority is actual P1 locality map iota_I:one quotient interval has eight cover arcs. Jointly transport support,state,Theta,source charge,physicalP2 action and actualOS time with marked neutral Ward response. Neutral correlation/observable response can useDHR net action,boundedL_gamma andunitality; demand neither full localE8 observable extension nor added measurement apparatus. Sharp closable point limit required only for corresponding point-field claim,not smooth transporters. ActualNS14 comparison shows identical fullPhi marginal does not identify joint source/spinor transport. Do not genetically fit weights toPhi; test joint-source gauge/locality. Preserve original30 Ward/P2/charged-quarter bridge. Pprim/PTheta,admissibleA/A* net,actualOS,EM readout andspacetime evolution remain within full origin goal.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:transfer-os-word-anti-anti-type-to-single-chiral-ordinary-weyl-reflection",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Literally transfer OS word type to single-chiral ordinary Weyl reflection",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-eightfold-even-car-quotient-with-marked-charge-and-source-time",
        "premise:ordinary-weyl-product-and-explicit-reflection-type-comparison"
      ],
      "findingIds": [
        "finding:ordinary-weyl-type-obstruction-to-single-chiral-os-anti-anti-reflection"
      ],
      "explanationEN": "Combined scalar conjugation, product reversal and single-chiral coordinate reflection violate the nontrivial central Weyl phase, for both field signs and existing levels1 and8.",
      "changesRequiredEN": "Original OS reconstruction must supply a different product type or an actually symplectic target. Test common original faces, cross covariance and actual current product; opposite-oriented face swap is so far algebraically consistent only. Do not genetically fit weights to repair this central phase.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:use-original-schottky-time-and-graded-opposite-weyls-for-joint-source",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use original Schottky time and existing opposite Weyls for joint source",
      "outcome": "insufficient_for_goal",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:normal-even-sea-car-source-and-canonical-graded-hs-double",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:existing-normal-thermal-source-with-bounded-neutral-insertions"
      ],
      "findingIds": [
        "finding:given-two-face-source-derives-opposite-neutral-weyls-and-bounded-time-reflection"
      ],
      "explanationEN": "The given two-face source now has a joint bounded neutral response and time reflection with actual partner phases. This mathematical construction does not derive its physical P1 source map.",
      "changesRequiredEN": "Derive actual supported P1 insertion/sewing map preserving this joint functional and time/reflection. Within the existing elliptic source do not seek X or Schottky time again; do not substitute spatial quarter reversal for normal OS reflection or rename a GNS partner as physical boundary.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-audited-local-source-chain-and-test-actual-p1-joint-functional",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse existing local source chain and compare actual joint P1 functional",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:declared-p1-p2",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions"
      ],
      "findingIds": [
        "finding:verification-recovery-preserves-local-source-chain-and-eight-gate-completeness",
        "finding:paper-seed-source-needs-local-image-not-global-equivalence",
        "finding:actual-two-face-projector-reduces-free-source-test-to-cross-coherence",
        "finding:given-two-face-source-derives-opposite-neutral-weyls-and-bounded-time-reflection"
      ],
      "explanationEN": "Do not construct another free CAR net or KMS source. Existing microscopy,given cross kernel and bounded histories are reusable. Focus on actual local P1 insertion/sewing map and original time; full target remains common T1 through T8 parent.",
      "changesRequiredEN": "Derive actual local unital star embedding iota_I from original seed,preserving full joint state/cross block,charge,eight fold arcs,Theta and time. Do not assign geometric projection as physical covariance by choice. Full projector test replaces higher CAR words only for an actual full positive CAR source;otherwise directly compare joint neutral histories. Compose existing consequences,then close all eight gates on the same parent.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:infer-joint-p1-source-by-pointwise-positive-spectral-reweighting-alone",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive joint P1 source through pointwise positive spectral reweighting alone",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:finite-reflected-spectral-weight-preservation-test"
      ],
      "findingIds": [
        "finding:positive-spectral-reweighting-does-not-establish-original-source-rp"
      ],
      "explanationEN": "Pointwise positive spectral weights do not ensure the OS form. Fixed positive reference denominator determines no missing joint field coefficients. This claim cannot replace the desired provenance map.",
      "changesRequiredEN": "When using this measure route,check actual full weighted reflected source or prove suitable RP factorization from original data. Geometric/BRST constraints must demonstrably exclude violation. Alternatively derive actual local neutral P1 observable embedding directly,preserving functional,support,Theta and time,without requiring whole geometric measure. Choose no free compensating coupling,profile or state.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-gapped-quarter-source-time-with-borchers-translation",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use gapped source time directly as Borchers translation",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:same-gapped-quarter-source-as-borchers-translation"
      ],
      "findingIds": [
        "finding:gapped-quarter-energy-cannot-be-same-borchers-translation"
      ],
      "explanationEN": "The full spectral gap excludes the required nontrivial unitary scaling of this same energy. A single parameter value or finite-period test does not replace the group law.",
      "changesRequiredEN": "For another standard-pair route derive the actual gapless translation generator and local standard inclusion from original data. Do not freely substitute another generator. Prioritize the original local field action or a direct neutral source identity.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:repair-standalone-finite-pfaffian-by-changing-only-internal-J",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Repair standalone finite Pfaffian by internally rechoosing J",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-v252-real-finite-block-and-selfdual-field-test"
      ],
      "findingIds": [
        "finding:finite-ko6-pairing-does-not-supply-standalone-pfaffian-source"
      ],
      "explanationEN": "Gamma J changes both relevant signs. The actual Majorana countercase has simple eigenvalues and permits no commuting square-minus J at the same D.",
      "changesRequiredEN": "Derive the actual local total real structure and domain from original data or pursue the direct complex/neutral source route; do not declare freely added spacetime or a Grassmann law derived from P1.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:derive-neutral-cayley-standard-pair-from-original-currents",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Derive Moebius standard pair from actual neutral original currents",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-quarter-neutral-vacuum-current-core"
      ],
      "findingIds": [
        "finding:actual-neutral-current-source-has-constructive-moebius-standard-pair"
      ],
      "explanationEN": "All-mode construction and local current-net connection are closed for the supplied vacuum source. The source and state were not derived from P1.",
      "changesRequiredEN": "Reuse this theorem. Next work is the actual local original source map preserving complete words/time/Theta, or a separately justified thermal bridge; do not refit P from a finite matrix.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:embed-full-local-current-net-directly-in-finite-spectral-coordinate-algebra",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Embed full local current net directly into finite spectral coordinates",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-local-weyls-and-finite-fiber-coordinate-target"
      ],
      "findingIds": [
        "finding:continuous-local-current-weyls-cannot-live-in-finite-coordinate-fibers"
      ],
      "explanationEN": "The actual continuous Weyl phase contradicts ordinary determinants in every finite matrix fiber.",
      "changesRequiredEN": "Identify the actual original quantum local algebra A_loc as target and test insertions there. Correct quantization or only the needed W8 subalgebra remain open; do not assert a universal A_+ exclusion.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:recognize-original-neutral-current-sector-from-actual-ward-and-state",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Recognize neutral source space through actual current action and state",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:neutral-current-recognition-with-actual-time-state-and-local-image"
      ],
      "findingIds": [
        "finding:actual-folded-current-ward-and-state-determine-all-neutral-words"
      ],
      "explanationEN": "The sufficient all-word theorem with original frequency8, KMS zero-mode limit and actual local reflection scope is proved and checked. Do not repeat independent word matching in the already supplied free current space.",
      "changesRequiredEN": "Supply actual P1 insertion operators, common domain, local Weyl/CCR and actual H time Ward; do not insert a desired vacuum/KMS contract into P1. Retain original zero-mode law, delta and actual common second face for corresponding joint assertions. Isolated W8 can use a smaller direct image.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:use-mixed-currents-and-test-complete-constant-product-time-reduction",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Use mixed currents in the existing field and complete constant time reduction",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:charged-car-pure-two-face-cauchy-graph-state",
        "premise:constant-finite-dirac-product-mixed-current-test",
        "premise:given-finite-sm-triple-yukawa-inputs",
        "premise:given-normal-spin-line-and-genuine-circle-product"
      ],
      "findingIds": [
        "finding:mixed-vector-axial-current-is-existing-full-car-subalgebra",
        "finding:constant-product-time-stable-current-level-is-kernel-index"
      ],
      "explanationEN": "The free mixed route is constructed under the old fullCAR premise; constant product attachments are completely classified. Old normal index source and actual time Ward are checked together. Neither extend the old vector exclusion to mixed generators nor genetically search the same classified constant class again.",
      "changesRequiredEN": "Identify the already specified normal product/family pushforward, including connection/admissibility, in the actual original operator. Net index suffices only for the phase; an all-word/time source must test extra counter-modes and actual state. Extending to variable/dynamical operators requires an originally derived new premise.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:test-paired-quarter-source-at-original-filter-and-full-graph",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Test quarter pairing against original filter and full boundary graph",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:paired-quarter-external-lowest-block-candidate"
      ],
      "findingIds": [
        "finding:paired-quarter-source-candidate-needs-original-filter-and-oriented-conjugation"
      ],
      "explanationEN": "Pairing and oriented full-graph conjugation are established conditionally. The external lowest block is not selected by the original highpass. Do not relabel standard linear algebra as a new origin.",
      "changesRequiredEN": "Derive original J,normal Clifford action,domain and actual P2 carrier map jointly. A different selection needs its original rule; no repeated search using a misread lowpass or transfer of balance to another internal type.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:use-canonical-graded-boundary-clifford-functor",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reconstruct the full original field in geometric Clifford boundary type",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:given-finite-sm-triple-yukawa-inputs",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing"
      ],
      "findingIds": [
        "finding:graded-boundary-clifford-typing-transports-full-scalar-and-finite-coupled-source",
        "finding:actual-product-reflection-and-same-time-have-full-positive-clifford-source-intertwiner"
      ],
      "explanationEN": "Free and coupled full graph,entire even RP,and natural HS field chart with same geometric time are analytically closed. Do not reintroduce a free right source,J search,parity phase or inverse-time gap in this class. Physical P1 selection is not thereby proved.",
      "changesRequiredEN": "Identify the actual Clifford source rule,charge J/Pfaffian,markings and coupled dynamical state in original P1/P2. Test physical reflection and time jointly. Do not substitute a fixed bosonic background for quantized bosons or demand an extra measure or free Gaussianity universally.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-full-charge-dirac-transport-in-graded-chart",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse full charge and Dirac transport",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:actual-product-collar-two-face-data",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:original-v252-real-finite-block-and-selfdual-field-test"
      ],
      "findingIds": [
        "finding:actual-charge-j-transport-retains-full-dirac-and-distinct-pairings"
      ],
      "explanationEN": "Full Jhat/Jloc/D maps and both pairings are analytically determined. Do not repeat the direct KO6 mass test or substitute an arbitrary new J search.",
      "changesRequiredEN": "Prove actual original use of total J,domain and chiral/unrestricted fermion integration.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-fixed-chart-for-normal-dependent-and-mixed-source",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Transport normal-dependent sources and mixed moments in fixed chart",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:fixed-frame-graded-normal-dependent-source-family"
      ],
      "findingIds": [
        "finding:fixed-graded-chart-transports-normal-dependent-source-and-given-mixed-moments"
      ],
      "explanationEN": "The whole fixed product family is transported; do not search further constant filters or fitted crossing blocks.",
      "changesRequiredEN": "Insert original field integration and actual insertion map. Do not exclude an averaged interacting source by imposing free-projector purity.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:identify-full-os-time-with-finite-rank-geometric-dirac",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Identify full OS time directly with compact geometric Dirac",
      "outcome": "excluded_scoped",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:given-quarter-many-body-source-and-compact-dirac-comparison"
      ],
      "findingIds": [
        "finding:neutral-many-body-source-time-is-not-finite-summable-geometric-dirac"
      ],
      "explanationEN": "Exact neutral occupation growth prevents any finite p-summability of this full H; the tested unitary time identification is excluded.",
      "changesRequiredEN": "Derive an actual one-particle map,direct field-net dictionary or separately justified D_coll with a time intertwiner. Do not infer exclusion of all P1 sources from this narrow test.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:reuse-actual-p2-and-decoupled-quarter-source-dictionary",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "titleEN": "Reuse actual P2 and decoupled quarter source dictionary",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:oriented-p2-exterior-carrier",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:fixed-local-quarter-channel-in-constant-odd-source"
      ],
      "findingIds": [
        "finding:actual-v252-positive-grade-has-global-p2-wedge-dictionary",
        "finding:old-quarter-full-source-embeds-locally-exactly-on-decoupled-channel"
      ],
      "explanationEN": "Global SM representation and exact local subsource are matched; Phi e0 completely decides fixed constant channels. No repeated random channel search or rediscovery of old level4 finding.",
      "changesRequiredEN": "Derive original common source rule and actual field/sector map. Interacting state may change; preserve actual charges,Ward,reflection,time and original references for needed readouts. Do not replace whole cover data by spectra.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "strategy:r098-test-whole-response-families-before-more-enumeration",
      "problemId": "problem:automatic-origin-response-decision",
      "titleEN": "Obtain composite response from original source and test whole families",
      "outcome": "reuse_result",
      "premiseIds": [
        "premise:finite-positive-kernel-search-class",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:r098-withheld-response-search-has-exact-conditional-affine-certificates",
        "finding:r098-whole-finite-process-segment-preserves-2245-moments"
      ],
      "explanationEN": "More points or unchanged low moments do not decide this segment. Derive a matching composite response or justified class exclusion from the same original common source;retain v534 selector within its conditional scope.",
      "changesRequiredEN": "Obtain actual original insertion,carrier,state,time,reflection and reference map with full matter source. No candidate value as source axiom,no free FK or Yukawa fit. Retain known four-mark object and resolved subresults.",
      "reviewState": "reviewed-authored"
    }
  ],
  "connections": [
    {
      "id": "connection:future-kernel-to-common-source",
      "problemId": "problem:future-quotient-and-gns-reconstruction",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:future-answer-functional",
        "premise:positive-word-kernel-null-stability"
      ],
      "findingIds": [
        "finding:future-equivalence-minimizes-declared-answer-process",
        "finding:positive-word-kernel-reconstructs-cyclic-gns"
      ],
      "explanationEN": "Future classes and the GNS representation are determined given complete r or a supplied positive K. This does not select the original answer alphabet or K; their common source selection remains open in the target problem.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:common-source-full-collar-reconstruction",
      "problemId": "problem:common-source-state-event-selection",
      "targetProblemId": "problem:physical-time-projector-transfer",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:local-geometric-dirac-deck-lift",
        "premise:literal-carrier-after-positive-compression",
        "premise:actual-product-collar-two-face-data",
        "premise:charged-car-two-face-graph-state",
        "premise:given-holomorphic-kms-inclusion-and-local-global-modular-domains"
      ],
      "findingIds": [
        "finding:geometric-deck-not-calderon-polarization",
        "finding:positive-compression-erases-carrier-minus-sector",
        "finding:fixed-interval-rotation-modular-chain-fails-local-state-takesaki-repairs"
      ],
      "explanationEN": "The complete original boundary graph can determine B and, under CAR identification, the state jointly. The source must supply this graph, fiber comparison and scale. This replaces separate spectral/state searches; physical marking additionally needs the original local operator algebra. ReviewedKMSlocalcorrection:globalrotationmovesintervals,localTakesakitimedependsonrestrictedstate;deriveitsstate/netcomparisonfirst.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:marked-family-transport-to-common-source",
      "problemId": "problem:seam-family-connection-compatibility",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures",
        "premise:parallel-irreducible-family-connection"
      ],
      "findingIds": [
        "finding:parallelity-excludes-2plus2-only-conditionally",
        "finding:joint-discrete-data-vs-connection"
      ],
      "explanationEN": "The 2+2 exclusion holds only with the added premise of parallelity to the marked irreducible family connection. Whether the common original source induces this connection and marking belongs to the target problem’s open source selection.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:full-time-transfer-to-common-source",
      "problemId": "problem:physical-time-projector-transfer",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:sign-covariance-only",
        "premise:known-faithful-kms-or-full-transfer"
      ],
      "findingIds": [
        "finding:sign-projector-does-not-determine-time-magnitude",
        "finding:full-faithful-kms-or-transfer-recovers-magnitudes"
      ],
      "explanationEN": "The sign projector loses |H|; unique dynamics returns only with faithful KMS covariance or the same complete transfer T. This ties the time question to the open joint selection of tau_t, state, and operator in the target problem.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:full-collar-construction-to-common-source",
      "problemId": "problem:physical-time-projector-transfer",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:charged-car-two-face-graph-state"
      ],
      "findingIds": [
        "finding:full-two-face-collar-recovers-signed-operator",
        "finding:two-face-graph-state-time-same-datum"
      ],
      "explanationEN": "Joint reconstruction replaces independent time/state fitting by selection of one full original graph kernel plus physical field identification. Marking needs its local algebra; inversion does not settle source selection.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:absolute-flavor-readout-to-common-source",
      "problemId": "problem:flavor-ratio-amplitude-readout",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:flavor-ratio-closed-absolute-anchor-open"
      ],
      "explanationEN": "The ratio 55/117 is closed on the documented discrete stratum; U_f* remains open as the absolute scale. Its physical selection needs an original rule for connection and readout and belongs to the target problem’s open source selection.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:alpha-physical-response-to-complete-native-source",
      "problemId": "problem:alpha-fixed-input-root",
      "targetProblemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:fixed-input-models-scoped",
        "premise:marked-e8-regularized-charged-grade-response"
      ],
      "findingIds": [
        "finding:marked-e8-sector-grade-response-realizes-five-quarters",
        "finding:alpha-exact-coefficients-and-root-retain-specific-physical-ward-obligation"
      ],
      "explanationEN": "Reuse the existing direct circle line, proved W8 completion and full-projector-covariance uniqueness in joint source reconstruction. Do not demand an independent Gaussian state choice after actual full positive projection covariance is proved. For original EM establish the actual insertion, same state/time/reflection and unnormalized relative response; matching exponents or freely selected face states do not replace this.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:gravity-response-to-common-source",
      "problemId": "problem:gravity-flow-normalization",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:declared-p1-p2",
        "premise:typed-source-structures",
        "premise:fixed-input-models-scoped"
      ],
      "findingIds": [
        "finding:matter-observations-do-not-fix-geometric-response"
      ],
      "explanationEN": "The matter-only ambiguity belongs to a larger observation class and does not automatically change the fixed original Gamma_grav. The missing common off-shell geometry family and normalization must come from the original source; this is the same open source selection in the target problem.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:quadratic-response-constrains-common-source",
      "problemId": "problem:clock-linked-neutral-response-reconstruction",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:native-current-clock-ope-access"
      ],
      "findingIds": [
        "finding:four-clock-fields-complete-quadratic-response"
      ],
      "explanationEN": "The complete response restricts neutral matrix equivalences; it selects neither source nor physical instruments.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:j-transport-constrains-common-source",
      "problemId": "problem:clock-source-covariant-transport",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:stipulated-e8-clock-tuple"
      ],
      "findingIds": [
        "finding:actual-j-covariant-source-transport",
        "finding:fixed-source-affine-j-obstruction"
      ],
      "explanationEN": "A common source must specify which data physically change and which are merely redescribed together.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:charged-identifiability-limits-neutral-tomography",
      "problemId": "problem:charged-twist-response-identifiability",
      "targetProblemId": "problem:clock-linked-neutral-response-reconstruction",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:neutral-current-vacuum-insertions"
      ],
      "findingIds": [
        "finding:neutral-vacuum-allword-twist-blindness"
      ],
      "explanationEN": "Complete quadratic coefficient reconstruction does not remove twist blindness of its vacuum probes.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:charged-discriminator-constrains-common-source",
      "problemId": "problem:charged-twist-response-identifiability",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:normalized-charged-primary-time-access"
      ],
      "findingIds": [
        "finding:eight-charged-responses-reconstruct-twist"
      ],
      "explanationEN": "An available original charged-probe contract would make different twist candidates distinguishable.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:native-symmetry-to-charged-twist",
      "problemId": "problem:native-charged-seam-selection",
      "targetProblemId": "problem:charged-twist-response-identifiability",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:native-full-charge-field-source",
        "premise:native-c-invariant-start"
      ],
      "findingIds": [
        "finding:native-opposite-charge-response-symmetry"
      ],
      "explanationEN": "Charged Fock discriminator tested on original native T fields.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:native-selection-to-common-source",
      "problemId": "problem:native-charged-seam-selection",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:native-full-charge-field-source",
        "premise:native-c-invariant-start"
      ],
      "findingIds": [
        "finding:native-opposite-charge-response-symmetry"
      ],
      "explanationEN": "The common seam/state map must account for this response symmetry.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:constructive-seam-to-common-source",
      "problemId": "problem:constructive-seam-lift-state",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:fixed-car-crossed-half-charge-search",
        "premise:fixed-positive-crossed-state",
        "premise:unchanged-quarter-car-qwz-source-comparison",
        "premise:stipulated-even-e8-seam-lift"
      ],
      "findingIds": [
        "finding:constructive-phase-class-and-full-winding",
        "finding:constructive-positive-state-extension",
        "finding:constructive-current-group-selects-positive-p-lift",
        "finding:constructive-state-algebra-resolution-and-source-test",
        "finding:constructive-all-phases-fail-unchanged-source"
      ],
      "explanationEN": "Reuse algebra, winding and positive extension. The common source candidate must first supply actual Cartan, ground-space and time compatibility; an identical shift functional is insufficient.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:partner-types-to-common-source",
      "problemId": "problem:seam-partner-charge-state-time",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:oriented-p2-exterior-carrier",
        "premise:fixed-e8-fold-quarter-dictionary",
        "premise:actual-chiral-opposite-quarter-domains",
        "premise:given-first-marked-quarter-character",
        "premise:given-d5-a3-free-fermion-realization"
      ],
      "findingIds": [
        "finding:partner-carrier-charges-and-state-types",
        "finding:partner-fixed-quarter-time-splits-sm-multiplet",
        "finding:partner-original-carrier-cross-sheet-conjugation",
        "finding:partner-chiral-quarter-conjugation-state-time",
        "finding:joint-bilinear-hermitian-correction",
        "finding:joint-quarter-transports-marking",
        "finding:joint-fixed-time-marking-repair-excluded",
        "finding:joint-spinor-not-source-coefficient"
      ],
      "explanationEN": "The two conjugations are typed; the actual quarter source determines transport of the supplied marking. No fixed time-stabilizing repair exists. Original selection of the first marked field source remains with the common selector; no new spinor16 replacement source.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:operator-synthesis-to-positive-kernel",
      "problemId": "problem:automated-operator-source-synthesis",
      "targetProblemId": "problem:future-quotient-and-gns-reconstruction",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:typed-source-structures",
        "premise:declared-finite-operator-synthesis-inputs",
        "premise:finite-positive-kernel-search-class",
        "premise:actual-product-collar-two-face-data",
        "premise:actual-car-graph-and-oriented-boundary-pairing"
      ],
      "findingIds": [
        "finding:typed-operator-search-calibrated",
        "finding:positive-kernel-construction-with-exact-discriminator",
        "finding:collar-car-projection-multifield-ray"
      ],
      "explanationEN": "Existing GNS reconstruction now has executable synthesis of unknown positive kernels. Exact finite completions provide checks and discriminating responses; original source constraints and physical identification remain to be derived.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:multifield-collar-to-original-time",
      "problemId": "problem:automated-operator-source-synthesis",
      "targetProblemId": "problem:physical-time-projector-transfer",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:actual-product-collar-two-face-data",
        "premise:actual-car-graph-and-oriented-boundary-pairing"
      ],
      "findingIds": [
        "finding:collar-car-projection-multifield-ray"
      ],
      "explanationEN": "With actual CAR and amplitude identification the full boundary projection determines all field-product amplitudes, not only a restricted density. Original physical identification and the absolute scalar remain source-level tasks.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:joint-source-functional-to-origin-selection",
      "problemId": "problem:automated-operator-source-synthesis",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:given-complex-fermion-source-quantization",
        "premise:given-angular-quarter-zeta-cut",
        "premise:actual-chiral-opposite-quarter-domains",
        "premise:charged-car-negative-sea-source",
        "premise:given-thermal-sea-abel-subtraction",
        "premise:first-order-perturbation-graph-estimate",
        "premise:fixed-field-four-mode-inverse-data-control",
        "premise:typed-source-structures",
        "premise:complete-labeled-even-car-kernel"
      ],
      "findingIds": [
        "finding:joint-fermionic-source-schur-functional",
        "finding:quarter-circle-absolute-zeta-green-eta",
        "finding:quarter-sea-absolute-thermal-central-phase",
        "finding:original-operational-seed-and-given-green-pairing",
        "finding:order-one-infinitesimal-bound-inference-fails",
        "finding:joint-ward-two-field-data-miss-fixed-four-field-response",
        "finding:complete-car-kernel-fixes-nongaussian-link-functional"
      ],
      "explanationEN": "The joint absolute source and eta/sea/Ward identity remain valid conditionally. Originals use a stronger operational seed; classical Green pairing follows from supplied Dirac data. The corrected search requires total operator/domain and original fixed multifield response; matching traces and two-field data is insufficient in the tested inverse contract.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:actual-whole-source-to-universalraum-futures",
      "problemId": "problem:automated-operator-source-synthesis",
      "targetProblemId": "problem:future-quotient-and-gns-reconstruction",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:fixed-local-quarter-channel-in-constant-odd-source",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:actual-diagonal-lepton8-common-insertion-contract"
      ],
      "findingIds": [
        "finding:whole-quarter-channels-identified-by-exact-internal-kernel",
        "finding:actual-joint-insertion-hull-resolves-eight-coefficient-directions"
      ],
      "explanationEN": "The whole given Clifford source realizes the old positive-word/GNS bridge with marked R and circle time. The new kernel identifies all scalar-future channels; shared insertion images exhibit distinguishing continuations. This selects neither the original physical alphabet nor an absolute Universalraum ontology.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:source-q-spin-kernels-to-native-theta-clock-insertion",
      "problemId": "problem:automated-operator-source-synthesis",
      "targetProblemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:recovered-genus-two-cover-with-retained-signed-coefficients",
        "premise:actual-original-a0star-fuchsian-connection-and-c4-clock",
        "premise:typed-source-structures",
        "premise:given-split-carrier-and-actual-genus-two-q-sign-family",
        "premise:canonical-recomplexified-graded-boundary-clifford-typing",
        "premise:actual-product-collar-two-face-data",
        "premise:constant-odd-quarter-circle-source-sea-and-full-graph",
        "premise:given-relative-unit-seam-on-specified-collar-faces",
        "premise:whole-constant-odd-coefficient-on-scalar-unit-clutch-domain",
        "premise:actual-full-v252-unimodular-p2-gauge-lift",
        "premise:declared-q-column-to-v252-generation-slot-comparison",
        "premise:oriented-p2-exterior-carrier",
        "premise:declared-q-column-to-v252-chiral-slot-comparison",
        "premise:actual-car-graph-and-oriented-boundary-pairing",
        "premise:original-hard-holonomy-and-closed-triangle-readout-contract",
        "premise:full-unitary-e8-field-conjugacy-with-transported-marks",
        "premise:one-e8-bracket-weyl-pairing-with-single-anchor-dressing",
        "premise:given-original-e8-cx-current-cocycle-and-compact-adjoint",
        "premise:original-d5-base-current-action-on-given-p2-e8-source",
        "premise:relative-spin-scalar-hardy-cable-on-original-three-cover",
        "premise:original-gap-normalized-primitive-relative-action",
        "premise:given-finite-sm-triple-yukawa-inputs",
        "premise:common-leading-distance-flavor-readers",
        "premise:original-closed-real-delta-transport-action",
        "premise:four-original-diagonal-paths-and-regularized-endpoints",
        "premise:native-clock-adjoint-compensation-for-hardypair",
        "premise:declared-positive-cubic-hardy-direction-for-gram-differential",
        "premise:whole-same-mu01-induced-ns-halfmode-reader"
      ],
      "findingIds": [
        "finding:source-selected-spin-and-q-signs-have-three-explicit-global-kernels",
        "finding:actual-q-quarter-extends-common-k-connection-and-real-coefficient-lifts",
        "finding:actual-spin-kernel-determinant-has-inverse-q-norm-character",
        "finding:closed-source-flavor-spin-has-functorial-pfaffline-with-charged-type-limit",
        "finding:original-relative-seam-has-explicit-whole-graph-fredholm-mismatch",
        "finding:whole-constant-coupled-clutch-defects-are-exact-internal-kernels",
        "finding:old-complex-scalar-clutch-separates-c0-and-product-reflection",
        "finding:scalar-defect-circle-character-does-not-select-projector-holonomy",
        "finding:source-spin-is-canonical-ramified-base-spin-pullback",
        "finding:original-v117-has-explicit-algebraic-q-cover-fundamental-frame",
        "finding:actual-fuchs-real-map-transports-whole-given-finite-source-state-and-time",
        "finding:actual-e0-compensator-extends-whole-k-e8-with-transported-quarter",
        "finding:actual-v252-entire-real-basis-has-signed-p2-dual-dictionary",
        "finding:chiral-fuchs-source-transport-has-distinct-majorana-phase-and-torus-absorption",
        "finding:native-theta-composition-retains-conjugate-source-and-parity-square",
        "finding:single-graph-range-isometry-does-not-give-local-whole-seed-map",
        "finding:hard-holonomy-selfduality-leg-and-finite-character-phase-separation",
        "finding:original-z6-positive-structural-kernel-does-not-supply-oriented-phase-observable",
        "finding:original-genus-two-hexagonal-rotation-has-concrete-rho-hodge-line",
        "finding:original-mixed-spin-products-realize-positive-u6-cycle",
        "finding:actual-spin-quadratics-reach-original-hexagonal-hodge-line",
        "finding:spin-pair-car-transport-retains-parity-and-whole-source-types",
        "finding:real-total-trace-does-not-exclude-coherent-phase-reader",
        "finding:geometric-six-spin-clock-differs-from-marked-native-clock",
        "finding:whole-q-to-p-pullback-transports-given-source-state-and-time",
        "finding:actual-fixpoint-evaluation-keeps-coefficient-signs-and-source-type",
        "finding:original-source-naturality-needs-no-second-p-image-background",
        "finding:canonical-spin2-lift-carries-whole-annulus-source-with-reversed-time",
        "finding:geometric-spin-collar-map-closes-weighted-image-domain-with-total-deck-action",
        "finding:claude33-annulus-map-is-valid-distinct-type-not-unique-geometric-spin-selection",
        "finding:original-mixed-spin-products-already-have-complete-dual-hom-coefficients",
        "finding:whole-f5-graph-supplies-canonical-reverse-qp-hom-kernel",
        "finding:actual-spin-product-weight-has-canonical-trace-class-form-pairing",
        "finding:fully-descended-covariant-reverse-kernel-removes-rho-form-channel",
        "finding:original-a4-linear-quarter-does-not-supply-proposed-scalar-mu3-repair",
        "finding:offdiagonal-hom-matches-a4-family-six-but-not-two-triplet-e8-product",
        "finding:compact-e8-adjoint-completes-family-six-with-carrier-rank-retained",
        "finding:three-family-cx-recursion-closes-exact-d8-with-minimal-original-escape",
        "finding:original-weak-current-coefficient-has-explicit-finite-oneform-consumer",
        "finding:original-d5-zero-mode-closes-triplet-carrier-and-fixed-glue-is-minimal-escape",
        "finding:original-poisson-normal-trace-fixes-whole-calderon-graph",
        "finding:induced-original-hardy-defect-gives-finite-whole-source-reader",
        "finding:original-weak-quartic-action-has-nonzero-nonlinear-response",
        "finding:all-common-leading-distance-clutches-fail-original-flavor-lengths",
        "finding:actual-hardy-response-has-weak-clifford-odd-and-ko-real-completion",
        "finding:actual-fuchs-halfpath-has-canonical-g-metric-c6-kernel-map",
        "finding:two-entry-hardy-adjoint-hierarchy-fails-full-ko-and-su2",
        "finding:original-real-delta-jet-reads-same-marked-hardy-open-word",
        "finding:four-actual-fuchs-spine-edges-recover-marked-meridians-and-nonzero-open-word",
        "finding:native-adjoint-quarter-clock-cannot-compensate-hardypair-odd-character",
        "finding:whole-cubic-gram-differential-retains-hardy-phase-and-cross-resonance",
        "finding:complete-original-mu01-hardy-reader-has-two-calibrated-entries"
      ],
      "explanationEN": "Retain the entire scoped structure/spin/deck/Fuchs/domain/source chain, actual reverse kernel, native D5/glue E8 action, state/reflection/time. Actual induction of the old unit winding gives a finite reader with a proved nonzero moment. Whole96 Clifford/KO continuation passes, and original primitive wedge consumer explicitly reads it with the fixed KO sign. No missing weak-operation gate remains. Next shared-source comparison concerns the original HolK coefficient formula, possibly through actual variation/summand, without requiring universal Hardy=Y. Full physical generation is not proved; preserve prior scoped exclusions and avoid new O/p-source/state/quarter/QY gates. ActualGmetric path closesU6/Kstrframe; The reviewedfailsKO/SU2. Next is originalinsertion,not freemetric. Actualoriginalreal delta jet and allfour openpaths are nowexecuted. Typedendpointquarter actions preclude a universaltracecancellation; execute the originalwholeconsumer. Preserve completeGram differential and allfour openedgecharacters; rank1compression and real-onlyresonance approximation do not replace the whole source.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:reverse-bootstrap-field-response-to-automated-operator-source-synthesis",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "targetProblemId": "problem:automated-operator-source-synthesis",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:reverse-bootstrap-e8-closure-framework",
        "premise:local-e8-current-response-realization"
      ],
      "findingIds": [
        "finding:reverse-bootstrap-retained-operator-scope",
        "finding:e8-current-dictionary-all-separated-responses"
      ],
      "explanationEN": "The numerical reverse chain and explicit normalized current dictionary are available; the common physical source derivation must supply the actual local insertion map with quarter time, statistics and unnormalized field dependence.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:reverse-bootstrap-field-response-to-common-source-state-event-selection",
      "problemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:reverse-bootstrap-e8-closure-framework",
        "premise:local-e8-current-response-realization"
      ],
      "findingIds": [
        "finding:reverse-bootstrap-retained-operator-scope",
        "finding:e8-current-dictionary-all-separated-responses"
      ],
      "explanationEN": "The numerical reverse chain and explicit normalized current dictionary are available; the common physical source derivation must supply the actual local insertion map with quarter time, statistics and unnormalized field dependence.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:clock-defect-operational-core-to-original-source",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "targetProblemId": "problem:common-source-state-event-selection",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:declared-p1-p2"
      ],
      "findingIds": [
        "finding:complete-native-six-effect-covariant-instrument-classification",
        "finding:native-six-effect-readout-on-existing-erasure-output",
        "finding:new-clock-feedback-origin-input-audit",
        "finding:native-event-channel-cone-intersection-is-tenth-to-half",
        "finding:native-six-ovoid-observation-first-occurs-at-tensor-degree-three",
        "finding:original-quartic-erasure-and-hamming-octic-share-marked-ovoid-response",
        "finding:native-octic-field-ray-is-explicit-but-retained-clock-stress-preparation-fails",
        "finding:actual-quarter-fold-stress-has-nonzero-octic-eighth-jet",
        "finding:native-octic-is-an-original-even-car-current-composite",
        "finding:original-geometric-source-jet-and-partial-p1-seed-closure",
        "finding:paper-microscopic-car-composes-with-native-octic-ward",
        "finding:microscopic-neutral-octic-has-controlled-smeared-limit",
        "finding:paper-seed-source-needs-local-image-not-global-equivalence",
        "finding:full-car-positive-time-forces-source-vacuum",
        "finding:original-winding-theorem-does-not-select-seam-ray",
        "finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel",
        "finding:original-os-step-needs-full-moments-not-connected-cumulants",
        "finding:graded-field-image-precedes-physical-observable-restriction",
        "finding:older-original-circle-representative-already-realizes-ward-and-index",
        "finding:old-quarter-heat-transfer-has-controlled-rank-one-limit-and-odd-product",
        "finding:historical-em-rank-one-and-full-heat-traces-have-different-contracts",
        "finding:older-frg-functional-already-supplies-formal-full-moment-parent",
        "finding:earliest-c3-route-quantizes-level-but-needs-physical-kinetic-normalization",
        "finding:a4-spin-lift-fixes-local-ns-and-unordered-quarter-pair",
        "finding:cover-winding-exchanges-quarter-sectors-before-its-square",
        "finding:retained-winding-preserves-local-support-and-neutral-time",
        "finding:marked-glue-square-is-the-e8-fermionization-character",
        "finding:fixed-canonical-d8-is-not-transported-source-d8",
        "finding:actual-winding-has-four-module-e8-defect-extension",
        "finding:ramond-lift-sign-is-common-intertwiner-basis-gauge",
        "finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class",
        "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor",
        "finding:schur-carrier-plus-complement-preserves-original-relative-determinant",
        "finding:v258-forward-source-gap-is-reused-not-solved-by-inversion",
        "finding:one-sided-source-and-real-em-norm-need-response-map-not-chiral-phase",
        "finding:trace-class-pair-index-fixes-relative-factor-without-primitive-ray",
        "finding:matrix-clutch-degree-connects-weak-determinant-class-without-ray-selector",
        "finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index",
        "finding:inner-carrier-is-infinite-spacetime-module-not-finite-circle-cut",
        "finding:normal-spin-determinant-line-exactly-transports-whole-circle-in-given-product",
        "finding:normal-index-line-source-match-is-holonomy-condition-not-vertical-degree",
        "finding:full-normal-product-polarization-change-is-not-trace-class",
        "finding:massive-transverse-zero-index-retains-positive-determinant-response",
        "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel",
        "finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection",
        "finding:tetrahedral-quarter-face-phase-does-not-identify-original-quarter-marked-curve",
        "finding:existing-elliptic-cover-correspondence-has-exact-c6-image-and-retained-mixed-clock",
        "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
        "finding:global-split-joint-carrier-admits-parallel-native-c12-clock",
        "finding:pure-weak-clutch-clock-identification-fails-despite-quarter-matches",
        "finding:same-chern-clutch-native-compiler-does-not-select-physical-connection"
      ],
      "explanationEN": "Old spin-lift premise supplies local NS/quarter origin; neutral source and complete mathematical E8 defect connect in actual frame. Physical CAR/OS source selection and coupled EM action/measure remain shared required inputs. Existing F8,relative-weight and UV results are preserved. Faithful KMS persistence and exact carrier transport are now closed; original forward source and real EM readout remain to identify. General pair-index response now connects to original weak determinant class; common circle image and real EM variation remain physically open. Finite NS sampling has an exact UV index partner. Normal spin-line pushforward now provides sufficient exact circle transport in the genuine product class;original operator and horizontal connection remain to identify. Full projection change is not L1 and massive zero-index channels still respond. Direct Callias shortcut requires actual closed operators and complex kernel components;doublet multiplicityone is not a complex source line. Moving-fiber connection and two existing elliptic cover images are now explicit. Equal tetrahedral quarter phase is not a direct Mobius or field intertwiner;joint C6 image loses a C4 sign while clock12 remains faithful.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:parallel-native-clock-to-joint-family-connection",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "targetProblemId": "problem:seam-family-connection-compatibility",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:natural-joint-spin-family-lift-with-given-split-connection",
        "premise:fixed-kappa-toral-third-centralizing-split-carrier"
      ],
      "findingIds": [
        "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
        "finding:global-split-joint-carrier-admits-parallel-native-c12-clock"
      ],
      "explanationEN": "Given split connection plus naturally induced determinant-family part now admits parallel native clock representative. An additional nonabelian flavor transport and its original selection remain separate;the older conditional2+2 versus3+1 boundary is preserved.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:cartan-source-globalization-to-family-connection",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "targetProblemId": "problem:seam-family-connection-compatibility",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:native-cartan-four-in-full-clock-conjugate-source",
        "premise:primitive-normal-sphere-joint-k-bundle-class-two"
      ],
      "findingIds": [
        "finding:native-gaussian-four-is-cartan-subspace-in-whole-sixtyfour",
        "finding:native-family-factor-is-not-gaussian-four-despite-symmetric-coincidences",
        "finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice"
      ],
      "explanationEN": "Joint64 contains the Cartan four,not an identical family factor. Parallel whole Cartan transport forces flatness;parallel clock alone does not. Separate H1 flavor source still needs mapping.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:invariant-quantum-octic-glues-without-global-cartan-choice",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "targetProblemId": "problem:seam-family-connection-compatibility",
      "kind": "constrains_under",
      "premiseIds": [
        "premise:declared-original-octic-quantum-completion-ansatz",
        "premise:full-existing-local-e8-field-hull-observer-code",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:global-cartan-choice-is-optional-for-original-scalar-source-fields",
        "finding:explicit-primary-e8-invariant-octic-completes-same-neutral-car-source"
      ],
      "explanationEN": "Internal W8 singlet glues across K transitions and is parallel for induced zero-mode connection,without Cartan choice. This resolves neither charged clock-field transport nor original conformal collar and reflection identification.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:old-winding-current-net-to-quarter-partner",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "targetProblemId": "problem:seam-partner-charge-state-time",
      "kind": "requires_result",
      "premiseIds": [
        "premise:existing-cut-cover-car-with-actual-winding-and-sea",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:old-cover-winding-reconstructs-local-quarter-current-net",
        "finding:untransported-independent-quarter-stress-pair-is-not-current"
      ],
      "explanationEN": "The existing cover winding is now an explicit state-preserving comparison of the used quarter subalgebras and closes their local current construction. Whole charged winding,factor comparison and physical P1 reflection remain distinct documented types.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:full-cover-green-reflection-to-original-quarter-source",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "targetProblemId": "problem:seam-partner-charge-state-time",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover",
        "premise:given-flat-mobius-dirac-boundary-family-and-full-sea",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea",
        "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity",
        "finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp",
        "finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum"
      ],
      "explanationEN": "The whole geometric NS cover now has full free Green RP. Old quarter CAR remains a different state/time realization whose original common P1 field map is still missing. This distinction prevents wrongly transferring the isolated Pin witness or thermal kernel to W8.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:elliptic-moebius-boundary-to-marked-compiler-source",
      "problemId": "problem:atlas-clock-defect-and-operational-reconstruction",
      "targetProblemId": "problem:marked-seam-monodromy-and-lattice-lifts",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks",
        "premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus",
        "premise:original-quarter-car-fold-current-subalgebra",
        "premise:original-p1-seed-boundary-and-local-restriction-definitions",
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower",
        "finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent",
        "finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms",
        "finding:tfpt-origin-investigation-full-source-coverage-and-current-frontier"
      ],
      "explanationEN": "Concrete existing C2 cut now reproduces the quarter boundary source. Known local E8 extension and compiler clocks remain complete conditional results;actual original P1 field map does not yet connect these sides. Common overview now links all early E6/E7/E8 and original C12 results with current W8,spin and theta state;distinct cover contracts remain separate.",
      "reviewState": "reviewed-authored"
    },
    {
      "id": "connection:r098-response-search-to-physical-source-dictionary",
      "problemId": "problem:automatic-origin-response-decision",
      "targetProblemId": "problem:reverse-bootstrap-physical-field-dictionary",
      "kind": "shares_unresolved_input",
      "premiseIds": [
        "premise:typed-source-structures"
      ],
      "findingIds": [
        "finding:r098-whole-finite-process-segment-preserves-2245-moments"
      ],
      "explanationEN": "The exact automated test requires the same original physical insertion/source map;the finite search family does not replace it.",
      "reviewState": "reviewed-authored"
    }
  ],
  "patterns": [
    {
      "id": "pattern:finite-e8-code-quantum",
      "titleEN": "One lattice links error correction, G31 and two-qubit structure",
      "summaryEN": "Hamming [8,4,4] produces E8 by Construction A. For the specified J, L/(1+i)L ≅ F₂⁴ is the RM(1,3) information alphabet: 240 roots lie in 15 fibers of 16. In the stated chart the 60 Gaussian lines are exactly the two-qubit stabilizer rays; G31 is projectively the Clifford group.",
      "kind": "source_reviewed_connection",
      "relatedIds": [
        "claim:E8.CODE.01",
        "claim:E8.CODESEM.01",
        "claim:E8.GAUSSCODE.01",
        "claim:E8.ST31.01",
        "claim:E8.CLIFFORD2Q.01",
        "topic:e8",
        "topic:quantum",
        "topic:clocks"
      ],
      "conditions": [
        "Requires the stated E8 lattice, compiler-compatible J and explicit equivariant dictionary/chart together. These are linked representations, not independent evidence to multiply."
      ],
      "counterevidence": [
        "No derivation of physical matter or universal quantum computation. The stronger syndrome-algebra reading remains excluded; the Clifford index bit is not J↔−J."
      ],
      "sourceRefIds": [
        "review-source:959a821f508adf475e8b",
        "review-source:f296c6c23b218ad5960f",
        "review-source:63bd4a3450f35b1020a3"
      ],
      "reviewState": "source-reviewed-relationship",
      "reviewScope": "Source-grounded relationship and status mapping; no new execution or mathematical certification."
    },
    {
      "id": "pattern:actual-clock-actions",
      "titleEN": "Clocks interlock through explicit actions",
      "summaryEN": "The quarter structure is not a subcycle of C30: G C5 G⁻¹=C5² and G⁴=I describe its Galois action. The G31 compiler satisfies c=Jσ, σ=c⁴ and J=c⁹. These relations connect quarter, carrier and family structure through operators rather than equal orders alone.",
      "kind": "source_reviewed_connection",
      "relatedIds": [
        "claim:SEAM.GALOIS.01",
        "claim:E8.ST31.01",
        "claim:COX.CLOCK.01",
        "topic:e8",
        "topic:clocks"
      ],
      "conditions": [
        "Keep the explicit cyclotomic representation distinct from the specified G31 compiler; identification requires the named dictionary."
      ],
      "counterevidence": [
        "The compiler clock is not the regular Springer order-12 element. Finite group action alone selects neither physical time nor duration."
      ],
      "sourceRefIds": [
        "review-source:b5a7c3df66dbdd4d8bac",
        "review-source:f56526d86815d4720661"
      ],
      "reviewState": "source-reviewed-relationship",
      "reviewScope": "Source-grounded relationship and status mapping; no new execution or mathematical certification."
    },
    {
      "id": "pattern:e8-holomorphic-invariants",
      "titleEN": "E8 and G31 share an explicit invariant map",
      "summaryEN": "The holomorphic restriction of E8 root sums at degrees 8,12,20,24 yields algebraically independent G31 invariants. Under the cited Chevalley theorem they generate the full G31 invariant ring: a structural map between two compiler representations.",
      "kind": "source_reviewed_connection",
      "relatedIds": [
        "claim:E8.QUARTICHALF.01",
        "claim:E8.ST31.01",
        "topic:e8",
        "topic:quantum"
      ],
      "conditions": [
        "Compiler-compatible complex structure, exact invariance and independence, and the cited Chevalley theorem together."
      ],
      "counterevidence": [
        "Vanishing at degrees 2,14,18,30 already follows trivially from μ4; it is not the same result as generating the full ring."
      ],
      "sourceRefIds": [
        "review-source:3dcc36ee731badd02cf6"
      ],
      "reviewState": "source-reviewed-relationship",
      "reviewScope": "Source-grounded relationship and status mapping; no new execution or mathematical certification."
    },
    {
      "id": "pattern:marked-seam-cover-clock",
      "titleEN": "Four marks → genus-three cover → lifted clock",
      "summaryEN": "Within the stated conformal seam axioms, mark equivalence and μ3 monodromy force uniform weights and y³=x⁴−1 of genus three. The explicit lift of the 16-site NS circle is a connected 48-site circle; L⁴=deck and L¹²=I hold on every point.",
      "kind": "source_reviewed_connection",
      "relatedIds": [
        "claim:QGEO.SEAMFORCE.01",
        "claim:QGEO.COVERSEAM.01",
        "claim:QGEO.NCENSUS.01",
        "topic:origin",
        "topic:clocks",
        "topic:quantum"
      ],
      "conditions": [
        "Conformal four-mark axioms, selected μ3 cover branch, uniform monodromy and NS lift. Do not identify the genus-three curve with the elliptic four-mark curve."
      ],
      "counterevidence": [
        "These finite and geometric results alone do not identify the original physical seam. This lift is not a complete interacting continuum theorem."
      ],
      "sourceRefIds": [
        "review-source:47d29a3317b20b7249f7",
        "review-source:6d4087f12195532bceae"
      ],
      "reviewState": "source-reviewed-relationship",
      "reviewScope": "Source-grounded relationship and status mapping; no new execution or mathematical certification."
    },
    {
      "id": "pattern:flavor-operator-budget",
      "titleEN": "Flavor ladder and alpha budget meet at the same anchor",
      "summaryEN": "The explicit Q/K/R/L operators have determinants 3,4,8,20 with product 1920. The same K anchor block yields 1ᵀK1=25, aᵀKa=41 and difference 16. Mass volume and the EM budget are linked through shared operators, rather than independent number fits.",
      "kind": "source_reviewed_connection",
      "relatedIds": [
        "claim:FLAV.R.01",
        "claim:FLAV.KQ.01",
        "claim:EM.FP.01",
        "topic:flavor",
        "topic:alpha",
        "topic:e8"
      ],
      "conditions": [
        "The defined projection, involution and residue operators, and a=(1,1,2). Physical readouts retain their transfer premise."
      ],
      "counterevidence": [
        "1920 alone proves no isomorphism to a horizon or Weyl action. Absolute masses and parameter provenance do not follow from determinants alone."
      ],
      "sourceRefIds": [
        "review-source:f6d0d2a17ed5d63eef63"
      ],
      "reviewState": "source-reviewed-relationship",
      "reviewScope": "Source-grounded relationship and status mapping; no new execution or mathematical certification."
    },
    {
      "id": "pattern:existing-mirror-and-dynamics",
      "titleEN": "Mirror mechanism and local dynamics already have constructions",
      "summaryEN": "The decoupled DET16 product parent has a proved spectrum {0,…,N}, unique product ground state and gap 1 in every finite volume. Separately, the specified uniformly local Hamiltonian class on Γ=Z² has norm-limit dynamics, a gauge-invariant quasilocal algebra and ground/KMS states. These subtheorems exist; the additional 3+1D scaffold is a different construction.",
      "kind": "source_reviewed_connection",
      "relatedIds": [
        "claim:CHIRAL4D.MIRROR.DET16.01",
        "claim:QFT4D.LATTICE.FUNDAMENTAL.01",
        "topic:quantum",
        "topic:spacetime"
      ],
      "conditions": [
        "Decoupled DET16 product Hamiltonian for the exact volume theorem; Γ=Z² with finite local spaces, uniformly bounded finite range and gauge covariance for the dynamics theorem."
      ],
      "counterevidence": [
        "This does not automatically close a common 3+1D TFPT realization, dynamical gauge fields, phase uniqueness, limiting gap or IR universality."
      ],
      "sourceRefIds": [
        "review-source:e1230e35ce5eb9a29012",
        "review-source:b43647e3e71a101d2f06",
        "review-source:32a31a96f4b08f4b8147",
        "review-source:97eff58a81cb799d8797"
      ],
      "reviewState": "source-reviewed-relationship",
      "reviewScope": "Source-grounded relationship and status mapping; no new execution or mathematical certification."
    },
    {
      "id": "pattern:alpha-root-existence-uniqueness",
      "titleEN": "The fixed alpha equation already has a global uniqueness proof",
      "summaryEN": "For the original fixed F function, log-convexity of φ proves exactly one positive simple root analytically. This supplements the numerical reciprocal 137.0359992168. The proof holds for every positive budget M, so uniqueness alone does not select M=41.",
      "kind": "source_reviewed_connection",
      "relatedIds": [
        "claim:EM.FP.01",
        "topic:alpha"
      ],
      "conditions": [
        "F(x)=x³−2c³x²+C log φ(x) with the specified seam response and stated positive inputs. The x-dependent response means F is not a cubic polynomial."
      ],
      "counterevidence": [
        "Mathematical root uniqueness is completed; parameter, projector and physical Thomson-transfer provenance is a distinct task. Ledger remains Numerical."
      ],
      "sourceRefIds": [
        "review-source:faea1e7b9127924deb7a"
      ],
      "reviewState": "source-reviewed-relationship",
      "reviewScope": "Source-grounded relationship and status mapping; no new execution or mathematical certification."
    },
    {
      "id": "pattern:website-kernessenz-source-comparison",
      "titleEN": "Website ↔ Atlas ↔ Kernessenz: reviewed source comparison",
      "summaryEN": "The source comparison led to six corrected labels, seven positive connection patterns and the new20-page Kernessenz dated15 October2026. The old25-page PDF remains as historical comparison; the revised editable source is included in the corpus.",
      "kind": "source_comparison",
      "relatedIds": [
        "topic:e8",
        "topic:clocks",
        "topic:flavor",
        "topic:alpha",
        "topic:quantum"
      ],
      "conditions": [
        "Targeted content review on 15 October 2026; source mapping is not a new proof or Lean verification."
      ],
      "counterevidence": [
        "The public website and PDF were not overwritten. Historical attempts and missing contract indexes are not yet fully scientifically reconciled."
      ],
      "sourceRefIds": [],
      "reviewState": "source-reviewed-relationship",
      "reviewScope": null
    },
    {
      "id": "pattern:clock-response-and-charged-discriminator",
      "titleEN": "Clock fields identify the matrix; charged responses identify the twist",
      "summaryEN": "Four actual clock images generate 36 quadratic directions and an exact response inverse. Yet all vacuum words remain twist-blind when each insertion preserves all eight Cartan charges. Eight independent charged response directions (each ±) determine δ at known time scale. This specifies which data can discriminate automated-search candidates. The criterion is tested on the actual native charge field: invariant starts yield equal opposite-charge returns; fixed hopping quarter phases do not change this.",
      "kind": "source_scoped_derivation",
      "relatedIds": [
        "topic:clocks",
        "topic:quantum",
        "topic:origin",
        "contract:clock-jordan-response-reconstruction-20261015",
        "contract:clock-source-twist-transport-20261015",
        "contract:native-charged-conjugation-20261015"
      ],
      "conditions": [
        "Specified free Heisenberg/E8 Fock representation; mixed OPE responses or normalized charged primary preparations and common time scale.",
        "Native lattice/scalar source: original cocycle and hopping, C-invariant start; with fixed link phases an A=CK-invariant start and positive Euclidean return responses."
      ],
      "counterevidence": [
        "Four generating fields are not four measurements. Global charge transport is not a derived local instrument. This does not select the source from P1/P2."
      ],
      "sourceRefIds": [
        "review-source:d0187036f4a9c25d8495",
        "review-source:a468eabcff9bf1899ce2",
        "review-source:2b3dd3f5ecfa5699061a",
        "review-source:caa99b7ab1764e5a3db1"
      ],
      "reviewState": "source-reviewed-relationship",
      "reviewScope": null
    }
  ],
  "attempts": [
    {
      "id": "contract:adiabatic-source-round17",
      "titleEN": "adiabatic-source-round17",
      "questionEN": "adiabatic-source-round17",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:a87c2172c0ac4765d923",
        "source:84e7f5a16ba99e2ce951",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:all-electric-majorant",
      "titleEN": "all-electric-majorant",
      "questionEN": "All-event convergence of the fixed-parent local high-field source",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "FIXED_PARENT_ALL_EVENT_LOCAL_SOURCE_MAJORANT",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:9b582a4af09ae614626b",
        "source:41a48a879ccc931b8b5e",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:atlas-defect-synthesis-20261024",
      "titleEN": "atlas-defect-synthesis-20261024",
      "questionEN": "Can a cross-Atlas projection reconstruct a common original clock, finite quartic channel and operational structure, and which origin choices are actually removed?",
      "date": "2026-10-24",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Original Construction-A E8 with actual J and all60 native Gaussian reflections; original quartic tensor constructors. Separately, the already established same-conformal unitary E8 extension and full inner clock conjugacy with transported marks. Finite CP instruments are classified only on the derived six-effect native H5 POVM. No physical source or spacetime promotion.",
      "sourceRefIds": [
        "source:7f62838920770e547878",
        "source:a6edceeab88fca92d683",
        "source:6549db4493aac7652fa8",
        "source:04319f4840a7a614437f",
        "source:a053e2ba8059f7b9dea9",
        "source:8446c360fb5ff38d9983",
        "source:fbcb1923f73f3d510acd",
        "source:6471f4fb3df87cb9f64a",
        "source:a33418e8a7e55bfce209",
        "source:bbc540703c5e2b9e4bc7",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:actual-clock-doily-ovoid-kernel-is-native-quartic-five",
        "finding:glue-clock-twisted-sectors-share-marked-quadratic-module",
        "finding:complete-native-six-effect-covariant-instrument-classification",
        "finding:native-six-effect-readout-on-existing-erasure-output",
        "finding:relational-quartic-singlet-and-invariant-density-separation",
        "finding:new-clock-feedback-origin-input-audit",
        "finding:native-event-channel-cone-intersection-is-tenth-to-half"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:auxiliary-domain-round14",
      "titleEN": "auxiliary-domain-round14",
      "questionEN": "auxiliary-domain-round14",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:34b28127a78fb5e04aba",
        "source:203249125f067ea25d49",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:auxiliary-dynamics-round35",
      "titleEN": "auxiliary-dynamics-round35",
      "questionEN": "Round35: a standalone 20-state time-local auxiliary model",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "CERTIFIED_20_STATE_TIME_LOCAL_AUXILIARY_REALIZATION",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:0adce0ce17f248c9e829",
        "source:88df73d1a293d8528439",
        "source:894dfcd5467601236833",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:auxiliary-source-obstruction-round18",
      "titleEN": "auxiliary-source-obstruction-round18",
      "questionEN": "auxiliary-source-obstruction-round18",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b17e58c93ebdcbab6b89",
        "source:7ecaef18e8ba55d722f7",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:bulk-word-round47",
      "titleEN": "bulk-word-round47",
      "questionEN": "Round47: controlled cubic bare-column evaluation of the word target",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EVALUATED_CUBIC_BARE_RESUMMED_TARGET_WITH_EXPLICIT_ALL_LATER_M_TAIL",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:17eff05120cca4c2b0e6",
        "source:c29422e08847f7849184",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:canonical-seam-fermionization-20261025",
      "titleEN": "canonical-seam-fermionization-20261025",
      "questionEN": "Do original A4 spin data determine the local NS/quarter dictionary, and does the retained CAR winding admit a complete E8 sector-changing extension in its actual source frame?",
      "date": "2026-10-25",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Literal same-geometric-identification order-four A4 Pin lift; spin-reference longitudinal circle without extra flat gauge holonomy; supplied full CAR/positive-time/fold/cocycle dictionary; standard four-D8-module AIA parent. Complete finite-energy affine extension, not a bounded physical local-net endpoint or physical origin theorem.",
      "sourceRefIds": [
        "source:b4951d11889d1c5cbbdb",
        "source:a38f601f881558accc4d",
        "source:5b01d934187edf9bb877",
        "source:09639cf9a29ba4cb6ac3",
        "source:31248595c9cf3ac533d5",
        "source:467b6b5ddf6f106101cb",
        "source:2fb9226b01e201158a73",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:original-color-center-extends-to-folded-ns-but-full-current-action-needs-spin-sector-transport",
        "finding:a4-spin-lift-fixes-local-ns-and-unordered-quarter-pair",
        "finding:cover-winding-exchanges-quarter-sectors-before-its-square",
        "finding:retained-winding-preserves-local-support-and-neutral-time",
        "finding:marked-glue-square-is-the-e8-fermionization-character",
        "finding:fixed-canonical-d8-is-not-transported-source-d8",
        "finding:actual-winding-has-four-module-e8-defect-extension",
        "finding:ramond-lift-sign-is-common-intertwiner-basis-gauge"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:canonical-shear-round12",
      "titleEN": "canonical-shear-round12",
      "questionEN": "Round12: exact shear, including kinetic terms and observables",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:405a77688194b6ce7b08",
        "source:28cd0c419f4ea97992bf",
        "source:80436ac2405505cb346b",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:carrier-module-conjugation",
      "titleEN": "carrier-module-conjugation",
      "questionEN": "Sind die beiden unorientierten Clifford-/Compiler-Wahlen durch eine carrier-modul-erhaltende E8-Weyl-Symmetrie K äquivalent, und welche mikroskopische Wahl (Feldlift, Nullmoden-Präparation) bleibt ...",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "pass-module-level; microscopic lift open",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:fd50fea5cc53fe925e80",
        "source:a934460c8138f880a469",
        "source:711d5aae561daf4fbf70",
        "source:d90554330870bfd00f20",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:charge-hodge-round18",
      "titleEN": "charge-hodge-round18",
      "questionEN": "charge-hodge-round18",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:efc32b7ea0f88c010a6f",
        "source:eb8261e8eeef73a96e3e",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:charge-momentum-round21",
      "titleEN": "charge-momentum-round21",
      "questionEN": "charge-momentum-round21",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:37e1a39898c91634e68d",
        "source:787cf879347ffa8d0cca",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:charge-propagation-round20",
      "titleEN": "charge-propagation-round20",
      "questionEN": "charge-propagation-round20",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:72fea8afd1f5bb7535f7",
        "source:33b5850ce5f14d9fea00",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:charged-cocycle-lift",
      "titleEN": "charged-cocycle-lift",
      "questionEN": "Charged cocycle lift: the missing dual bits and deck-paired Clifford factors",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "CHARGED_SIGN_REFINEMENT_AND_DECK_PAIRED_CLIFFORD_LIFTS_EXACT_PHYSICAL_BRIDGE_OPEN",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:5af8ee45c782af8fd47c",
        "source:06d28a588ecc220ba161",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:charged-lift-round16",
      "titleEN": "charged-lift-round16",
      "questionEN": "charged-lift-round16",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:dbd37ef1ab55dcac0e99",
        "source:75dfcc502b5bec528074",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:charged-sector-memory-gate-20260920",
      "titleEN": "charged-sector-memory-gate-20260920",
      "questionEN": "Does the same spinor complement generate affine response, Feshbach dressing and memory under the proposed common H=aL0+c; what conditional locality criterion selects sixteen Majoranas?",
      "date": "20260920",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:35ad732925f3d28c3111",
        "source:ff0db429f61e3cf036c8",
        "source:9ca8371936a2b87f490b",
        "source:e7ac26375142cded1d0a",
        "source:92305e01caae430762b4",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:charged-sector-readout-clock-20261013",
      "titleEN": "charged-sector-readout-clock-20261013",
      "questionEN": "Can the original marked E8 charged response realize the alpha factor with exponent5/4 under the same source time and actual clocks?",
      "date": "2026-10-13",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Conditional original E8 lattice-VOA vacuum with marked D5/A3 sector, regularized charged state and actual C/J matrices; no microscopic source selection.",
      "sourceRefIds": [
        "source:619a9c73cbe5dd0b36de",
        "source:47b0e3b9f6e16758b9ae",
        "source:5fcb3085f475d13227d9",
        "source:0ca31b254e3d6f413128",
        "source:1422cecdf94168acf5be",
        "source:b032b80af600d2f58434",
        "source:959eab6330d7ab138d95",
        "source:3c978bb85ad76c53e584",
        "source:fc9fdd48867c90bed8b3",
        "source:b233b1e306e54867289f",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:marked-e8-sector-grade-response-realizes-five-quarters"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:charged-source-time-audit-20260920",
      "titleEN": "charged-source-time-audit-20260920",
      "questionEN": "Does the proposed charged E8 extension preserve the original quarter-holonomy time and actual C/J action, and does a common omitted Q sector alone unite charged algebra with dynamical memory?",
      "date": "20260920",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b8d85d018bb3c08a725e",
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        "source:649b11ffb5705a921040",
        "source:1d37fea6fb5e8ab77379",
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        "source:5c30a4a7a93bd48ac485",
        "source:00bc2bb6a1d251f121ad",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:clock-bilinear-response",
      "titleEN": "clock-bilinear-response",
      "questionEN": "Sind die primitiven Majorana-Bilineare der Clock-Grade exakte Eigenoperatoren der eingefrorenen Quelldynamik, und gibt es am geprüften Quellpunkt eine langsame zahlneutrale Vakuumantwort?",
      "date": "20260908",
      "kind": "contract",
      "status": null,
      "verdictRaw": "finite-dynamics-derived; slow-vacuum-response-null; no-TFPT-selection",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:d79b80b063fc0353c429",
        "source:016c4907b23d01c20dce",
        "source:333d38d046549900ee17",
        "source:46d9f38127bc1b8bfbc0",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:clock-interaction-provenance",
      "titleEN": "clock-interaction-provenance",
      "questionEN": "Woher könnte die quartische Clock-Wechselwirkung stammen – aus der 16-Majorana-Quelle selbst oder aus einem anderen vorhandenen Parent?",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "partial",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:1d2220d70d537dcc3adf",
        "source:aeb966c37f438399436e",
        "source:bce499fdd8520e141789",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:clock-jordan-response-reconstruction-20261015",
      "titleEN": "clock-jordan-response-reconstruction-20261015",
      "questionEN": "Do the four actual clock-carrier fields provide a complete source-defined probe menu for arbitrary neutral quadratic response, including off-diagonal alignment?",
      "date": "2026-10-15",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Original eight-current vacuum Heisenberg sector and same-coordinate C/J/P5; mixed two-point responses to iterated weight-two OPE coefficients. Not a physical detector, charged-sector or complete-source theorem.",
      "sourceRefIds": [
        "source:66bcab259b93699c383d",
        "source:d0187036f4a9c25d8495",
        "source:4e5032ef73f51fa440cb",
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        "source:3e32b1ff1de5d06fd425",
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        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:four-clock-fields-complete-quadratic-response"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:clock-marking-audit",
      "titleEN": "clock-marking-audit",
      "questionEN": "Primitive Clock-Bilineare: Ladung ist keine Verletzung einer Quellen-Symmetrie",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "UNKNOWN",
      "verdictClass": "unknown",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:d5023d04be2e302b7b6c",
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        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:clock-neutral-access",
      "titleEN": "clock-neutral-access",
      "questionEN": "Was ist der kleinste gerade CAR-Grad einer echten O- und N-invarianten Boundary/Clock-Wechselwirkung, und kann ein expliziter quartischer Zeuge das neutrale primitive Gewicht <A*A> aus einer Randko...",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "pass",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:0ce5b12a34aaf2a96298",
        "source:29f7639d941fb4b6d1fc",
        "source:2c1009604b6be905302b",
        "source:5dc8ae5ffcbdbae484a8",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:clock-rotor-joint-charge",
      "titleEN": "clock-rotor-joint-charge",
      "questionEN": "Clock and electric rotor: complete local phase-lift classification",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "LOCAL_CLOCK_ROTOR_LIFT_IS_GAUGE_TRIVIAL_AND_SPECTRALLY_INCOMPATIBLE",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:e5ac3c249c904fa35751",
        "source:bad75f228ebdf8c32a7b",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:clock-shell-round13",
      "titleEN": "clock-shell-round13",
      "questionEN": "Exact clock-assisted constraints for the chosen finite positive model",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:1227471a67706c19b293",
        "source:c45396c6085aad3d7c18",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:clock-source-twist-transport-20261015",
      "titleEN": "clock-source-twist-transport-20261015",
      "questionEN": "Can the actual Gaussian compiler J act on the retained source time, charge, cocycle and uncompensated quarter transition, either in one fixed source frame or covariantly across its twist orbit?",
      "date": "2026-10-15",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact affine fixed-sector obstruction and phase-corrected order-four covariance in the already stipulated even E8 lattice Fock representation. The entire tuple delta, q and quarter-transition cocharacter is transported. This is not a derivation of physical twist sectors, source selection or switching dynamics.",
      "sourceRefIds": [
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        "source:0d947302fd6d571b170b",
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        "source:630d2c35f109f836f1cd",
        "source:29a621625bc6f0f8ccd5",
        "source:fda8320b5b438e5b7bbe",
        "source:44f02fa0b84fb9f7de9e",
        "source:dda280f13b66779aa925",
        "source:28bc4698845b23d24792",
        "source:c64f4bb6f8e381f3ad4e",
        "source:e8354c8ef27edf941b48",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:actual-j-covariant-source-transport",
        "finding:fixed-source-affine-j-obstruction",
        "finding:neutral-vacuum-allword-twist-blindness",
        "finding:eight-charged-responses-reconstruct-twist"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:clock-vertex-round16",
      "titleEN": "clock-vertex-round16",
      "questionEN": "clock-vertex-round16",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:6e3d7dd360509bc633c7",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:cocycle-sign-obstruction-round26",
      "titleEN": "cocycle-sign-obstruction-round26",
      "questionEN": "cocycle-sign-obstruction-round26",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:78c8eaab909331980471",
        "source:099a646851bfc53e6c02",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:coherent-family-round36",
      "titleEN": "coherent-family-round36",
      "questionEN": "Round36: one reduced dynamics for a coherent preparation family",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "COMMON_HERMITIAN_DYNAMICS_WITH_UNIFORM_COHERENT_FAMILY_CERTIFICATE",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:80c7ca798195ccab1821",
        "source:fed16ee1f71b9ad499d9",
        "source:067c4beea62353053fd5",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:collar-current-source-bridge-20261021",
      "titleEN": "collar-current-source-bridge-20261021",
      "questionEN": "Which part of the scalar two-face current bridge survives the original complete Dirac lift, physical boundary domain and chiral-measure identification?",
      "date": "20261021",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:75c126b394c4f7faf0cb",
        "source:1b8187832d1744f4e3af",
        "source:9fdbdf808ebfabccfa5f",
        "source:5acbf6a756147926b8e7",
        "source:49c379970ad114fef545",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:collective-native-marginal-origin-20261026",
      "titleEN": "collective-native-marginal-origin-20261026",
      "questionEN": "Does the actual E8/J native source first distinguish its literal five-code through four-register correlations, and can any <=3-local Hamiltonian select that whole code as its exact ground space?",
      "date": "20261026",
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_SCOPED_FOURTH_MOMENT_AND_MARGINAL_OBSTRUCTION; PHYSICAL_ORIGIN_OPEN",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b265ad99c61d4db55653",
        "source:20118f8f118a3660f03c",
        "source:14fa12dccdb3104a0e3f",
        "source:dcb71f7961bacc08c241",
        "source:c4ab862404b39fe3c5ad",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:native-source-first-nonuniform-moment-is-four-with-literal-five",
        "finding:native-whole-five-ground-space-needs-four-register-interaction",
        "finding:native-fourth-root-frame-has-signed-collective-sixty-mode-dual",
        "finding:native-root-gram-spectrum-is-not-canonical-source-energy-selection",
        "finding:identical-overlapping-native-five-codes-have-no-common-state",
        "finding:horizontal-e8-invariant-octic-cannot-isolate-native-five-ground-space",
        "finding:declared-recursive-native-som-is-u35-equivariant",
        "finding:declared-recursive-native-som-clocks-depend-on-chosen-rates",
        "finding:declared-recursive-machine-baseline-controls-and-recovery-are-finitely-measured",
        "finding:declared-recursive-machine-long-run-retains-motion-at-stable-aggregate-rank",
        "finding:recursive-kohonen-source-investigation-has-source-verified-atlas-handoff"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:common-domain-round14",
      "titleEN": "common-domain-round14",
      "questionEN": "common-domain-round14",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:8523e31d2f6d5a9b2df3",
        "source:f73cc7b4c8bab1c91701",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:common-engine-threeway",
      "titleEN": "common-engine-threeway",
      "questionEN": "Lassen sich die drei Wege – exakter Rotor-Transport mit Rückwirkung, E₈-Rückwärtskonstruktion des Halb-Twists und numerische Robustheit – zu einem gemeinsamen TFPT-selektierten Motor verbinden?",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "NOT_CONSTRUCTED (T1–T8 bleiben offen)",
      "verdictClass": "open",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:564988a60e6302f59c1b",
        "source:0a9c80f1680c7f99e14a",
        "source:d5e41f1db3630b6b5f2a",
        "source:96702f0c469ec4c54ccb",
        "source:2f56413ef0078d7c697d",
        "source:51123aa283dfa2c1204f",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:common-source-gauge-grade-transfer-20260920",
      "titleEN": "common-source-gauge-grade-transfer-20260920",
      "questionEN": "Can the existing E8 edge coframe, graded native cubic, two-source event reduction and phase response supply one source-derived physical interaction, and what precisely prevents the unmodified candidates from doing so?",
      "date": "20260920",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Pinned finite source tensors and a selected extended boundary model. QWZ, E8 edge and compiler source remain distinct constructions. None of the algebraic maps is silently identified with a physical common source.",
      "sourceRefIds": [
        "source:2b3cb0825df93ffd28bb",
        "source:fe99b59ba971520a6309",
        "source:048fd3702be9340b033b",
        "source:75a6f6c5db2f4d40a7be",
        "source:3f0b895f22bf8c3616f3",
        "source:f3877a412e3e48c225cf",
        "source:02d19ec374fd9f6aa710",
        "source:6b1d901ed2aa981d2986",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-bond-response-20260919",
      "titleEN": "compiler-bond-response-20260919",
      "questionEN": "Which two-source bond observables, weak-coupling statements and subsequent three-source binding responses follow exactly from the pinned native source, which global ground claims remain premises, and what affine-current connection is actually defined?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite pair-source observable algebra and grade-one Cartan observable target; pair weak-coupling stability only under the stated full-space Assumption G; numerical evidence only for the full two-source ground theorem. The three-source addendum proves only an invariant two-packet Hamiltonian and one quartic binding line; its global complement theorem remains reported and unreplayed. No Hamiltonian/current-vacuum transport, physical instrument, spatial continuum or TOE gate is claimed.",
      "sourceRefIds": [
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        "source:fef28c10aea703558d53",
        "source:ee42a4cdba27bf5ced49",
        "source:35bd291159784f82ea00",
        "source:3502c88cc4f7e7dc8087",
        "source:861b6105ed3592bc7315",
        "source:4c1e27faec39cc2052cb",
        "source:0214b8945f64d475f931",
        "source:c2c837ae0913adf4342c",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-boundary-selection-20260914",
      "titleEN": "compiler-boundary-selection-20260914",
      "questionEN": "compiler-boundary-selection-20260914",
      "date": "20260914",
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_COVARIANT_BOUNDARY_MARKER_INSTRUMENT_CONDITIONAL_CONSTRUCTION",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:58e635b0209e46aa865c",
        "source:f4d01e887e35dfa55d50",
        "source:092e3944d762600c37d9",
        "source:0e203b5fa481474aae1f",
        "source:275124687fa03d2f69fb",
        "source:fa63ab66427bdc917386",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-clifford-bridge",
      "titleEN": "compiler-clifford-bridge",
      "questionEN": "Compiler-to-Clifford bridge: recovering structure omitted by the scalar prototype",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_COMPILER_CLIFFORD_BRIDGE_WITH_PHYSICAL_EMBEDDING_OPEN",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:6370059a4dc609440029",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-clock-current-closure-20260919",
      "titleEN": "compiler-clock-current-closure-20260919",
      "questionEN": "In the fixed existing D8 current dictionary, does local covariance under the actual C clock force the selected 128-current spinor completion, and does C descend to the old 60 J-orbit labels?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Fixed original v1 E8 Cartan coordinates and the existing D8/Majorana current dictionary. The closure is conditional on a local covariant C implementation. No changed-Cartan or conjugate compact D8 obstruction, no independent chirality selection, no raw source derivation, and no physical detector or event process is claimed.",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-cone-object-audit",
      "titleEN": "compiler-cone-object-audit",
      "questionEN": "Trägt der positive Kegel des integralen Anker-Kommutanten (mit seiner eindeutigen maximalen Ordnung) als gemeinsames physikalisches Compiler-Objekt für alle TFPT-Arbeitsfronten?",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "math-conditional-pass-physics-open",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:abb3fb64f235b3dd4fe5",
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        "source:f9810b28f8d6be98d202",
        "source:5b818dfe7ceb5c2216b8",
        "source:ab5fba4a76b8363de2a8",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-continuous-event-origin-20260919",
      "titleEN": "compiler-continuous-event-origin-20260919",
      "questionEN": "UR.COMPILER.CONTINUOUS_EVENT_ORIGIN.15: Does the submitted interacting continuous endpoint lift work, and does its minimal-positive-log rule follow from native source composition and the recorded frame?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite conditional dynamics and source-provenance tests. Physical generator, refresh, frame and space are not selected. No T1-T8 gate is closed.",
      "sourceRefIds": [
        "source:d2080fa1c9df3d1e1120",
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        "source:2ba8125d3ce22055e255",
        "source:3714d4169d21fd49b46b",
        "source:f71c56683db034e1299f",
        "source:74dbd19caaceabc75e8f",
        "source:dbec82203bcf5bfb5a3e",
        "source:6532cd9afa00832a087a",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-correlated-event-clock-20260919",
      "titleEN": "compiler-correlated-event-clock-20260919",
      "questionEN": "Can the full correlated sixty-event quantum source and a faithful Petersen jump readout belong to one recorded process, while retaining all intervening events and phase bookkeeping?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite source, instrument, histories and recorded readout. No physical TOE, local field dynamics, continuum or native clock selection.",
      "sourceRefIds": [
        "source:5f77475b414a01923d7b",
        "source:4512ceaf97c89f61d7c1",
        "source:c63e9a766366a6dc7423",
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        "source:64aec6b3a0dc3001fba8",
        "source:661c7983e74f8d138c7e",
        "source:cb9ad9e20f0bfb482c35",
        "source:b67d65135a0d4042d780",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-critical-bridge-20260920",
      "titleEN": "compiler-critical-bridge-20260920",
      "questionEN": "Can the .28 critical packet compression be the full native vacuum and carry the marked E8 current/clock dictionary; what actual source structure and controlled current limit survive when that identification is tested?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Continuation toward the common physical source. Exact exclusions apply to specified dictionaries and the bare packet family. Positive frame covariance and Fermi-patch convergence do not select a physical Hamiltonian, vacuum, chirality or complete continuum.",
      "sourceRefIds": [
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        "source:5ae4cbd666475a6b6fdc",
        "source:f3b69ae558062810f098",
        "source:485125781cfc76126d59",
        "source:9d4f55d43157a34d1cfa",
        "source:781bb4fbd8d700faaaf2",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-current-descendant-20260919",
      "titleEN": "compiler-current-descendant-20260919",
      "questionEN": "UR.COMPILER.CURRENT_DESCENDANT.16: Does a graded, charge-compatible and phase-faithful operator map embed Bell10 and all sixty interacting paths into the existing A3_1 / D5_1 / E8_1 structure?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:48313c627fd11e3dd291",
        "source:38c5248e0d35e0c08750",
        "source:82a56f90afb71b60e950",
        "source:497403a8caa13643c7ff",
        "source:89552a29cf28a4008d0b",
        "source:fea476807ed97e9aa7f2",
        "source:744cd39a72f465b2417c",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-current-product-20260919",
      "titleEN": "compiler-current-product-20260919",
      "questionEN": "Do phase-faithful native E8 level-one current products reconstruct the prior quartic Bell source and its readout, beyond equality of one-current effects?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:6851b1c14fe239697a71",
        "source:94dc67e8ee2627437c84",
        "source:14d232f606aaf0777f80",
        "source:1c96bbce775259ecbf46",
        "source:6deda1784d386b2c4210",
        "source:29759e01f0cfa9b09457",
        "source:d5d3b01b48643b093c4f",
        "source:b1b9aa6c168771d1dd8c",
        "source:3ee2e8796ee692d31714",
        "source:4fe18e14f3338214537c",
        "source:7ea2e0e177a82b263670",
        "source:fcb9595de86c07d49c92",
        "source:24aa6f49e20e0f8ff6db",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-domain-wall-core-20260919",
      "titleEN": "compiler-domain-wall-core-20260919",
      "questionEN": "Do the proposed alternating Omega/s chains and domain wall define admissible states and a physical Dirac excitation in the pinned source Hamiltonian, and what exact finite wall dynamics survives the first decisive energy and leakage tests?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite and arbitrary-length tensor statements inside the chosen 240-label source-chain Hamiltonian, plus one copied numerical local resolvent snapshot. The exact Phi-core result is a noninvariant operator compression and the m4 result excludes only the named bare alternating source sectors in the stated weak-coupling regime. No large-chain vacuum, controlled wall EFT, physical Dirac particle, original-source derivation, T1-T8 closure or TOE claim is made.",
      "sourceRefIds": [
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        "source:b61a4a6500801927bdb9",
        "source:a16d2959e9a8c1cf3150",
        "source:f1bcef58384989673407",
        "source:0bff2a88a64734edcdc7",
        "source:2687b4e7eb2efdf77e69",
        "source:61bb9b210f69e764dfc4",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-e6-seam-readout-20260918",
      "titleEN": "compiler-e6-seam-readout-20260918",
      "questionEN": "Can the original seam D4 module be completed to the native SU4 family module and E8 algebra, and does the same operator structure connect 16x4 to 27x3?",
      "date": "20260918",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:44934218a0b6e352ab28",
        "source:eb5b50c223c7b1eafe99",
        "source:2d1d8a42a4e76cba07a6",
        "source:da8892c3ec25dbda62da",
        "source:1b4c70d43bd4c43573b5",
        "source:ef4b1228361f68b0ce74",
        "source:88dc6652f478d1f593da",
        "source:208ed586ac88f5e2c92a",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:recovered-e6-closed-81-current-module-and-unique-source-cubic"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-extension-audit-20260914",
      "titleEN": "compiler-extension-audit-20260914",
      "questionEN": "Sind die im zugesandten Zwei-Qubit-Clifford-Strahlmodell behaupteten Spektren, Faktorisierungen, die CQ-Ausführung, die SU(4)-Vierträgerzelle und die Alpha-Eindeutigkeit exakt verifizierbar – und f...",
      "date": "20260914",
      "kind": "contract",
      "status": null,
      "verdictRaw": "pass-non-rh",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:428ebf7bcd0de79274e5",
        "source:081d8f696ab0bc1f6af3",
        "source:7892bec8e6513f1956a5",
        "source:217aa8d591df3c4966ab",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-four-followups-20260920",
      "titleEN": "compiler-four-followups-20260920",
      "questionEN": "What do the actual E8 clocks select about a common source rule, what operational geometry survives compression, does the full finite m4 vacuum comparison close, and does the unchanged packet grammar produce a controlled large-chain critical candidate?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Four coordinated research follow-ups. Exact finite vacuum closure is restricted to the stated small system and coupling range. Affine current selection has a stated target-space premise. The Ising limit is a noninvariant packet compression, not a physical derivation or full-source effective theory.",
      "sourceRefIds": [
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        "source:7ef008b9306d7f20a729",
        "source:232cfff3699619eb48f6",
        "source:4fbbb86a0e6156376398",
        "source:3e63440dae56aa40209a",
        "source:1661434b9bbf146573b7",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-frame-group-20260919",
      "titleEN": "compiler-frame-group-20260919",
      "questionEN": "UR.COMPILER.FRAME_GROUP.14: Which exact phase-aware finite group is sufficient to carry the .13 recorded frame, and is it the native Weyl D5 group?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite group and readout compression. No physical spatial dimension, Weyl carrier identification, autonomous record or TOE gate follows.",
      "sourceRefIds": [
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        "source:44b0210fee58e0940478",
        "source:7e39af490cbbb6a05433",
        "source:4e3f0b556678fabc04f7",
        "source:4ba9b3013539b62cb851",
        "source:3fbe2d87f04b06d4a19a",
        "source:969e9d6aca700cc37674",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-integral-triality-20260918",
      "titleEN": "compiler-integral-triality-20260918",
      "questionEN": "Does the actual E8 clock representation admit an integral norm-composing triality, and is this structure selected by the source compiler?",
      "date": "20260918",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:5cb6c2e0ef1f4109e684",
        "source:d9e1216450e5ee7dc1fb",
        "source:1b47a2fab0d0dacb8f96",
        "source:959eab6330d7ab138d95",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-involution-types",
      "titleEN": "compiler-involution-types",
      "questionEN": "Two 16D carriers have inequivalent involution types",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "WHOLE_16D_K_TO_INVERTIBLE_SOURCE_REFLECTION_IDENTIFICATION_EXCLUDED",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:bf46b13ec7024bda0f7f",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-kernel-foundation-20260914",
      "titleEN": "compiler-kernel-foundation-20260914",
      "questionEN": "compiler-kernel-foundation-20260914",
      "date": "20260914",
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_SMALL_COMPILER_KERNEL_AND_BRIDGE_BOUNDARIES",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:80610f43dbba9e7bf7d4",
        "source:a960a1cd2e4ec954652c",
        "source:d8d746f16f393a2552fa",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-local-current-origin-20260919",
      "titleEN": "compiler-local-current-origin-20260919",
      "questionEN": "Can the native clocks and the newly supplied coherent coupled-cell construction derive the local rank-eight current source without independent replicas?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact algebra and conditional all-length model theorems. No new physical gate, source-local map, or Theory of Everything. Pasted execution logs were unavailable; formulas and original local source inputs were independently recomputed.",
      "sourceRefIds": [
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        "source:5607cbc86379e4029e29",
        "source:8f04eaf32da1cd31c968",
        "source:43ba6ac5b915887bd401",
        "source:1b93d2fe7b89e68357fd",
        "source:53657bbe9ee4a649edb1",
        "source:4a63efea53c8907f036b",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-native-root-dictionary-20260918",
      "titleEN": "compiler-native-root-dictionary-20260918",
      "questionEN": "Does the integral root-space triality respect the original charged carrier action, and what is the correct native E8 root/CAR/clock dictionary?",
      "date": "20260918",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:71cdc1d9983240da49db",
        "source:3534d91100f8e6ec00af",
        "source:8a6ea7b4cde3d845a411",
        "source:1881e84a4eef2daa8894",
        "source:39b2ed1d512333ec4434",
        "source:8e46c92407fbb0a1bb79",
        "source:e562f8cae668a952940d",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-origin-audit-20260913",
      "titleEN": "compiler-origin-audit-20260913",
      "questionEN": "Welches Zustands-/Ereignismodell beschreibt die im ursprünglichen Compiler vorhandene Übergangsmatrix K=B/7, und ist ihre Quanten- bzw. Zeitvervollständigung durch die Quelle eindeutig bestimmt?",
      "date": "20260913",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:84ed9c9f8dcb1a802d48",
        "source:4101282169ee2777fc40",
        "source:9f596f53b86f86960ddf",
        "source:621b861b79c2cc87f665",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-overlap-phase-lock-20260919",
      "titleEN": "compiler-overlap-phase-lock-20260919",
      "questionEN": "UR.COMPILER.OVERLAP_PHASE_LOCK.19: Does relative source-phase exchange select a unique state on the genuine overlapping two-source ABC chain, and can its state, readout and Hamiltonian be identified with the existing E8 current structure?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:278be273ee408a6ef668",
        "source:f30aba2cbc5e6fe0d395",
        "source:42e2f96f8c890e185623",
        "source:25915397f305e15a1354",
        "source:7fb7f90b5c1847ada213",
        "source:38fe14ab8921b7e67df7",
        "source:a9243daf08cd8dc74176",
        "source:d2f3024c92e2f87a0dde",
        "source:bc35edb7072175136fec",
        "source:2f92985492e54cdfce95",
        "source:57d42362c0b37ee7d3fa",
        "source:0569cf8d53519ce84e6c",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-pair-sector-audit-20260919",
      "titleEN": "compiler-pair-sector-audit-20260919",
      "questionEN": "Which claims in the newly supplied pair-sector formulas are independently reconstructible from the existing native sixty-ray source, and what is their exact connection to the C60 reflection clock and .21 Bell10 readout?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite J=mu=0 results in the named invariant bar4 and mixed 640 sectors, plus an explicit full-240 variational comparison. The actual affine-current phase is retained. No larger full-chain ground theorem, general leakage theorem, physical source process, continuum result, or TOE gate is claimed.",
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        "source:804a3bbfc9a699561c79",
        "source:0bf0682d2829d75f017a",
        "source:e658ae9d187725da93ac",
        "source:e272a54ad635d289b2de",
        "source:5798b948cab4bfcd618d",
        "source:2a93e7c24561950ddb1c",
        "source:f5d69217cd81d916090a",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-paper-v1_2-20260914",
      "titleEN": "compiler-paper-v1_2-20260914",
      "questionEN": "Gesamtpaper v1.2: versionierter Konsolidierungsexport",
      "date": "20260914",
      "kind": "contract",
      "status": null,
      "verdictRaw": "UNKNOWN",
      "verdictClass": "unknown",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:c851322f1ad7aecf69b4",
        "source:4dfc3786a30ab42eccae",
        "source:ab69c453c80ef91ef564",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-process-reconstruction-20260918",
      "titleEN": "compiler-process-reconstruction-20260918",
      "questionEN": "Do the original marked E8 roots give one composition-preserving operation, Choi-state and Lorentz-cone dictionary, and does uniform execution recover the original TFPT transport?",
      "date": "20260918",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:a29cbbac436c16ececc3",
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        "source:185061b3c0baca6087fb",
        "source:bd26b247616034850925",
        "source:18b260e859574dad09c8",
        "source:8a8087d81a3b699cdc53",
        "source:aa1051f697d61837541e",
        "source:d1076b094d4c56f8326e",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-quartic-carry-20260919",
      "titleEN": "compiler-quartic-carry-20260919",
      "questionEN": "Can the native fourth-moment S6 representation be lifted without a Pauli carry, and do the complete composition law and existing population/clock data select physical evolution?",
      "date": "20260919",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite projective Clifford extension and full mu4 word replay; this is not a physical probability law, quantum universality theorem, continuum limit, or TOE.",
      "sourceRefIds": [
        "source:d1d3dcc779c758258663",
        "source:5c40e7d551736480d7f0",
        "source:88d0fb940f482571abb8",
        "source:6c90923d3272a53b080c",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-quartic-holonomy-20260919",
      "titleEN": "compiler-quartic-holonomy-20260919",
      "questionEN": "Does one native source geometry determine both the quartic-carrier and C4-family phase transport needed by the marked D5+A3 E8 glue?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact source-space geometry and finite charged lift. No physical Hamiltonian, vacuum, locality, continuum, affine level or TOE derivation.",
      "sourceRefIds": [
        "source:18f0ef6219dcd0b9ed64",
        "source:286ba65787ba58235174",
        "source:c044dab2b1b97ce3ebbe",
        "source:4cdc104b1a1b05ba63da",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-relational-incidence-20260920",
      "titleEN": "compiler-relational-incidence-20260920",
      "questionEN": "Does the native binding Hamiltonian already change physical incidence, and does its unchanged positive graph extension select connected geometry?",
      "date": "20260920",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Only the stated finite simple labelled graph direct sum with J>=0, kappa>0, mu>=0, no graph hops, no graph offsets and all matchings admitted. No general obstruction to emergent geometry, operational reconstruction, constrained graph ensembles or other native dynamics.",
      "sourceRefIds": [
        "source:39f137dcf4ad6a80b5a4",
        "source:b4cdf2fb5fa8ac0a1bf0",
        "source:f34d6dc906639a193ee0",
        "source:068cc7a04bef3c7b363d",
        "source:d17cc726d448121b36a2",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-relaxed-wall-20260919",
      "titleEN": "compiler-relaxed-wall-20260919",
      "questionEN": "Does the native four-source Phi/Omega core remain a controlled low-energy object after exact H0 relaxation, what native transfer survives, and which full-source classes still block a complete vacuum theorem?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite native-source relaxation, full unperturbed two-source theorem, complete K1 block theorem and final m4 phase reduction in the chosen four-source/five-matter Hamiltonian. K3 energy ordering, the full m4 vacuum, large-chain dynamics, relativistic IR physics and T1-T8 closure remain open.",
      "sourceRefIds": [
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        "source:37cfcf12fabd319a987b",
        "source:0fbf8e7fb69aa361e69d",
        "source:c2a5cef43e88ed0781c8",
        "source:feed1b705e8178b1553b",
        "source:794604a6c06a97088ae4",
        "source:86baa819b4e975582e66",
        "source:08734f0159e9efc437d0",
        "source:aa18bb01742d43d3ff9f",
        "source:3aabd2084f001e316a58",
        "source:112a004c4d0004ca2996",
        "source:74e54b4239e15842a929",
        "source:3ee233a67ca8801c45f4",
        "source:45a0f4ef6d9def441667",
        "source:993067eba876e8ee92f8",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-root-phase-lift-20260919",
      "titleEN": "compiler-root-phase-lift-20260919",
      "questionEN": "UR.COMPILER.ROOT_PHASE_LIFT.18: Can the .17 moving source be made compatible with the native E8 current brackets, and does the existing quartic descendant furnish the common state and readout without an extra source?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:d142d9669ff10564b108",
        "source:93e9aeb7b122b6128783",
        "source:3a1ac19732432a56f4bc",
        "source:cc31027cda8b753f594f",
        "source:c836d430250a24aad3b0",
        "source:b5e4344572642ae15450",
        "source:ea05a311a8c6867565e9",
        "source:85d2755aa1ce2ef53945",
        "source:bc5cd8608e73b20fdb7b",
        "source:d6d89eb0b0238aede363",
        "source:a7d167b1a08a917ef56c",
        "source:c3290607b0940454b92e",
        "source:02fb3a50c92d641e9860",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-root-source-backreaction-20260919",
      "titleEN": "compiler-root-source-backreaction-20260919",
      "questionEN": "UR.COMPILER.ROOT_SOURCE_BACKREACTION.17: Does the full240-root dynamical source have the claimed unique invariant ground, exact gap and backreaction, and can it reproduce the existing correlated event process and current embedding?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b811325b054f6879c524",
        "source:5fbe9ef2d09e4e253e25",
        "source:ff3bdb7c6e4171407869",
        "source:1479a589a2b272591c85",
        "source:98849a9cf5f3a25ce06e",
        "source:1fe61eef26af7e40caad",
        "source:e57a20ec668676a15f36",
        "source:3ca92b3a3f02dd886725",
        "source:66eda46573dbaf1f6158",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-single-execution-20260914",
      "titleEN": "compiler-single-execution-20260914",
      "questionEN": "Erzeugt dieselbe korrigierte Vermittlungsoperation U0 innerhalb des eingefrorenen Ressourcenvertrags ein kohärentes Aufzeichnungsregister, ein kontrolliertes Präparationsfilter ohne vorausgesetztes...",
      "date": "20260914",
      "kind": "contract",
      "status": null,
      "verdictRaw": "NON-RH, alle exakten Checks bestanden (231 eigene + 1073 geerbte), T1–T8 explizit nicht beansprucht",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:1e4a4e87364df1e62bac",
        "source:b52f6bc3153631ff0ad4",
        "source:2793fa990e3c03cf9c63",
        "source:3a944b0006346bcf0a6a",
        "source:16c5215a5a0b4e53a13b",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-source-channel-gate-20260918",
      "titleEN": "compiler-source-channel-gate-20260918",
      "questionEN": "Does the actual one-copy QWZ source yield eight independent local currents, and how does the marked seam deck relate to the established charge-carry clock?",
      "date": "20260918",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:029ad4dadd93e60ceb7e",
        "source:e0629168201f3601e86e",
        "source:23936a42fa784dcfacbf",
        "source:803464bf5d0a11fc25dd",
        "source:bdefa38c6d9f1d98c8fa",
        "source:25194b22a49e940dd550",
        "source:3fe9a8598d6179a2e2d0",
        "source:1165ab5c0889994eaef4",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-spatial-response-20260919",
      "titleEN": "compiler-spatial-response-20260919",
      "questionEN": "Does the source-lock chain support local spatial response, and can the same native quartic readout be linked phase-faithfully to the original E8 current modes and their actual bracket closure?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:322bb88778a4898252aa",
        "source:31ac3d9b6b77b1c2a936",
        "source:03f31d920ef7500414ca",
        "source:c225ce2d0fb305adb364",
        "source:361e79d0227f979f8fd0",
        "source:d7602f232c5b2bb1057b",
        "source:964578464ca2de76c5ba",
        "source:a53a10de8d847bfed354",
        "source:90e2ed7b9af8d5ac5af9",
        "source:e9662b88c58842d3b9cf",
        "source:fc5455252c1f2435fa01",
        "source:d4416446829443c4e47a",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-triality-rigidity-20260918",
      "titleEN": "compiler-triality-rigidity-20260918",
      "questionEN": "Does the actual E8 lattice intrinsically determine the integral graded Clifford carrier, and do its C/J clocks uniquely determine the primitive integral triality?",
      "date": "20260918",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:0a710cbc4436a8f83217",
        "source:1230ac49923384db4ebd",
        "source:83adcf809e636b4827e4",
        "source:09930e22ffc340db61d9",
        "source:2aaca781ddc948889f83",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:compiler-vacuum-current-cubic-20260918",
      "titleEN": "compiler-vacuum-current-cubic-20260918",
      "questionEN": "Does the original affine E8 vacuum leave the preceding D4 family-density freedom in its current response, and does it fix the marked three-family cubic?",
      "date": "20260918",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:3b5ef71b6cc2fb86bf7a",
        "source:4835060df537815031e4",
        "source:976541fb2b33eb54c84d",
        "source:e947c91dfded62221383",
        "source:239da57dee4f9d000c69",
        "source:4f40a0a494c40c1d92bc",
        "source:7d0c2fa134cbb18b31c8",
        "source:26c4fadfb4014511fe11",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:recovered-e6-closed-81-current-module-and-unique-source-cubic"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:constraint-dressing",
      "titleEN": "constraint-dressing",
      "questionEN": "Lässt sich das g^2-Residuum der Constraint-Algebra aus Round 7 durch ein kanonisches Dressing exakt cancellen, und was kostet eine universelle Komplettierung an Lokalität?",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "ORDER_G2_CANONICAL_CONSTRAINT_CLOSURE_EXACT; FORMAL_ALL_ORDER_LIE_COMPLETION; INVERSE_DERIVATIVE_LOCALITY_OBSTRUCTION; NOT_A_LOCAL_GRAVITY_INTERACTION; NON_RH",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:e20a05262d3b66a67c8e",
        "source:6815d77a1592c8c5e1f0",
        "source:daef885a55aa87ba0a9e",
        "source:c42f2c38ea5fc843228f",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:coupled-charge-parent-round19",
      "titleEN": "coupled-charge-parent-round19",
      "questionEN": "coupled-charge-parent-round19",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:5117fc0da6ac6ebd56cc",
        "source:b4e6bd182c2446fe2144",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:coupled-source-domain-round19",
      "titleEN": "coupled-source-domain-round19",
      "questionEN": "coupled-source-domain-round19",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:538c3c035eac70c6f571",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:coupled-trace-round29",
      "titleEN": "coupled-trace-round29",
      "questionEN": "Round29: genuine scalar-charge coupling through a positive trace",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "NONZERO_U_PARTITION_ENCLOSED_AND_GEOMETRIC_SELECTION_BOUNDARY",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:4169eaa0b848f33257ca",
        "source:07daaea7a0249ee99bca",
        "source:fafb81bcd3a65e512776",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:covariant-domain-round13",
      "titleEN": "covariant-domain-round13",
      "questionEN": "Actual constraint-characteristic dynamics: normal form and domain barriers",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b818a1d894daeb8c8a03",
        "source:dbd93b6058935c8bb481",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:cross-domain-synthesis-20261013",
      "titleEN": "cross-domain-synthesis-20261013",
      "questionEN": "Which existing TFPT results constrain a common physical source, and can the existing marked CP channel preserve a fixed three-of-four sector?",
      "date": "2026-10-13",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite M4 CP channel and its conditional correlated (16,4) group lift; uniform P/3 state for each rank-three projector. No identified W48 operator map or physical instrument selection.",
      "sourceRefIds": [
        "source:2b8b6f80c757c6766465",
        "source:e8cdbfa00b5647b014af",
        "source:5e69a2d9a60693142291",
        "source:55dd42631f63157fa4b4",
        "source:2d0242973b6395ee6a6d",
        "source:be3b70bbe1f9940a03ca",
        "source:016c27e9f1709dc74e70",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:cubic-charge-selection-round19",
      "titleEN": "cubic-charge-selection-round19",
      "questionEN": "cubic-charge-selection-round19",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:1f89d4b1bc55d6f3c53f",
        "source:8dae180c58424c34da81",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:cubic-resummation-round44",
      "titleEN": "cubic-resummation-round44",
      "questionEN": "Round44: evaluated full-cubic resummation with all-exit error control",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EVALUATED_FULL_CUBIC_HYBRID_WITH_CERTIFIED_CONFIGURATION_EXIT",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:fdf97142816b9ab527de",
        "source:4a5403c92f61113a1d79",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:current-fourpoint-limit",
      "titleEN": "current-fourpoint-limit",
      "questionEN": "Konvergiert der normal-geordnete geordnete Current-Weyl-Vierpunkt-Kernel für alle sechs neutralen Vorzeichenwörter in L1 auf dem gesamten vierdimensionalen Endpunkt-Torus gegen den expliziten Konti...",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "proved",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:9f5ed76ede43453cdf88",
        "source:fed4dceff7f13503c25e",
        "source:53255a80c0682aeb3da8",
        "source:9ab33f6f1837f9ff54f3",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:current-truncation-bridge",
      "titleEN": "current-truncation-bridge",
      "questionEN": "Konvergiert die endliche Fock-Galerkin-Kompression der Referenzstrom-Determinante gleichmäßig in den Endpunkten (inklusive Zentralphase) gegen das Strom-Zweipunktfunktional C_t^cur?",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "pass",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:78fd9a333f8c70954648",
        "source:6a551d02e753c9fb5e18",
        "source:93b6b68776758126f6ec",
        "source:29391df5eb075dbb23f5",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:cy-joint-equivariance-round11",
      "titleEN": "cy-joint-equivariance-round11",
      "questionEN": "Round11: simultaneous elliptic clock and inversion",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:6a9679651677366e61f2",
        "source:53404ea59284636036f6",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:cy-seam-round10",
      "titleEN": "cy-seam-round10",
      "questionEN": "CY seam continuation — Round 10",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:3d070eb4af470a68e81e",
        "source:b817199b0263452aab86",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:det-wall-hh-rule",
      "titleEN": "det-wall-hh-rule",
      "questionEN": "Die fehlende HH-Regel ist die Onsite-DET-Wand: exakte Reduktion",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "DET_WALL_HH_RULE_CONDITIONAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:d1d309b8f4c74f7af902",
        "source:0c1e339703241a78660e",
        "source:93618fd2ccbcc8597f20",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:direct-defect-round48",
      "titleEN": "direct-defect-round48",
      "questionEN": "Round48: direct full-H defect certificate for the pinned cubic column",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "DIRECT_FULL_H_DEFECT_CERTIFIES_PINNED_BULK_COLUMN_MORE_TIGHTLY",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:2233b327fe56797f9463",
        "source:0245983403d84e1a1004",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:dressed-hopping-round21",
      "titleEN": "dressed-hopping-round21",
      "questionEN": "dressed-hopping-round21",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:45a3b0969e7073f09a03",
        "source:26875f4dd3657b6b75fd",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:e-series-compiler-closure-20261023",
      "titleEN": "e-series-compiler-closure-20261023",
      "questionEN": "Complete the four compiler follow-ups: full lattice-field lifts of E7 pairs, all E6/E7 compatibility with the native D5+A3 split, exact common covers and actual clock intertwiners, and a common representation dictionary for the existing48,4/3 and5/4.",
      "date": "2026-10-23",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Fixed original E8 lattice, epsilon, Gaussian J, D5+A3 compiler split, neutral4/5/20 and existing marked cyclic covers and Burau matrices. All four comparisons are solved in this declared mathematical category. The established P1/P2 compiler and seed derivations are retained.",
      "sourceRefIds": [
        "source:15eb891084c8840831ad",
        "source:9197b7fd243cb772136b",
        "source:a5de821a6e52ad558cc9",
        "source:445238d403d18a2825be",
        "source:874a67603a95d39e80a6",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:e7-pair-full-lattice-field-character-torsor",
        "finding:e-series-complete-native-compiler-cut-dictionary",
        "finding:common-cover-clock-and-maximal-integral-phi12-intertwiner",
        "finding:native-four-cut-projectors-unify48-fourthirds-fivequarters"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:e-series-incidence-algebra-20261024",
      "titleEN": "e-series-incidence-algebra-20261024",
      "questionEN": "Close the supplied independent E6/E7/E8 finite incidence classification against the original marked field lifts and global cover monodromies, and identify whether the tetrahedral incidence retains all E6 information.",
      "date": "2026-10-24",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Standard E8 roots, regular A2-normal E6 and root-normal E7 systems, actual Weyl action on transported full D5+A3 compiler flags; original cocycle and fixed Jhat sign-lift equivalence; original induced Burau deck local system. No physical-origin or corner-selection claim.",
      "sourceRefIds": [
        "source:c1d7fa9a12cac8b737c8",
        "source:a5e8fbbe1d87f020b56f",
        "source:f7d49f149943232c8957",
        "source:ae8441b5b27ea1d7a17f",
        "source:956a4ec9eb55d44f418c",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:e8-cut-five-orbital-incidence-algebra-complete",
        "finding:compiler-d8-frame-requires-full-d5-a3-flag",
        "finding:tetrahedron-incidence-lossless-e6-reconstruction",
        "finding:restricted-clock-lift-and-global-cover-audit-reconciled"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:e-series-joint-source-20261023",
      "titleEN": "e-series-joint-source-20261023",
      "questionEN": "Determine the complete joint mathematical compatibility object of the existing compiler flags, E7 pair operations, full lattice fields and marked covers, preserving their actual transitions and all previously proved obstructions.",
      "date": "2026-10-23",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Fixed original E8 lattice VOA and epsilon, native D5+A3 compiler flags, J/sigma/c/Y, quartic/erasure diagram, existing oriented C2/C3/C4 covers and retained Burau deck module. Transition groups transport marks. Cyclic field lift equivalence is character gauge fixing Jhat. The Burau local system used in the peripheral comparison is induced from its supplied marked cover and deck representation, not an independently geometric Gauss-Manin family.",
      "sourceRefIds": [
        "source:5247590bb48b44bcb798",
        "source:7571e0e83aaaf47a1597",
        "source:4a80e16c54491c161db7",
        "source:0209b84b27b69cb7fccb",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:complete-covariant-compiler-voa-source-and-weyl-closure",
        "finding:complete-fixed-jhat-cyclic-field-lift-and-associated-clock",
        "finding:relative-native-burau-clock-hom-faithful12-transport",
        "finding:e6-vertex-nonselection-survives-full-field-clock-phases"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:e-series-quarter-clock-20261023",
      "titleEN": "e-series-quarter-clock-20261023",
      "questionEN": "How do the original E6/E7/E8 windows and regular root slices interact with the actual Gaussian quarter clock and the original G31 reflections?",
      "date": "2026-10-23",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Fixed standard E8 root lattice and actual J with J^2=-I. Root slices, full E7-pair bracket/lattice closure, integral glue quotients, intrinsic square-curve family and double-cover descent for the supplied all-J local system. Normalization prescriptions compared conditionally. No arbitrary Lie-subalgebra embedding classification, no noncentral lift-class result or P1 normalization derivation.",
      "sourceRefIds": [
        "source:220b96ebf4e1b1e13d5d",
        "source:06a68502c0177d935f86",
        "source:449342bfa4a41f50c9ff",
        "source:75121c9086d56f99d823",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:e7-quarter-pairs-literal-native-g31-reflections",
        "finding:e6-root-subsystem-quarter-clock-discriminant-obstruction",
        "finding:e-series-square-cover-family-and-quarter-descent",
        "finding:e-series-integral-glue-and-normalization-nonidentifiability"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:e-series-source-reconstruction-20261024",
      "titleEN": "e-series-source-reconstruction-20261024",
      "questionEN": "Reconstruct the canonical local E8 field completion from the already established marked D5+A3/C4 compiler glue; determine which original source and dynamics implications are actually proved.",
      "date": "2026-10-24",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Fixed unitary U=V_D5 tensor V_A3 and marked h=(1,1) in its discriminant C4xC4. All connected local unitary VOA extensions sharing its conformal vector are classified: U, V_D8 and two labelled V_E8 extensions over fixed U. Occurrence of M_h forces the diagonal V_E8, with support and multiplicities derived rather than assumed. Primitive P1 membership in this local conformal realization is not derived. Historical source/domain audits retain their stated hypotheses.",
      "sourceRefIds": [
        "source:86c61aa0e7ee8e6c877a",
        "source:e9cb2b32f2b4575c7693",
        "source:5a005205710ce43310ad",
        "source:3bab84c798bce374fa3a",
        "source:d9312817fbf668265c80",
        "source:0e187c258468a55ecbcf",
        "source:841454d6328e5e03da79",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:original-minimality-does-not-reconstruct-operational-source",
        "finding:generic-first-order-relative-bound-zero-counterexample-and-correct-domain-repair",
        "finding:normal-clutch-orbit-index-equivariantly-recovers-given-weak-module",
        "finding:charged-scaling-microscopic-map-still-unspecified",
        "finding:original-slater-proxy-fitted-bound-fails-actual-norm",
        "finding:periodic-microscopic-zero-modes-distinguish-source-state",
        "finding:marked-c4-glue-unique-local-e8-vacuum-source",
        "finding:canonical-vacuum-clock-preserves-e6-nonselection",
        "finding:marked-generator-forces-e8-without-support-multiplicity-or-minimality-input",
        "finding:double-scalar-quarter-is-marked-glue-with-two-step-index",
        "finding:scalar-quarter-two-involutive-e8-extensions",
        "finding:native-quarter-glue-inner-conjugacy-and-oriented-tetrahedron-flags",
        "finding:native-cyclic-compiler-inner-conjugacy"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:e8-octic-mark-selection-20261013",
      "titleEN": "e8-octic-mark-selection-20261013",
      "questionEN": "Does extremizing the first anisotropic native E8 root moment S8 choose the natural 5+3 and3+2 marking vectors, and how does this compare with finite order4 holonomy?",
      "date": "20261013",
      "kind": "contract",
      "status": null,
      "verdictRaw": "REFUTED",
      "verdictClass": "refuted",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Only specified natural marking vectors and scalar S8 extremization; no general exclusion of source symmetry breaking or tensor/group-valued selectors.",
      "sourceRefIds": [
        "source:b1974395f22a513af1fc",
        "source:d346898a878dc63dd37d",
        "source:2baa7683845d334ec6c1",
        "source:fb181cc849a84e12ed35",
        "source:25d2605d71588ca3cb57",
        "source:ebf7ab6a0e2a8630d162",
        "source:0c34d2a0a611fcd70531",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:electric-propagation-round42",
      "titleEN": "electric-propagation-round42",
      "questionEN": "Round42: propagated electric sources and a fifth-order error bound",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EVALUATED_MEM_MME_WITH_FIFTH_ORDER_REMAINDER",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:dfb30df7ace30f59cbce",
        "source:0e793b3b5a7bbb9792eb",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:electric-source-round41",
      "titleEN": "electric-source-round41",
      "questionEN": "Round41: nonlinear electric source and a certified correlation witness",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EVALUATED_NONLINEAR_ELECTRIC_SOURCE_WITH_THREE_SITE_RESPONSE_CEILING",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:0cdc884ffe0aecef6bfa",
        "source:d80ae5f40893efe95df2",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:elliptic-moebius-source-bridge-20261026",
      "titleEN": "elliptic-moebius-source-bridge-20261026",
      "questionEN": "Realize the existing elliptic parity cover as the Moebius orientable double and reproduce the old NS/quarter boundary source without fitted phases or temperature.",
      "date": "2026-10-26",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Supplied marked square C2 curve with the full lifted base D4 including r=(1/x,i y/x^2), raw flat spin data and expressly free chiral CAR quantization. The full equatorial pullback is a ramified V4/E8 graph, not the old smooth seam circle. The boson-spin pushforward has the P2 holomorphic splitting but a different local cusp connection. Primitive physical source/measure/time and index response are not derived. Continuation: complete holomorphic NS NS Szego spin trace on the actual four-mark carrier, and phase-normalized modular theta-square representation with an exact common v117 intertwiner. Geometric Q is modular S, whereas v117 U matches modular T. Holomorphic kernels are not automatically positive equal-time CAR covariances. Current real-boundary continuation retains actual half-form L2 trace, oblique versus orthogonal Cauchy distinction and fixed-reflection counterexample only on specified free checkerboard algebra. Recovered28Sep proof analytically closes actual v115/v117 ODE through (4,3,2) C4 quotient with U inverse marking; actual puncture image A4 differs from extended S4. Genuine D4 theorem applies to a distinct marked connection. Wall splitting does not exclude stable v117 parabolic bundle. Negative q two-torsion packet and its actual C4 lift identify exact coefficient source. Minimal common root/sign cover has degree48, A4 times C4 group and genus41; geometric quarter differs from commuting compiler clock. Source theta continuation: minimal six-line completion, unique cubic-invariant even S0 and selected beta; Pauli translations rather than Gaussian code contexts. Joint finite lift under imposed beta->J is one centralizer conjugacy class, not automatically physical gauge. Ordinary rigidified determinant-of-cohomology has chi0 and loses spin central sign. Canonical S0-relative Poincare normalization trivializes full marked q norm family via O(Dq)=S0^3. One inverse norm copy restores central phase geometrically. Original boundary selection of that one-copy operation remains open; no physical gate promotion. Continuation27Oct: original z has divisor Dq-Dp and unit winding selects exactly one inverse norm in the explicitly defined relative spin/reference Hardy cable. Physical D_rel/D_ref coefficient and state/polarization identity is not inferred.",
      "sourceRefIds": [
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        "source:6096bf4615dcb2481f9d",
        "source:6dfdc485cc476af30aef",
        "source:221bdb2402f0181d92c9",
        "source:6b6ced3be17581130232",
        "source:0b64f530a71c239ec104",
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        "source:47b47e845c1fed8e0b40",
        "source:d199b2de05e51e8e1f39",
        "source:ed70660883ea11f7ae3a",
        "source:2db4e6a3191e32e46622",
        "source:58ce23cbc8025652b339",
        "source:7186dd0532a2438670ab",
        "source:ab50ee143df89ad84a4d",
        "source:911ab9fc7f23593bee33",
        "source:27acf4bccad55f423bc6",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:quarter-cover-pairing-does-not-supply-local-normal-or-select-scale-measure",
        "finding:e8-hodge-event-perfectly-distinguishable-from-every-unitary",
        "finding:common-five-slot-transfer-preserves-e8-bracket-not-automatic-tp",
        "finding:e-series-operational-role-review-and-source-time-centralizer",
        "finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower",
        "finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent",
        "finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms",
        "finding:finite-crosscap-cauchy-state-is-not-original-quarter-vacuum-by-normal-filtering",
        "finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots",
        "finding:full-marked-equatorial-pullback-is-ramified-graph-not-smooth-seam-circle",
        "finding:same-elliptic-szego-green-functional-has-all-word-free-rp-and-calderon-marginal",
        "finding:elliptic-scalar-spin-pushforward-has-original-holomorphic-p2-anchor",
        "finding:natural-elliptic-anchor-connection-is-not-original-p2-cusp-connection",
        "finding:elliptic-ns-spin-trace-has-complete-global-quarter-kernel",
        "finding:source-induced-ramified-resolutions-do-not-select-quarter-circle-domain",
        "finding:fixed-native-and-fermat-c3-carriers-do-not-identify-marked-v117-pair",
        "finding:theta-square-modular-pair-reconstructs-v117-with-distinct-geometric-q",
        "finding:archived-d4-puncture-formula-fails-and-existing-v117-repairs-existence",
        "finding:geometric-square-clock-is-not-theta-v117-quarter-generator",
        "finding:actual-equatorial-half-form-trace-fixes-orthogonal-hardy-range",
        "finding:actual-holomorphic-quarter-cauchy-idempotents-are-not-positive-car-covariances",
        "finding:full-equatorial-checkerboard-free-algebra-fails-fixed-reflection-positivity",
        "finding:genuine-d4-orbifold-branch-has-unique-irreducible-v117-class",
        "finding:wall-weight-additivity-does-not-exclude-stable-v117-parabolic-bundle",
        "finding:recovered-september-c4-triangle-closes-original-a0star-monodromy",
        "finding:actual-a0star-connection-does-not-have-rational-base-inversion-lift",
        "finding:actual-v117-sign-lines-are-negative-weierstrass-triangle-two-torsion",
        "finding:antipodal-and-positive-sign-packets-fail-actual-marked-v117-ramification",
        "finding:common-cyclic-twelve-cover-does-not-trivialize-v117-unramified-sign-lines",
        "finding:negative-sign-packet-has-source-selected-quarter-clock-lift",
        "finding:original-root-and-sign-lines-have-minimal-degree48-common-cover",
        "finding:source-inversion-forces-six-line-theta-completion",
        "finding:literal-geometric-quarter-is-not-central-gaussian-quarter-on-labels",
        "finding:source-cubic-and-quarter-select-even-theta-and-spin-half-turn-lift",
        "finding:source-cubic-matches-native-pauli-translations-after-context-target-correction",
        "finding:joint-source-clock-relations-have-one-native-clifford-gauge-class",
        "finding:ordinary-theta-determinant-erases-selected-spin-central-character",
        "finding:marked-negative-point-norm-restores-required-spin-central-character",
        "finding:point-normalized-theta-family-correction-fails-original-cubic-action",
        "finding:source-spin-relative-poincare-normalization-closes-point-norm-family",
        "finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package",
        "finding:tfpt-origin-investigation-full-source-coverage-and-current-frontier",
        "finding:full-clock-norm-power-class-and-canonical-eighth-period",
        "finding:original-unit-winding-selects-one-inverse-norm-in-three-cabled-hardy-pair",
        "finding:original-boundary-audit-and-h1-point-restriction-limit",
        "finding:eta-phase-conventions-do-not-identify-relative-spin-reference-pair",
        "finding:same-spin-unit-shift-gives-native-module-class-with-odd-determinant-line",
        "finding:original-even-odd-operator-split-is-compatible-with-same-spin-seam-reference",
        "finding:elliptic-projector-and-weyl-results-retain-their-source-type-at-cubic-spin-bridge",
        "finding:cubic-spin-cauchy-range-is-three-hardy-with-strong-domain-distinction",
        "finding:original-negative-sea-three-mode-ket-is-dual-to-required-hardy-line",
        "finding:auxiliary-theta-route-needs-no-physical-cubic-bulk-or-eta-selected-dual",
        "finding:primitive-gaussian-theta-frame-constructs-e8-pair-with-retained-spin-action",
        "finding:existing-c12-lift-induces-coherent-two-object-e8-vertex-groupoid",
        "finding:actual-winding-functional-calculus-preserves-ns-ramond-split",
        "finding:single-chiral-cycle-exchange-selects-e8-in-four-extension-class",
        "finding:affine-source-involution-pairs-full-d8-sector-spectra",
        "finding:marked-local-e8-with-unchanged-source-time-fails-euclidean-clustering",
        "finding:original-parity-audit-does-not-supply-local-spinor-gauging",
        "finding:hypergraph-local-update-repaired-with-full-family-clock",
        "finding:petersen-polar-step-has-exact-double-cover-family-intertwiner",
        "finding:petersen-source-current-and-hodge-candidates-fail-physical-identification",
        "finding:a7-clock-direction-identifies-neutral-e7-zero-root",
        "finding:oriented-sewing-cocycle-distinguishes-continuation-and-reversal",
        "finding:calderon-single-face-compression-is-not-perron-projector",
        "finding:hodge-born-magnitudes-and-filtered-petersen-jump-match",
        "finding:five-complement-amplitudes-form-full-petersen-quantum-channel",
        "finding:original-twenty-events-factor-through-hodge-and-conditional-phase-record",
        "finding:actual-e8-mixed-current-response-is-full-clifford-channel",
        "finding:carrier-su5-centralizer-gives-direct-e8-petersen-response",
        "finding:su5-covariance-and-petersen-support-fix-complete-quantum-response",
        "finding:neutral-pair-witness-separates-old-events-and-hodge-response",
        "finding:original-degree-clock-is-not-carrier-slot-cycle-at-fixed-source",
        "finding:full-mark-transport-and-isospectrality-do-not-select-hodge-channel",
        "finding:original-pair-source-fixes-state-but-not-selected-epsilon-process",
        "finding:single-positive-process-saturation-selects-full-hodge-channel",
        "finding:original-five-slot-wedge-is-exact-e8-hodge-coefficient",
        "finding:native-pauli-f20-metric-and-quarter-bridge",
        "finding:two-actual-coherent-events-herald-hodge-at-one-over-twenty-five",
        "finding:original-color-center-removes-only-extra-h8-ground-state",
        "finding:marked-symplectic-functor-fixes-native-hodge-kraus-space",
        "finding:f20-record-repair-removes-chart-induced-three-plus-two",
        "finding:theta-scalar-square-lift-is-distinct-from-symplectic-f20-lift",
        "finding:full-admissibility-vacuum-test-needs-source-image-and-transfer-reduction",
        "finding:canonical-native-spin5-hodge-is-already-one-source-record-subchannel",
        "finding:native-hodge-record-selector-is-image-projector-not-kraus-kernel",
        "finding:irreducible-f20-four-cannot-host-original-independent-native-family-clock",
        "finding:native-hodge-is-exact-collective-five-current-action",
        "finding:six-ovoid-clock-bundle-replaces-unnecessary-fixed-form-condition",
        "finding:six-hodge-responses-have-exact-full-current-barycenter",
        "finding:coxeter-seventh-power-has-complete-thirty-e8-lattice-lifts",
        "finding:spin5-hodge-five-is-plucker-kernel-not-original-quartic-hessian",
        "finding:ising-complement-current-mechanism-needs-typed-normal-field-map",
        "finding:neutral-native-a3-hodge-does-not-identify-physical-p2-carrier",
        "finding:compact-ope-coevaluation-normalizes-given-charged-hodge-line",
        "finding:old-ward-root-generates-exact-charged-fifty-module",
        "finding:tp-charged-bracket-support-forces-entire-carrier-marginal",
        "finding:original-ward-and-p2-grading-select-smaller-creation-thirty",
        "finding:charged-source-quarter-recovers-inverse-internal-glue",
        "finding:state-independent-creation-branch-removes-whole-process-hodge-demand",
        "finding:given-source-current-constructs-half-kink-spinor-transport",
        "finding:neutral-ward-response-needs-no-spinor-observable-membership",
        "finding:actual-source-sector-transport-distinguishes-identical-hodge-marginals",
        "finding:ordinary-weyl-type-obstruction-to-single-chiral-os-anti-anti-reflection",
        "finding:given-two-face-source-derives-opposite-neutral-weyls-and-bounded-time-reflection",
        "finding:verification-recovery-preserves-local-source-chain-and-eight-gate-completeness",
        "finding:positive-spectral-reweighting-does-not-establish-original-source-rp",
        "finding:gapped-quarter-energy-cannot-be-same-borchers-translation",
        "finding:finite-ko6-pairing-does-not-supply-standalone-pfaffian-source",
        "finding:full-free-projector-forces-joint-commuting-source-factorization",
        "finding:actual-neutral-current-source-has-constructive-moebius-standard-pair",
        "finding:continuous-local-current-weyls-cannot-live-in-finite-coordinate-fibers",
        "finding:petersen-population-full-cptp-p5-range-zero-to-ten",
        "finding:marked-sm-phase-p5-exact-range-and-response-collision",
        "finding:shared-epsilon-tp-process-fixes-hodge-marginal-even-for-correlated-inputs"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:em-positive-root-convexity-20261013",
      "titleEN": "em-positive-root-convexity-20261013",
      "questionEN": "Can the fixed original EM closure function be proved to have exactly one simple positive root without relying on the numerical derivative scan?",
      "date": "2026-10-13",
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      "titleEN": "equivariant-monodromy-20261023",
      "questionEN": "Determine strict, peripheral and equivariant central lifts; evaluate all original G31 quarterclocks, integral monodromies, and compare actual sign-lift and reflection groups.",
      "date": "2026-10-23",
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      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
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      "scopeEN": "Original 60 G31 reflections, four ordered punctures, 17 simultaneous conjugacy classes, 62 exact-order-four clock markings; existing central Z4 extension with determinant cocycle. Relaxed transport equations and equivalence are explicitly defined. No identification with noncentral lattice lifts or the effective diagonal quotient.",
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        "finding:actual-sign-lift-g31-group-comparison",
        "finding:complete-g31-lift-invariants-and-explicit-collisions"
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:escape-round14",
      "titleEN": "escape-round14",
      "questionEN": "escape-round14",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:f4-modular-period-readout-20260914",
      "titleEN": "f4-modular-period-readout-20260914",
      "questionEN": "F4 modular period readout: native compiler lane (factorization firewall)",
      "date": "20260914",
      "kind": "contract",
      "status": null,
      "verdictRaw": "BLOCKED_MISSING_NATIVE_COMPILER",
      "verdictClass": "fail",
      "stage": null,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:family-symmetry-gateb-20261005",
      "titleEN": "family-symmetry-gateb-20261005",
      "questionEN": "Which family group can be an exact symmetry of the common source process at the moment the Gate-B interaction acts?",
      "date": "20261005",
      "kind": "contract",
      "status": null,
      "verdictRaw": "REAL_FAMILY_GROUP_REQUIRED",
      "verdictClass": "other",
      "stage": null,
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      "reviewState": "inventoried-not-reviewed",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:finite-density-background-round24",
      "titleEN": "finite-density-background-round24",
      "questionEN": "finite-density-background-round24",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
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      "reviewState": "inventoried-not-reviewed",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:firstclass-completion-round14",
      "titleEN": "firstclass-completion-round14",
      "questionEN": "firstclass-completion-round14",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:fixpoint-ward-frontier-20260917",
      "titleEN": "fixpoint-ward-frontier-20260917",
      "questionEN": "Fixpunkt-Ward-Suche auf drei Frontier-Ziele — 17. September 2026",
      "date": "20260917",
      "kind": "contract",
      "status": null,
      "verdictRaw": "TRIVIAL_FROM_EXISTING_E",
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      "stage": null,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:fixpoint-ward-mpratio-20260917",
      "titleEN": "fixpoint-ward-mpratio-20260917",
      "questionEN": "Fixpunkt-Ward-Suche für m_p/m_e — 17. September 2026",
      "date": "20260917",
      "kind": "contract",
      "status": null,
      "verdictRaw": "NO_CANDIDATE",
      "verdictClass": "candidate",
      "stage": null,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:foundational-process-classification-20261016",
      "titleEN": "foundational-process-classification-20261016",
      "questionEN": "Which joint structural consequences follow from four independently defined finite process classes, with TFPT used only for later comparison?",
      "date": "2026-10-16",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL_COMPOSITION_THEOREM_AND_OBSERVABILITY_COUNTERMODELS_NO_PHYSICAL_SELECTION",
      "verdictClass": "partial",
      "stage": null,
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        "finding:three-inequivalent-repeatable-observation-countermodels",
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        "finding:finite-sequential-data-admit-classical-history-realization"
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:free-scalar-3d",
      "titleEN": "free-scalar-3d",
      "questionEN": "Round 8 — full-3D free-scalar Ward complex on the staggered regulator",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_FREE_MATTER_THEORY_CONTRACT_UNPROMOTED",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:full-constraint-parent-round17",
      "titleEN": "full-constraint-parent-round17",
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      "status": null,
      "verdictRaw": "PASS",
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:full-reference-control-round27",
      "titleEN": "full-reference-control-round27",
      "questionEN": "full-reference-control-round27",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
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      "sourceRefIds": [
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:galerkin-control-round14",
      "titleEN": "galerkin-control-round14",
      "questionEN": "galerkin-control-round14",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
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      "historical": true,
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:gaussian-vacuum-filter",
      "titleEN": "gaussian-vacuum-filter",
      "questionEN": "Kann ein allein aus dem Quell-Hamiltonian abgeleiteter Gauß-Filter mit Eichrampen-Kompensation den Zielsektor-Vakuum-Energieüberschuss ohne Zusatzsektor zum Verschwinden bringen, und was bleibt dab...",
      "date": "20260908",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS-UNSCALED / BLOCKED-Fock-implementability",
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      "stage": null,
      "evidenceClass": null,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:global-g31-lattice-lift-20261023",
      "titleEN": "global-g31-lattice-lift-20261023",
      "questionEN": "Decide splitting of the actual character-valued lattice lift extension over all original G31; completely classify lifts of the original17monodromies and62quarterclock objects.",
      "date": "2026-10-23",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Original E8 lattice cocycle and A=Hom(E8,Z2) with nontrivial coefficient action. Global G31 extension, inclusion-minimal16element witness, all22proper subgroup restrictions, ordered original reflection monodromies and exact-order4clock markings. Inner conjugation in the full lift group. No scalar-central replacement and no extra order2relation for lifted puncture meridians.",
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      "id": "contract:ground-state-loop-response",
      "titleEN": "ground-state-loop-response",
      "questionEN": "Ground-state coercivity and nontrivial low-energy Wilson response",
      "date": null,
      "kind": "contract",
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      "verdictRaw": "FIXED_PARENT_SHARPENED_GROUND_COERCIVITY_AND_LOW_ENERGY_WILSON_SPECTRAL_WEIGHT",
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      "stage": null,
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      "historical": true,
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    },
    {
      "id": "contract:half-charge-energy-bridge",
      "titleEN": "half-charge-energy-bridge",
      "questionEN": "Kann die Quellholonomie auf dem konditionalen E8-Ziel beibehalten werden, sodass der verschobene Generator H_sigma dieselben polynomialen Energie-Domänen wie der konforme Standardgenerator L0 liefe...",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "CONDITIONAL_TARGET_ENERGY_DOMAIN_BRIDGE",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
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      "historical": true,
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:half-loop-source-transport",
      "titleEN": "half-loop-source-transport",
      "questionEN": "Lässt sich auf dem vorhandenen Zustandsraum des kleinen Rotor-Parents ohne neue Sektoren ein energieverträglicher Halb-Schritt S mit S²=W konstruieren, und besteht er die Halb-Ladungs- und die präz...",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "partial",
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      "stage": null,
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      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:half-twist-grade-carry",
      "titleEN": "half-twist-grade-carry",
      "questionEN": "Trägt der als Halb-Twist realisierte Ordnung-4-Glue-Vektor auf dem realen QWZ-Zylinder einen echten ganzzahligen Ladungs-Carry, und verschwinden die bei Einschränkung auf eine Kante entstehenden De...",
      "date": "20260908",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
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      "sourceRefIds": [
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      "historical": true,
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:higher-electric-round45",
      "titleEN": "higher-electric-round45",
      "questionEN": "Round45: next electric sources with controlled fifth-order matching",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EVALUATED_NEXT_ONE_E_AND_FIRST_TWO_E_WITH_SIXTH_ORDER_IDEAL_REMAINDER",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:historical-two-phase-source-20260919",
      "titleEN": "historical-two-phase-source-20260919",
      "questionEN": "Does the historical a_top != a_QCD distinction survive the scoped same-field bound, and what exact rank-one condition is necessary for a photon-active QCD-flat phase?",
      "date": "20260919",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Historical source distinction plus a conditional local quadratic two-phase theorem and a same-field necessary energy bound; no source selection, complete dynamics, physical spacetime, or empirical fit.",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:history-determinant-solver-round25",
      "titleEN": "history-determinant-solver-round25",
      "questionEN": "Exact per-history scalar determinant and solve with cyclic temporal closure and signed original physical updates; O(T d^3) arithmetic only.",
      "date": "2026-09-07",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact per-history scalar determinant and solve with cyclic temporal closure and signed original physical updates; O(T d^3) arithmetic only.",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:history-reference-transport",
      "titleEN": "history-reference-transport",
      "questionEN": "Kann eine endliche quell-polarisierte Referenz mit exakt identischer neutraler Determinante, aber kleinerer voller History-Distanz konstruiert werden, und welche hinreichende Rate I_N folgt daraus ...",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "construction-proved-rate-unproven",
      "verdictClass": "pass",
      "stage": null,
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      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:history-sum-control-round26",
      "titleEN": "history-sum-control-round26",
      "questionEN": "Absolutely convergent neutral history expansion and certified finite tails at fixed finite spatial and Euclidean time regulator in original g=0 scalar/charge model.",
      "date": "2026-09-07",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Absolutely convergent neutral history expansion and certified finite tails at fixed finite spatial and Euclidean time regulator in original g=0 scalar/charge model.",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:homogeneous-completion-round11",
      "titleEN": "homogeneous-completion-round11",
      "questionEN": "Round11: two different constant-mode problems",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
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      "reviewState": "inventoried-not-reviewed",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:homogeneous-receiver",
      "titleEN": "homogeneous-receiver",
      "questionEN": "Kann das homogene Spur-Paar (Q,P) mit postulierter globaler Hamilton-Zwangsbedingung als interne Uhr dienen, die positive Gesamtenergie empfängt — glatt durchs Vakuum und bei beliebigem Gesamtimpuls?",
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      "kind": "contract",
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      "verdictRaw": "CONDITIONAL_POSITIVE_RECEIVER_A>0_FIXED_BRANCH_J=0; VACUUM_IRREGULAR; MOMENTUM_UNREPAIRED; NOT_TFPT_DERIVED",
      "verdictClass": "partial",
      "stage": null,
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:hopping-source-domain-round20",
      "titleEN": "hopping-source-domain-round20",
      "questionEN": "hopping-source-domain-round20",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
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      "sourceRefIds": [
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      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:interaction-mediator-20261005",
      "titleEN": "interaction-mediator-20261005",
      "questionEN": "Can the Theta_1 vertex -g sum_A O_A^2 arise by eliminating a heavy source mode, and does the source contain such a mode?",
      "date": "20261005",
      "kind": "contract",
      "status": null,
      "verdictRaw": "MEDIATOR_SPECIFIED_NOT_IN_ELEMENTARY_SOURCE",
      "verdictClass": "other",
      "stage": null,
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:joint-constraint-model-round14",
      "titleEN": "joint-constraint-model-round14",
      "questionEN": "joint-constraint-model-round14",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:joint-native-algebra-selection-20261016",
      "titleEN": "joint-native-algebra-selection-20261016",
      "questionEN": "Which actual native TFPT structures share a source, what is their joint algebra, and when do their complete channels determine dynamics?",
      "date": "2026-10-16",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL_NATIVE_COMMON_REPRESENTATION_AND_PRIMITIVE_MENU_RIGIDITY",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
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        "finding:original-decoder-versus-native-quarter-polynomial-erasure-test",
        "finding:original-decoder-product-time-and-all-unitary-erasure-lifts",
        "finding:native-clock-compatible-polar-fibre-and-canonical-distance",
        "finding:native-moment-parent-and-product-path-selection-boundary",
        "finding:original-e8-current-response-and-full-quarter-lifts",
        "finding:literal-charged-current-register-dictionary-fails-quarter",
        "finding:native-cartan-code-inner-e8-stabilizer-excludes-marked-quarter",
        "finding:native-code-neutral-weight-two-action-and-global-clock-exclusion",
        "finding:original-neutral-root-mixed-response-derived",
        "finding:actual-mixed-ordered-return-on-native-quartic-code",
        "finding:mixed-return-spectrum-does-not-select-original-polar-mark",
        "finding:actual-mixed-return-fails-native-trimer-erasure-lift",
        "finding:strict-trace-gap-excludes-positive-mixed-return-reweighting",
        "finding:original-source-erasure-ward-terms-derived",
        "finding:uncompressed-original-mixed-return-does-not-preserve-code",
        "finding:original-root-response-sum-also-leaks-from-code",
        "finding:original-full-source-return-exterior-feedback-derived",
        "finding:original-return-requires-memory-in-every-code-direction",
        "finding:native-conformal-primary-multiplicity-source-factorization",
        "finding:canonical-conformal-erasure-forces-primary-twenty-carry",
        "finding:all-canonical-stress-histories-scalar-on-native-code",
        "finding:original-local-current-ope-forces-erasure-and-carry",
        "finding:all-real-local-cartan-profiles-erasure-third-bound",
        "finding:closed-cartan-weyl-histories-only-logical-phase",
        "finding:full-existing-local-e8-hull-of-native-code",
        "finding:full-local-quartic-wick-ladder-and-unprojected-native-actions",
        "finding:unmarked-native-w6-simplex-from-full-quartic-ope",
        "finding:full-e8-current-products-fix-stress-and-exterior-ward-cancellation",
        "finding:full-source-simplex-does-not-select-original-polar-mark",
        "finding:original-full-field-event-gram-reconstructs-relative-polar-mark",
        "finding:raw-event-state-positivity-does-not-execute-polar-normalization",
        "finding:determinant-cover-not-literal-full-cartan-lattice-event",
        "finding:clock-free-quartic-product-spectral-sectors-and-native-five",
        "finding:six-complex-native-simplex-rays-from-holomorphic-product-quadrics",
        "finding:intrinsic-relative-response-covariance-and-state-boundary",
        "finding:intrinsic-event-composition-retains-shared-source-and-correlation-data",
        "finding:clock-free-event-geometry-fixes-clock-class-and-mark-orbit-not-member",
        "finding:original-charged-seam-character-recovers-global-native-event-pair",
        "finding:internal-seam-vacuum-and-original-neutral-tensor-do-not-select-flag-root",
        "finding:actual-quarter-fold-shift-removes-native-symmetry-obstruction-without-flag-selector",
        "finding:fold-shift-equivariance-needs-actual-source-response-map-not-another-symmetry-no-go",
        "finding:original-fold-covariance-current-counterterm-and-quartic-twisted-transport",
        "finding:fold-state-full-quartic-kernel-and-erasure-protected-low-order-response",
        "finding:original-fold-quartic-mean-and-spectral-responses-do-not-match-sixty-flags",
        "finding:original-winding-full-state-response-removes-vacuum-rank-two-shortcut",
        "finding:original-source-global-time-winding-history-factorization",
        "finding:original-local-density-folds-to-correlated-root-current-and-erasure-response",
        "finding:original-current-all-mode-energy-and-geometric-stress-bridge",
        "finding:original-current-geometric-response-pair-has-no-common-polar-sector",
        "finding:original-current-ordered-hall-kernel-and-actual-folded-field-products",
        "finding:original-seam-grades-full-density-geometric-products-and-energy-response",
        "finding:original-seam-complete-density-grading-not-sharp-32-input-sectors",
        "finding:original-density-all-profile-mean-work-scalar-on-native-packet",
        "finding:original-p1-gap-normalized-action-covector-and-scalar-holonomy-class",
        "finding:original-p1-gap-car-component-not-native-sharp-32-event",
        "finding:complete-positive-scalar-first-order-circle-source-normal-form",
        "finding:fixed-source-time-seam-ward-rigidifies-scalar-principal-symbol-with-carry",
        "finding:unit-spectral-flow-gap-and-four-marks-do-not-imply-fixed-source-ward",
        "finding:four-native-starts-have-distinct-original-fold-state-correlations",
        "finding:four-starts-full-joint-kernel-and-charged-covariant-transport",
        "finding:four-native-polar-marks-not-fixed-source-state-gauge-equivalent",
        "finding:original-pointer-template-requires-source-context-identification",
        "finding:four-polar-context-algebra-and-source-crosscoupling",
        "finding:every-native-quartic-has-all-eight-original-car-supports",
        "finding:bounded-proper-local-source-operation-cannot-exactly-prepare-positive-eigenpacket",
        "finding:full-original-erasure20-and-joint25-have-all-eight-source-supports"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:joint-singlet-pulse-source-20261013",
      "titleEN": "joint-singlet-pulse-source-20261013",
      "questionEN": "Can the stated singlet pair preparation and native Clifford pulse work together, including a thermal bath or the pair Hamiltonian retained during pulse?",
      "date": "20261013",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:9db4c0b1439626cd271d",
        "source:a045cc82fb62819a74e7",
        "source:b5bdec945d5196948e81",
        "source:61da8199c2753aecb14f",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:kms-coherence-selection-20260919",
      "titleEN": "kms-coherence-selection-20260919",
      "questionEN": "Within norm-continuous effective QMSs, do a fixed faithful state, strict KMS/GNS symmetry, modular covariance, primitivity, response-kernel positivity and a fixed Markov decay gap eliminate the coherence ambiguity; which independent source data reconstruct the dynamics?",
      "date": "20260919",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Finite effective quantum Markov dynamics, not a full P1 model. The reset example is not the TFPT 3-state transfer matrix. Permutation-clock covariance is asserted for the tracial subfamily. Closed Hamiltonian KMS time for a specified faithful Gibbs state and known beta is unique and is not refuted. No source construction or physical gate is closed.",
      "sourceRefIds": [
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        "source:698bf6bcfd82f1926ba2",
        "source:0002bcf3037aec245057",
        "source:a5458c11276d158b6d2b",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:local-charge-parent-round17",
      "titleEN": "local-charge-parent-round17",
      "questionEN": "local-charge-parent-round17",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:local-charge-transport-round20",
      "titleEN": "local-charge-transport-round20",
      "questionEN": "local-charge-transport-round20",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:local-flux-dynamics-round33",
      "titleEN": "local-flux-dynamics-round33",
      "questionEN": "Round33: local electric control and fully evaluated cycle readouts",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "LOCAL_ELECTRIC_CONTROL_AND_CERTIFIED_FULL_ROTOR_READOUTS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:local-gaussian-elimination-round24",
      "titleEN": "local-gaussian-elimination-round24",
      "questionEN": "local-gaussian-elimination-round24",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:3b0638b7b942238f6bbd",
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        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:local-parent-round15",
      "titleEN": "local-parent-round15",
      "questionEN": "local-parent-round15",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:cdf8ea3798426caeda91",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:local-positive-auxiliary",
      "titleEN": "local-positive-auxiliary",
      "questionEN": "Round 10: local constrained realization of the positive TT completion",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:local-source-round38",
      "titleEN": "local-source-round38",
      "questionEN": "Round38: an actually evaluated local 3D readout without a giant window",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EVALUATED_VOLUME_UNIFORM_LOCAL_HIGH_OCCUPATION_INTERVAL",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:local-source-stability-round18",
      "titleEN": "local-source-stability-round18",
      "questionEN": "local-source-stability-round18",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:local-window-round37",
      "titleEN": "local-window-round37",
      "questionEN": "Round37: explicit local 3D window and rotor error bounds",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXPLICIT_VOLUME_UNIFORM_LOCAL_WINDOW_AND_FLUX_BOUND",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:mark-projective-lift-20261005",
      "titleEN": "mark-projective-lift-20261005",
      "questionEN": "Without inserting a spin structure: do fermionic grading and the oriented marks force the nontrivial projective lift A4 -> 2T (central element = (-1)^F) instead of the trivial linear action?",
      "date": "20261005",
      "kind": "contract",
      "status": null,
      "verdictRaw": "NOT_FORCED_IN_SOURCE",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:marked-seam-cp-lift-20260921",
      "titleEN": "marked-seam-cp-lift-20260921",
      "questionEN": "Can the actual q*-marked 1+5+10 compiler process and the original seam transfer be joined by one completely positive operator step, and does that step define a product-preserving charged physical time?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:marked-seam-monodromy-20261023",
      "titleEN": "marked-seam-monodromy-20261023",
      "questionEN": "Classify all sign lifts of the native quarter-clock representation on the ordered four-punctured sphere, and determine their actual extension classes and native quartic/exterior cohomology.",
      "date": "2026-10-23",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Pure mathematics. Full sign-lift preimage of <J> with all four peripheral projections J, prescribed ordered peripheral conjugacy classes and simultaneous conjugation by that preimage. Full factor table on native <J,R>=C4xC2. Not unrestricted G31/W(E8) reflection moduli, a global splitting theorem, a mapping-class quotient or classification of spatial-reflection-equivariant lifts.",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:marked-seam-category-and-character-valued-full-lift-factor",
        "finding:quarter-clock-sign-lift-complete-four-puncture-classification",
        "finding:quarter-lift-central-quotient-class-and-all-subgroup-restrictions",
        "finding:native-clock-reflection-full-factor-cocycle-trivialization",
        "finding:native-quartic-exterior-local-cohomology-distinguishes-clock-monodromies"
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:marked-source-history-20261014",
      "titleEN": "marked-source-history-20261014",
      "questionEN": "Can the existing marked channel and its fixed state select a common original marking, state and event law, and which supplied synthesis formulas survive original-source checks?",
      "date": "2026-10-14",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Finite marked M4 channel, coherent endpoint dilation, and stationary covariant mixing counterprocesses with identical unperturbed interval channels. Native regulated g=0 scalar/charge histories are prior conditional results, not identified with M4 here.",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:matter-current-algebra",
      "titleEN": "matter-current-algebra",
      "questionEN": "Schließt die kanonische Algebra der fixierten freien Skalar-Energie- und Stromgeneratoren exakt, und welche Onsite-Potentiale sind bei unverändertem Strom mit der Impuls-Ward-Identität verträglich?",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_LAPSE_LAPSE_CLOSURE; CURRENT_RANGE_GROWTH; FIXED_CURRENT_ONSITE_POTENTIAL_MUST_BE_QUADRATIC; NO_NONLINEAR_GRAVITY_CLAIM",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
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      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:matter-geometry-round15",
      "titleEN": "matter-geometry-round15",
      "questionEN": "matter-geometry-round15",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
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      "scopeEN": null,
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:matter-hierarchy-round40",
      "titleEN": "matter-hierarchy-round40",
      "questionEN": "Round40: controlled matter hierarchy and certified bulk phase sensitivity",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EVALUATED_FOURTH_MATTER_HIERARCHY_WITH_SEPARATE_ELECTRIC_BUDGET",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:matter-resummation-round43",
      "titleEN": "matter-resummation-round43",
      "questionEN": "Round43: all-order matter row, an evaluated loop, and a canonicality boundary",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_MATTER_ROW_REPRESENTATION_WITH_EVALUATED_TREE_AND_CYCLE_HYBRIDS",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
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      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:mediator-covariance-20261005",
      "titleEN": "mediator-covariance-20261005",
      "questionEN": "Which family representation must the Gate-B mediator carry once the three-family version of Theta_1 is written explicitly?",
      "date": "20261005",
      "kind": "contract",
      "status": null,
      "verdictRaw": "R_PHI_DETERMINED_FOR_V1",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
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        "source:a1118043586acdc7712d",
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      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:mediator-rep-sieve-20261005",
      "titleEN": "mediator-rep-sieve-20261005",
      "questionEN": "From how many and which existing source modes can a bosonic, family-singlet Spin(10)-vector (10,1) mediator be built at all (before any spectral search)?",
      "date": "20261005",
      "kind": "contract",
      "status": null,
      "verdictRaw": "SU4_NEUTRAL_FORBIDDEN_ALL_DEGREES; SU3_SO3_A4_NEUTRAL_MIN_DEGREE_2",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:memory-closure-round34",
      "titleEN": "memory-closure-round34",
      "questionEN": "Round34: closed memory evolution and unchanged physical readouts",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "CLOSED_MEMORY_EVOLUTION_WITH_SOURCE_RECONSTRUCTION",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:eb106514b7ce25661016",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:microscopic-charged-car-limit",
      "titleEN": "microscopic-charged-car-limit",
      "questionEN": "A microscopic integer-charged CAR field from the same QWZ source",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "ONE_SOURCE_INTEGER_CHARGED_CAR_EDGE_LIMIT",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:microscopic-energy-linearization",
      "titleEN": "microscopic-energy-linearization",
      "questionEN": "Same-polarization energy linearization: an analytic sub-bridge",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "ANALYTIC_ENERGY_SUBBRIDGE_ONLY",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:microscopic-fourpoint-limit",
      "titleEN": "microscopic-fourpoint-limit",
      "questionEN": "Microscopic neutral four-point limit from the same source",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "MICROSCOPIC_NEUTRAL_FOURPOINT_COMPARISON_WRITTEN_PROOF",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:microscopic-neutral-limit",
      "titleEN": "microscopic-neutral-limit",
      "questionEN": "Microscopic neutral two-point limit: low-energy control of full histories",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "MICROSCOPIC_NEUTRAL_PAIR_PROOF_WITH_INTERNAL_REVIEW",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:microscopic-twist-charge-test",
      "titleEN": "microscopic-twist-charge-test",
      "questionEN": "Trägt ein vom Sektorwechsel entkoppelter polarer Träger die halbe Ladung mit messbar kleinerem Ward-Fehler und günstigerer Energie, ohne die bisherigen neutralen Quellenpaare zu verändern?",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "finite-charge-improved-field-open",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:96cee936930ee47058ca",
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        "source:4f1abf2562073e2f9b90",
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:minimal-runtime-reconstruction-20261005",
      "titleEN": "minimal-runtime-reconstruction-20261005",
      "questionEN": "Without inserting AX.MARKCLIFFORD or Theta_1: does the future-equivalence (Hankel/GNS) quotient of the existing P1/P2 source processes yield Cl(4) for the four marks, the bcc filter F, the minimal-doubling kinetic h_W and the quartic -g sum O_A^2 as the minimal executable representation; if not, what is the exact defect and the smallest missing input?",
      "date": "20261005",
      "kind": "contract",
      "status": null,
      "verdictRaw": "NOT_DERIVED",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:minimal-stability-round15",
      "titleEN": "minimal-stability-round15",
      "questionEN": "minimal-stability-round15",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:mixed-constraints-round11",
      "titleEN": "mixed-constraints-round11",
      "questionEN": "Finite mixed first-/second-class constraint completion",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:mixed-current-origin-20261014",
      "titleEN": "mixed-current-origin-20261014",
      "questionEN": "Does the actual original seam representative derive a local mixed spinor weight-one current through quarter-twist fusion, and does the pasted scalar pair response identify that field?",
      "date": "2026-10-14",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Original one-copy mass-one width-eight QWZ top-edge CAR scaling subnet; all finite quarter-twist fusions only in the explicitly stipulated fixed U(1) Heisenberg/Fock module class. Conditional eight-channel D8/E8 extension and root-lattice selector audits. No exhaustion theorem for all microscopic scaling sequences and no full TFPT exclusion. Continuation22Oct: full same-sea/same-source-time finite-energy spectral exhaustion and heat-trace convergence, not exhaustion of all scaling local nets. Complete relative-locality census of the four uniform scalar Z4 target classes, with both half-spinor chirality energy minima. Further22Oct: exact all-energy global odd-spinor re-fielding and SOURCE W1 transport, with an explicit unchanged-local-CAR counterwitness. Independently reviewed sharp half-flux local-nonnormality and original v746/v1033 controls; not all regularized P1 sector constructions. Later22Oct: all-joint-word register-grade obstruction includes unbounded renormalized candidates when local Z is retained; exact conditional parity-Gauss completion changes the local net,not physical even dimension or microscopic register H. Fixed-charge one-copy8fold half-flux monodromy differs from uniform D8 spinor twist; real charge-reversing quarter conjugacy explicitly retained. Further22Oct: actual register-neutral eight-preimage parity pairs have uniform folded-vector cut action and unchanged cover holonomy. The SINGLE cover-half-flux invariant does not exclude this pair. Full-Dirac vector Ward cancellation and finite complementary determinants remain; smooth-unitary return removal costs at least2pi/eps under fixed source time. No separated charged field limit. Continuation23Oct: arbitrary nonunitary insertions under full compact-source spectral identifications, unchanged bounded-observable low-window action, finite nonzero norm and continuous ORIGINAL Euclidean OR real-time kernels remain in the old representation folium. No bounded mean energy assumed. All4register vacuum offsets uniformly controlled with ONE common reference. Actual finite QWZ heat-filtered pair has full Slater-word/time formula; conditional chiral Weyl sharp-limit kernel kept distinct. No all-P1/local-scaling-net exclusion. Atlas/KMS continuation23Oct: source-reviewed holomorphic KMS theorem assumes the extension B; fixed-interval global-rotation modular inference in printed(4.7) is corrected using moving intervals or local restricted states. Exact source-W1/2pi-Cartan four-word is+Iold/-Itarget under the known Phi. Total-even two-edge Gibbs/GSO does not erase the witness; left-even projection removes SOURCE W1 compression. Conditional global/source dictionary only,no primitiveP1-circle identification and no refutation of independent expectation/KMS uniqueness.",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:unchanged-qwz-full-finite-energy-spectral-exhaustion",
        "finding:uniform-z4-d8-locality-and-both-spinor-chirality-time-census",
        "finding:odd-spinor-global-refielding-and-unit-source-winding",
        "finding:sharp-half-flux-register-quotient-and-local-normality-exclusion",
        "finding:all-word-register-charged-local-field-limit-obstruction",
        "finding:exact-parity-gauss-locality-completion-of-register-source",
        "finding:cover-half-flux-not-fixed-charge-eightfold-spinor-twist",
        "finding:original-neutral-eightpreimage-parity-pair-has-uniform-cut-action",
        "finding:complete-dirac-vector-phase-pair-has-zero-spinor-Ward-charge",
        "finding:smooth-unitary-endpoint-removal-diverges-at-fixed-source-time",
        "finding:continuous-original-time-nonunitary-limits-stay-in-old-source-folium",
        "finding:common-register-vacuum-reference-uniform-and-local-grade-reduction",
        "finding:actual-heat-filtered-neutral-pair-full-state-time-and-separate-chiral-limit",
        "finding:holomorphic-kms-extension-assumes-charged-net-and-not-microscopic-generator",
        "finding:fixed-interval-rotation-modular-chain-fails-local-state-takesaki-repairs",
        "finding:source-winding-cartan-four-word-and-two-edge-kms-gso-discriminator",
        "finding:p1-parity-gauss-net-selection-undecidable-without-original-localization-map"
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:modular-source-selection-audit-20260917",
      "titleEN": "modular-source-selection-audit-20260917",
      "questionEN": "Raw seam source selection: does v438 establish real modular dilation with one positive generator, and can target-only W/Casimir constraints select a state-preserving D4 intertwiner?",
      "date": "20260917",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "The finite certificate is mismatched; the genuine continuum HSMI theorem and possible nonlinear E8 field adapters remain viable. Raw physical net/state selection is unresolved.",
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        "source:c9545c3cc06b6b5bf062",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:momentum-deformation-round12",
      "titleEN": "momentum-deformation-round12",
      "questionEN": "Round12: first-order momentum repair and second-order obstruction",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:moving-history-memory-round25",
      "titleEN": "moving-history-memory-round25",
      "questionEN": "Uniform finite Euclidean memory bounds and actual cross-time scalar determinant response for moving neutral charges.",
      "date": "2026-09-07",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Uniform finite Euclidean memory bounds and actual cross-time scalar determinant response for moving neutral charges.",
      "sourceRefIds": [
        "source:225b9a1eeb09bcd4e328",
        "source:8f0e674128c5a5bc98a5",
        "source:ad0ccf3d2ffb723b90ab",
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:native-arc-charge-source-interface-20261026",
      "titleEN": "native-arc-charge-source-interface-20261026",
      "questionEN": "Can the actual native quartic insertions be generated from the additive original scalar density/stress algebra on their eight preimage arcs, and does the retained joint source supply the missing transfers?",
      "date": "20261026",
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_SCOPED_RELATIVE_ARC_CHARGE_OBSTRUCTION; FINITE_MODULAR_DIAGNOSTIC; PHYSICAL_SOURCE_SELECTION_OPEN",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:731c70ea3953eec4fe55",
        "source:5fa40bdb7b8a48dc637e",
        "source:c0aeaa78e74e2dbd7116",
        "source:1ef342498cd3c481d4f0",
        "source:92f62414cd2ddb339e2a",
        "source:8283d1b6253c2fbcc4e4",
        "source:a81428fab8b9288e2189",
        "source:86996d364b2762f175fc",
        "source:386f184a4b4f2da3210a",
        "source:1bac723c53a12d0d1f18",
        "source:d68ac420d2147d97ee99",
        "source:beb0a1d2ef5acfff57bc",
        "source:4511dd1e6728e2f6e60b",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:native-quartic-relative-arc-charge-excludes-additive-density-stress-insertion",
        "finding:retained-quarter-sea-finite-modular-transfer-preserves-integrated-native-cartan",
        "finding:original-neutral-interarc-fields-have-exact-connected-current-vertex-reconstruction",
        "finding:actual-elliptic-gaussian-source-determines-full-quarter-current-functional",
        "finding:elliptic-current-state-differs-from-hardy-on-every-proper-current-interval",
        "finding:canonical-conformal-boundary-trace-fixes-existing-elliptic-cauchy-state",
        "finding:conformal-factor-averaging-preserves-given-free-boundary-wick-words",
        "finding:full-projector-covariance-and-positivity-force-all-car-words",
        "finding:actual-two-face-projector-reduces-free-source-test-to-cross-coherence",
        "finding:existing-elliptic-half-period-has-canonical-graded-gns-intertwiner",
        "finding:standard-sewing-requires-maximal-affinity-linear-half-modular-field-law",
        "finding:chat-algorithmic-comparison-native-pauli-code-and-scoped-information-loss",
        "finding:chat-20261026-results-consolidated-with-corrected-assumptions"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:native-charged-conjugation-20261015",
      "titleEN": "native-charged-conjugation-20261015",
      "questionEN": "Does the actual original local charge source have an all-time opposite-charge response symmetry, and which uniform chemical markings remain visible to charged corners despite a total-zero starting sector?",
      "date": "2026-10-15",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:native-invariant-response-not-fixed-chiral-twist",
        "finding:native-opposite-charge-response-symmetry",
        "finding:native-chemical-mark-visible-in-charged-corners",
        "finding:fixed-hopping-quarter-phases-retain-antiunitary-discriminator"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:native-mark-memory-20261014",
      "titleEN": "native-mark-memory-20261014",
      "questionEN": "Which marking and response memory follow from the original charge source, and can the derived four-grade factor close under the same Hamiltonian and actual clocks?",
      "date": "2026-10-14",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:5d2fb7f8e0f6686f4f4e",
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        "source:97cfef4a4a68a1196308",
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        "source:6e6101a3704592774166",
        "source:85075119977ea5789416",
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        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:native-grade-carry-and-memory",
        "finding:four-clock-fields-complete-quadratic-response"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:native-observation-arity-20261025",
      "titleEN": "native-observation-arity-20261025",
      "questionEN": "At what native tensor stage can the actual clock ovoid labels first be observed, and is the corresponding original erasure response the derivative of the original quartic source?",
      "date": "2026-10-25",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Actual native G31 on V4, its normal Pauli kernel, original symmetric quartic code, and the six actual E8/J doily ovoid labels. Finite normalized positive operator effects on native tensor powers. Coherent-input formulas use a specified input x^tensor3 and the existing original erasure map. Comparison with the older source-product null locus preserves its declared local E8 field embedding.",
      "sourceRefIds": [
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        "source:0bf03fc224e3ec8d6d63",
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        "source:2324b4c7355520970fbc",
        "source:deb065581f530528b5a1",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:native-six-ovoid-observation-first-occurs-at-tensor-degree-three",
        "finding:original-quartic-erasure-and-hamming-octic-share-marked-ovoid-response",
        "finding:native-octic-field-ray-is-explicit-but-retained-clock-stress-preparation-fails"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:native-octic-seam-origin-20261025",
      "titleEN": "native-octic-seam-origin-20261025",
      "questionEN": "Does the ACTUAL shifted original quarter CAR/fold stress reach the normalized native octic without inserting a new octic coupling, and which original P1 identification remains?",
      "date": "2026-10-25",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "The already given original single-circle quarter CAR source, unitary eightfold fold, fixed conformal NS current reference and original M/O/U+ native dictionary. The octic is an even CAR current composite. The separate root-OPE result assumes the supplied full E8 vertex extension; that extension is not a prerequisite for the main source response.",
      "sourceRefIds": [
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        "source:142789ffb055ac6b1a5d",
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        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:native-octic-field-ray-is-explicit-but-retained-clock-stress-preparation-fails",
        "finding:actual-quarter-fold-stress-has-nonzero-octic-eighth-jet",
        "finding:native-octic-is-an-original-even-car-current-composite",
        "finding:original-geometric-source-jet-and-partial-p1-seed-closure",
        "finding:full-root-ope-has-normalized-native-octic-component"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:native-sector-calibration-20261013",
      "titleEN": "native-sector-calibration-20261013",
      "questionEN": "Which energy-calibration ambiguities of the existing four-sector source are determined by its native disorder operator, and which remain invisible?",
      "date": "2026-10-13",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Existing conditional v1033 C4 tensor Fock lift, full completed CAR+C action, native D and known baseline response at fixed background; relative energy calibration only, no P1/P2 selection or physical/gravity closure.",
      "sourceRefIds": [
        "source:539ffb5d14368ef9d409",
        "source:cf3695de03002ec8b831",
        "source:94c56422dff88f4a31d1",
        "source:2a9225f814dafa11f83f",
        "source:9f23d726afd878dfbe9f",
        "source:867df8659cbda79867f0",
        "source:f6e91cde41cf19b83f2a",
        "source:1797ae2f5bea7649120e",
        "source:1101eeff88323767f687",
        "source:ac5f54cc240c0f91425a",
        "source:b02bfbb24cd485059a9b",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:native-source-reconstruction-20261014",
      "titleEN": "native-source-reconstruction-20261014",
      "questionEN": "Does the existing signed neutral scalar/charge source generate a common time, state and ordered response law, and what information must an exact marked readout retain?",
      "date": "2026-10-14",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:3f4e8bc7dc06f641905b",
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        "source:4dd9245320d7d661ea33",
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        "source:18d340aeed16115daafa",
        "source:0d7cc9da475ee4945fe8",
        "source:ad0ccf3d2ffb723b90ab",
        "source:06d28a588ecc220ba161",
        "source:85595bd41e3a8b0f97dc",
        "source:4da937bba06d6413ddec",
        "source:8791bd055d910c91088f",
        "source:3031b5a001f751290d26",
        "source:baaf69ed044bf15aea2f",
        "source:c62af5d3542dc27e71dc",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:native-source-common-time-thermal-family"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:neutral-current-limit",
      "titleEN": "neutral-current-limit",
      "questionEN": "Konvergiert die phasenkorrigierte, endpunktnormierte mikroskopische QWZ-Neutraldeterminante im Skalenlimes (delta_N→0, N·delta_N→∞) gleichmäßig in Phase und Betrag gegen den exakten chiralen Strom-...",
      "date": "20260908",
      "kind": "contract",
      "status": null,
      "verdictRaw": "partial",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:ece4a18aa6e0d812e324",
        "source:956a71694e1c04bbd477",
        "source:45afcc1efdf4482d9d66",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:neutral-ground-state",
      "titleEN": "neutral-ground-state",
      "questionEN": "Neutral ground-state representations of the fixed parent",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "FIXED_PARENT_NEUTRAL_GROUND_STATE_EXISTENCE_AND_POSITIVE_PHYSICAL_GNS_ENERGY",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:fc1761dede597656e11b",
        "source:9ff5e1a34c80096fef18",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:neutral-pair-composition",
      "titleEN": "neutral-pair-composition",
      "questionEN": "Lässt sich die volle endliche neutrale Vakuumerwartung des Gauss-gefilterten Sources mit Phase und kontrollierter Connected-Log-Trunkierung berechnen, und ergibt sich daraus ein geladener Skalenlimes?",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "pass",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:27e8135eaf21667da22a",
        "source:5f2e72728470d975c463",
        "source:e7fb9a4f521879ae05aa",
        "source:f779acf54dc286eb5eab",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:neutral-port-identifiability-20261013",
      "titleEN": "neutral-port-identifiability-20261013",
      "questionEN": "Does the existing selected neutral R → P0 port retain or identify the D5 contribution sought for the 5/4 susceptibility?",
      "date": "2026-10-13",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Selected original neutral R and conditional rank-one P0 port on level two; an exact information-loss witness, not a no-go for full charged/defect responses or TFPT.",
      "sourceRefIds": [
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        "source:b44ab1961eb180a57844",
        "source:24503dab34858f784f33",
        "source:f46dce505123ed341893",
        "source:08100c7ab0d44a63c921",
        "source:1422cecdf94168acf5be",
        "source:1887124fcae4b80de30f",
        "source:fc9fdd48867c90bed8b3",
        "source:8fa8965b438e10abb827",
        "source:c276744de84cd1d97fd1",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:neutral-response-tomography-20261013",
      "titleEN": "neutral-response-tomography-20261013",
      "questionEN": "Which additional native neutral-field responses repair the information lost by the rank-one P0 port, and under which source-alignment assumptions?",
      "date": "2026-10-13",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact vacuum Wick responses of original neutral_source_response.py with fixed native rank5,2,1 projectors and block-scalar quadratic primaries; algebraic identifiability, not physical source selection or susceptibility derivation.",
      "sourceRefIds": [
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        "source:a6398954cb00882d2b68",
        "source:c7b7379dd5864ec58bc8",
        "source:3e17d68cec633cc1edd7",
        "source:7c9b56473dee378cb2dc",
        "source:1422cecdf94168acf5be",
        "source:b44ab1961eb180a57844",
        "source:f13b928c165980bb76f3",
        "source:fc9fdd48867c90bed8b3",
        "source:6647aef4e27afdf65e3a",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:four-clock-fields-complete-quadratic-response"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:observable-dynamics",
      "titleEN": "observable-dynamics",
      "questionEN": "All-observable dynamics of the fixed parent, and its continuity boundary",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "FIXED_PARENT_QUASILOCAL_AUTOMORPHISMS_WITH_CONTINUITY_BOUNDARY",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:ba5e3d303573fc6ff1da",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:older-paper-source-recovery-20261025",
      "titleEN": "older-paper-source-recovery-20261025",
      "questionEN": "Do older TFPT versions already contain the concrete seam operators, full source functional and rank-one transfer construction hidden by later compressed proofs, and can the old heat transfer recover the later single-mode factor without a freely chosen vector?",
      "date": "2026-10-25",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Historical original modules from Paper V1.06 and fullv2/fullv21 through v42, plus comparison with archived v4.5. Exact operator results concern the supplied scalar quarter-circle representation; they do not identify that space with the later original admissible source by definition.",
      "sourceRefIds": [
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        "source:00b8900a614ab7de5337",
        "source:43d9751617f7078c7346",
        "source:644d27f1b86103a0ffb9",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:older-original-circle-representative-already-realizes-ward-and-index",
        "finding:old-quarter-heat-transfer-has-controlled-rank-one-limit-and-odd-product",
        "finding:historical-em-rank-one-and-full-heat-traces-have-different-contracts",
        "finding:older-frg-functional-already-supplies-formal-full-moment-parent",
        "finding:earliest-c3-route-quantizes-level-but-needs-physical-kinetic-normalization",
        "finding:canonical-positive-circle-half-selects-the-toeplitz-line-and-sixth-order-correction"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:origin-composition-audit",
      "titleEN": "origin-composition-audit",
      "questionEN": "Bilden E8-Kaskade, endlicher Compiler, Ladungs-Kozykel-Algebra, neutrale Felder und arithmetische Korrespondenzen ein gemeinsames physikalisches System unter quellenerhaltender Identifikation ihrer...",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:afeaae186021ad88848a",
        "source:d16a979b22a8a4fb2643",
        "source:20d6d6348a37e153f38a",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:original-admissible-source-closure-20261025",
      "titleEN": "original-admissible-source-closure-20261025",
      "questionEN": "Does the recovered original seam circle canonically determine the minimal line and relative electromagnetic-shaped factor without a heat-to-EM identification, and what original source identities still need proof?",
      "date": "2026-10-25",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "The original fullv21 concrete circle after explicit orientation repair; existing full CAR with matching positive time where invoked; old SF-normalized relative defect action and its exact complete-sector ratio. No substitute continuum field source or free state is selected. The historical UV-profile map exclusion is reused from the 2026-10-13 audit and rechecked on the current registered archival source; it is not a new discovery.",
      "sourceRefIds": [
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        "finding:finite-antiperiodic-scalar-wall-has-no-exact-massless-normal-mode",
        "finding:quaternionic-sm-mass-winding-is-not-normal-determinant-clutch",
        "finding:old-seam-shift-canonically-gives-relative-car-line-and-fredholm-factor",
        "finding:old-index-coupling-removes-heat-map-and-has-sharp-residual-ward-test",
        "finding:original-admissibility-requires-image-membership-not-positive-half-or-commutation",
        "finding:old-closure-already-assumes-car-but-does-not-map-the-geometric-circle",
        "finding:historical-uv-map-infinite-mass-exclusion-already-proved-and-recovered",
        "finding:old-seam-relative-determinant-is-stable-in-faithful-kms-class",
        "finding:finite-circle-compression-cannot-retain-whole-thermal-winding-factor",
        "finding:schur-carrier-plus-complement-preserves-original-relative-determinant",
        "finding:v258-forward-source-gap-is-reused-not-solved-by-inversion",
        "finding:one-sided-source-and-real-em-norm-need-response-map-not-chiral-phase",
        "finding:trace-class-pair-index-fixes-relative-factor-without-primitive-ray",
        "finding:matrix-clutch-degree-connects-weak-determinant-class-without-ray-selector",
        "finding:finite-ns-ordinary-determinant-cannot-limit-to-nonzero-index",
        "finding:inner-carrier-is-infinite-spacetime-module-not-finite-circle-cut",
        "finding:normal-spin-determinant-line-exactly-transports-whole-circle-in-given-product",
        "finding:normal-index-line-source-match-is-holonomy-condition-not-vertical-degree",
        "finding:full-normal-product-polarization-change-is-not-trace-class",
        "finding:massive-transverse-zero-index-retains-positive-determinant-response",
        "finding:original-callias-doublet-count-does-not-supply-one-complex-circle-channel",
        "finding:exact-moving-kernel-reduction-forces-kato-offdiagonal-connection",
        "finding:tetrahedral-quarter-face-phase-does-not-identify-original-quarter-marked-curve",
        "finding:existing-elliptic-cover-correspondence-has-exact-c6-image-and-retained-mixed-clock",
        "finding:recovered-natural-joint-lift-and-given-connection-already-exist",
        "finding:global-split-joint-carrier-admits-parallel-native-c12-clock",
        "finding:pure-weak-clutch-clock-identification-fails-despite-quarter-matches",
        "finding:same-chern-clutch-native-compiler-does-not-select-physical-connection",
        "finding:native-gaussian-four-is-cartan-subspace-in-whole-sixtyfour",
        "finding:native-family-factor-is-not-gaussian-four-despite-symmetric-coincidences",
        "finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice",
        "finding:even-degree-pullback-removes-cartan-topology-without-selecting-clock-cover",
        "finding:global-cartan-choice-is-optional-for-original-scalar-source-fields",
        "finding:bare-native-octic-is-not-whole-e8-zero-mode-singlet",
        "finding:explicit-primary-e8-invariant-octic-completes-same-neutral-car-source",
        "finding:completed-octic-has-exact-old-root-ope-component-and-quarter-source-value",
        "finding:elliptic-normal-spin-pullback-doubles-index-and-deck-quarter-lifts-anticommute",
        "finding:exact-separated-w8-twopoint-in-original-quarter-current-source",
        "finding:unshifted-vacuum-fails-same-w8-source-state-time-dictionary",
        "finding:local-current-phase-and-conditional-cyclic-p1-w8-image",
        "finding:all-neutral-w8-correlations-identify-the-two-original-quarter-charges",
        "finding:original-w8-response-has-infinite-same-time-spectral-support",
        "finding:older-seam-equivalence-verifications-do-not-supply-marked-local-p1-map",
        "finding:full-original-c1-stress-cycle-reconstructs-neutral-w8-response",
        "finding:folded-c8-cycle-misses-intrinsic-w8-tangent-without-obstructing-original-stress",
        "finding:old-cover-winding-reconstructs-local-quarter-current-net",
        "finding:untransported-independent-quarter-stress-pair-is-not-current",
        "finding:current-public-paper-bytes-and-binding-source-gaps-recovered",
        "finding:winding-charge-conjugation-descends-fixed-pin-domain-but-not-full-dirac-sea",
        "finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea",
        "finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity",
        "finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp",
        "finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum",
        "finding:actual-pin-zero-branch-retains-quarter-car-state-time-but-no-uniform-scale-return",
        "finding:conformal-pin-source-geometry-fixes-exterior-return-and-unitary-memory",
        "finding:geometric-exterior-schur-response-transfers-proper-native-arc-charge-but-is-compact",
        "finding:actual-ns-half-cover-cauchy-graph-purifies-green-state-with-neutral-ground-time-obstruction",
        "finding:primitive-geometric-force-retains-coupled-reference-and-parity-variation",
        "finding:equal-finite-positive-heat-channel-values-do-not-fix-geometric-force",
        "finding:retained-seam-defect-has-derived-causal-geometric-response-with-contact",
        "finding:same-final-pin-geometry-retains-history-while-relative-index-factor-is-fixed",
        "finding:retained-marked-quarter-compiler-has-no-local-geometric-wick-correction",
        "finding:changed-elliptic-modulus-has-derived-cauchy-response-and-neutral-fourfield-variance",
        "finding:given-elliptic-flat-connection-family-has-explicit-quillen-norm-and-two-holonomies",
        "finding:bare-large-gauge-quillen-norm-does-not-equal-original-winding-counting-factor",
        "finding:recursive-kohonen-source-investigation-has-source-verified-atlas-handoff"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:original-source-functional-audit-20261013",
      "titleEN": "original-source-functional-audit-20261013",
      "questionEN": "Does the original source selection jointly derive charged operators, state, instruments, continuous clocks and geometry without a new auxiliary model?",
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      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact historical UV integral-map contradiction and finite native 2x2 instrument ambiguity; current source provenance audit. No full TFPT countermodel, continuous clock/geometry derivation or T1-T8 closure. 2026-10-15: exact seam/charge clutching-class prerequisite audit; no new physical source or full nonuniqueness theorem.",
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        "finding:historical-uv-map-infinite-mass-exclusion-already-proved-and-recovered"
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:paper-source-reconstruction-20261025",
      "titleEN": "paper-source-reconstruction-20261025",
      "questionEN": "Can the actual microscopic QWZ to one-CAR theorem in the existing TFPT papers be composed with the original quarter fold to derive the neutral octic field, its adjoint and geometric Ward response, and which original seed identification remains?",
      "date": "2026-10-25",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Fixed original width8/mass1/r1 QWZ top edge, its actual filled sea and positive time, unitary fold of the SAME one CAR channel, fixed original A=U+^T O^T M and shared current point-splitting/Wick prescription. Only neutral octic mechanism. Microscopic N limit precedes all continuum regulator removal. No full microscopic stress-unitary limit or charged E8 exhaustion.",
      "sourceRefIds": [
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      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:original-geometric-source-jet-and-partial-p1-seed-closure",
        "finding:paper-microscopic-car-composes-with-native-octic-ward",
        "finding:microscopic-neutral-octic-has-controlled-smeared-limit",
        "finding:paper-seed-source-needs-local-image-not-global-equivalence",
        "finding:full-car-positive-time-forces-source-vacuum"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:parent-selection-audit",
      "titleEN": "parent-selection-audit",
      "questionEN": "Parent-selection audit: what TFPT supplied, and what the test model supplied",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "DECLARED_PARENT_UNDERDETERMINED_AND_FROZEN_SCALAR_SYMBOL_NONWEYL",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:phase-origin-yukawa-defect-20260919",
      "titleEN": "phase-origin-yukawa-defect-20260919",
      "questionEN": "What exact anomaly, Yukawa-defect, seed-rank, Ward, and conditional period-lattice statements follow from the existing SM16 and positive real mass data, and which physical identifications remain open?",
      "date": "20260919",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact all-left-handed anomaly algebra, additive rank-one alignment, quadratic witness, conditional complex-seed rank and compact-torus/Smith calculations; no physical photon coupling, complex source, total anomaly response, physical QCD angle, or domain-wall index derived.",
      "sourceRefIds": [
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        "source:9e69c26512ff2d134a51",
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        "source:593e1b01b2daee6ddae2",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:physical-observable-bridge-round19",
      "titleEN": "physical-observable-bridge-round19",
      "questionEN": "physical-observable-bridge-round19",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:caeb21c6ba9a2b6d0e8a",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:plaquette-gap-certificate",
      "titleEN": "plaquette-gap-certificate",
      "questionEN": "Uncut plaquette and coupled-cube gaps, with a failed global extension",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "UNCUT_ORIGINAL_PLAQUETTE_AND_CUBE_GAPS_WITH_FAILED_BARE_Q_BULK_EXTENSION",
      "verdictClass": "fail",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:poisson-charge-round28",
      "titleEN": "poisson-charge-round28",
      "questionEN": "Round28: an evaluated partition, in a declared subcase",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "CERTIFIED_PARTITION_IN_DECLARED_SUBCASE",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:polarization-history-bridge",
      "titleEN": "polarization-history-bridge",
      "questionEN": "Reicht die volle Besetzt/Unbesetzt-Polarisation aus, um die normgeordnete Vakuumamplitude exakt auf eine Crossblock-Historie zu reduzieren, und gibt es eine dimensionsfreie Stabilitätsschranke für ...",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:667dfbe18c2af5cb9f24",
        "source:dd7896b979de2452d88d",
        "source:c0b100c6035796c14f10",
        "source:a0ceb3dab04311c39efd",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:positive-hopping-band-round22",
      "titleEN": "positive-hopping-band-round22",
      "questionEN": "positive-hopping-band-round22",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:positive-hopping-momentum-round22",
      "titleEN": "positive-hopping-momentum-round22",
      "questionEN": "positive-hopping-momentum-round22",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:ba282956141748a06b29",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:preconditioned-local-parent-round18",
      "titleEN": "preconditioned-local-parent-round18",
      "questionEN": "preconditioned-local-parent-round18",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:prescribed-source-kubo",
      "titleEN": "prescribed-source-kubo",
      "questionEN": "Liefert eine vorgeschriebene erhaltende c-Zahl-Quelle auf dem freien nullmittleren Tensor-Fock-Target eine exakte retardierte TT-Weyl/Kubo-Antwort, und welcher affine skalare Krümmungsterm ist zusä...",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "pass (proof + regressions, unpromoted pure math)",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:cc929d7629010049f52c",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:primitive-charged-source-response-20260921",
      "titleEN": "primitive-charged-source-response-20260921",
      "questionEN": "Can the primitive seam source independently determine charged fields, their common state and time response, and identify the specified boundary candidate without importing its lattice or energy form?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:ca1b1b48877663cdc653",
        "source:5037a54d5019017529a7",
        "source:67da87c9de89acb63e6e",
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:primitive-seam-operator-reconstruction-20261025",
      "titleEN": "primitive-seam-operator-reconstruction-20261025",
      "questionEN": "Do the original TFPT boundary and QFT papers construct the primitive seam line, its original time, and the full graded source; can their first unsupported identifications be repaired from the existing operators rather than a new source model?",
      "date": "2026-10-25",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Original archived TFPT 4.5 primitive boundary, carrier, EM and QFT passages, compared with the active P1/P2, Paper2 conditional QFT closure, and explicit lattice completion contracts. Infinite-dimensional analytic operator theorem and exact first-identification countercontrols, not a new physical model.",
      "sourceRefIds": [
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        "source:ec8fa9bf83ffae580029",
        "source:08f1903717131d70f6c5",
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        "source:80d79b9cbc865eac0053",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:original-winding-theorem-does-not-select-seam-ray",
        "finding:original-b-u-pair-conditionally-reconstructs-whole-circle-channel",
        "finding:original-os-step-needs-full-moments-not-connected-cumulants",
        "finding:graded-field-image-precedes-physical-observable-restriction"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:primitive-transfer-selection-20260912",
      "titleEN": "primitive-transfer-selection-20260912",
      "questionEN": "Unabhängiger Transfer-Vorwärtstest — Arbeitsstand 12. September 2026",
      "date": "20260912",
      "kind": "contract",
      "status": null,
      "verdictRaw": "UNKNOWN",
      "verdictClass": "unknown",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:projector-locality-round31",
      "titleEN": "projector-locality-round31",
      "questionEN": "Round31: projector geometry gives local, full-Fock and density control",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "CONDITIONAL_LOCAL_GEOMETRIC_CONTROL",
      "verdictClass": "partial",
      "stage": null,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:quotient-locality-e8-20261014",
      "titleEN": "quotient-locality-e8-20261014",
      "questionEN": "Does the proposed eightfold fold/multi-interval completion derive physical quotient locality and an E8 field extension from the same source while preserving the quarter phase, state and time?",
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      "status": null,
      "verdictRaw": "EXCLUDED_IN_UNCHANGED_SOURCE",
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      "stage": null,
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      "domain": null,
      "scopeEN": "Known single-complex-charged-CAR representative and the full mass=1, ny=8 QWZ source, with the stipulated canonical common-current time and E8 stress-form premise. The quarter phase is retained. The source-specific analytic spectral obstruction applies to this noninteracting source and a common-Hilbert, source-state/time-preserving limit. The KLM label count is only for KLMVACUUM_REFERENCEV2Z; the actual quarter-source global dual-index is not proved. This is not a derivation from raw P1/P2 or a universal TFPT no-go.",
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      "titleEN": "raw-carrier-origin-gate-20260920",
      "questionEN": "Can the raw primitive polarization and its compression yield the required internal3+2 carrier without another source operator?",
      "date": "20260920",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:reduced-locality-round11",
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      "questionEN": "Round11: actual-source locality and momentum preservation",
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      "verdictRaw": "PASS",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:reference-tail-planner-round27",
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      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:relational-observables-round12",
      "titleEN": "relational-observables-round12",
      "questionEN": "Finite reference frames: complete relational algebra and an exact locality boundary",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
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      "reviewState": "inventoried-not-reviewed",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:research-20261027-source-ground-state",
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      "questionEN": "research-20261027-source-ground-state",
      "date": null,
      "kind": "contract",
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      "verdictRaw": null,
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      "sourceRefIds": [
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      "reviewState": "inventoried-not-reviewed",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:rr-continuous-clock-20260921",
      "titleEN": "rr-continuous-clock-20260921",
      "questionEN": "Does the marked RR quarter-turn extend to a continuous symmetry of the unchanged native W process and its interacting response, and does this select physical source time?",
      "date": "20260921",
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      "status": null,
      "verdictRaw": "PARTIAL",
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      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:rr-positive-pair-source-20260921",
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      "questionEN": "UR.RR.POSITIVE_SOURCE.01: Traegt die positive RR-Form mit W eine hergeleitete gemeinsame Quelle, und welche Rekonstruktion sowie Zustands- und Zeitgrenzen folgen?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:rr-residue-memory-20260921",
      "titleEN": "rr-residue-memory-20260921",
      "questionEN": "Does the marked RR residue quotient identify the four marks with a continuously closed source subsystem, and can compatible metric or clock changes repair its missing constant mode?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:rr-three-family-state-20260921",
      "titleEN": "rr-three-family-state-20260921",
      "questionEN": "Does geometric augmentation U yield an exact native three-family sector and preserve the existing Omega/time?",
      "date": "20260921",
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      "verdictRaw": "PARTIAL",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:scalar-charge-energy-round20",
      "titleEN": "scalar-charge-energy-round20",
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      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:seam-collar-multifield-20261016",
      "titleEN": "seam-collar-multifield-20261016",
      "questionEN": "Does the corrected search accept the known collar source, and what full multi-field sewing follows from its actual boundary data?",
      "date": "2026-10-16",
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      "status": null,
      "verdictRaw": "PARTIAL",
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      "stage": null,
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      "scopeEN": "Corrected search classes, exact known-source controls and canonical CAR boundary quantization; no physical source selection from P1/P2.",
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        "finding:known-quarter-source-full-multifield-control",
        "finding:source-reference-amplitude-retained",
        "finding:joint-fermionic-source-schur-functional",
        "finding:quarter-circle-absolute-zeta-green-eta",
        "finding:quarter-sea-absolute-thermal-central-phase",
        "finding:source-covariance-jet-and-mixed-face-interface",
        "finding:e8-grade-two-explicit-spinor-current-action",
        "finding:intrinsic-source-jet-removes-pure-field-frame-motion",
        "finding:unchanged-ns-vector-generators-cannot-create-d5-spinor-fields",
        "finding:two-face-noncommuting-geometric-response-calculus",
        "finding:raw-face-mask-fails-source-kernel-null-descent",
        "finding:action-response-sewing-does-not-select-lf-intervention",
        "finding:fixed-quarter-jloc-pfaffian-closure-fails-local-skew-test",
        "finding:reverse-bootstrap-retained-operator-scope",
        "finding:e8-current-dictionary-all-separated-responses"
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-constructive-search-20261015",
      "titleEN": "seam-constructive-search-20261015",
      "questionEN": "Which full charged crossed-defect extensions of the fixed ordered CAR source preserve its marking, W4 composition and supplied time law, and which obligations remain for a joint source/state/event derivation?",
      "date": "2026-10-15",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
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      "scopeEN": "Complete finite mu4 character/P-lift classification; global parity equivalence, full T1, positive algebraic state extension and conditional E8 current-group lift. Original source-equivalence is excluded in the unchanged CAR/QWZ Hilbert/Cartan/time scope.",
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      "id": "contract:seam-equivariant-active-search-20261024",
      "titleEN": "seam-equivariant-active-search-20261024",
      "questionEN": "Classify native marked quarter-clock reflection and rotation lifts, their forgetful images and the pure mapping class quotient; compare local model construction with exact active hypothesis search.",
      "date": "2026-10-24",
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      "verdictRaw": "PARTIAL",
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      "stage": null,
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      "scopeEN": "Original E8 sign cocycle and fixed J,T0. Extra projected reflections J^s T0, s=0,1, and rotation J; simultaneous character conjugation for marked objects, Gamma conjugation after forgetting marks. Pure mapping class quotient of the original unmarked ordered four-J stratum.",
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      "titleEN": "seam-full-collar-reconstruction-20261015",
      "questionEN": "Which original seam information determines one common field, state and time action without confusing geometric reflection with boundary polarization?",
      "date": "2026-10-15",
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_CONDITIONAL_RECONSTRUCTION_WITH_SOURCE_CORRECTION",
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      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Original geometric-operator audit; exact closed-graph spectral reconstruction for a given selfadjoint product collar, identified boundary faces and known normal length; conditional quasifree CAR state/time connection; finite rational executable inverse and Lean algebra.",
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        "finding:two-face-graph-state-time-same-datum"
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-gravity-source-bridge-20261013",
      "titleEN": "seam-gravity-source-bridge-20261013",
      "questionEN": "Do the cited finite modular-covariance and coefficient identities establish a geometric horizon action and uniquely select the entropy/EH normalization in the Dorau-Much bridge?",
      "date": "20261013",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Finite modular-covariance checks and a conditional local Cartan-current bridge. The normalization non-identifiability argument applies to the abstract class of normalized fixed-background matter observations; it does not prove multiple admissible realizations of the specified original profile-free gravitational functional.",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-holonomy-generating-20261001",
      "titleEN": "seam-holonomy-generating-20261001",
      "questionEN": "Are T, R, B_Y, R_Y and a family operator Taylor coefficients of one object, the response W_S(z)=sum_{beta in S} exp(i z.beta) B_beta of the original local pair products to a Cartan seam holonomy z? What does the E8 7-design property force on the closed source, and which layer can select flavor? Second round: does a declared port-consistency condition plus finite-order Cartan holonomies select S=48 (3+1) instead of declaring it?",
      "date": "20261001",
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      "verdictRaw": "PARTIAL",
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-joint-automatic-search-20261015",
      "titleEN": "seam-joint-automatic-search-20261015",
      "questionEN": "seam-joint-automatic-search-20261015",
      "date": "20261015",
      "kind": "contract",
      "status": null,
      "verdictRaw": null,
      "verdictClass": "unknown",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-joint-conjugation-20261015",
      "titleEN": "seam-joint-conjugation-20261015",
      "questionEN": "What joint particle-hole, sheet, charge, state and time action follows from the actual retained quarter source, and can its marking be derived covariantly?",
      "date": "2026-10-15",
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_COVARIANT_QUARTER_TRANSPORT",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Actual given chiral source and its exact fold; E8 current lift conditional on the existing extension and coordinate dictionary; original P2 representation audit.",
      "sourceRefIds": [
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        "source:61640bd0004b572bf8db",
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        "source:f75e017104c2b0c5da2d"
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      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:partner-original-carrier-cross-sheet-conjugation",
        "finding:joint-bilinear-hermitian-correction",
        "finding:joint-quarter-transports-marking",
        "finding:joint-fixed-time-marking-repair-excluded",
        "finding:joint-spinor-not-source-coefficient"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-joint-source-origin-audit-20261016",
      "titleEN": "seam-joint-source-origin-audit-20261016",
      "questionEN": "Does the original source derive time, state and the internal 3+2 carrier together, or do the proposed Higgs/Yukawa repairs assume the missing field map?",
      "date": "2026-10-16",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL_SOURCE_DERIVATION_NOT_CLOSED",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Original-source implication audit; exact representation and bundle controls; fixed-background mixed-source identifiability on the reused free Gaussian integration path. No physical source or full P1/P2 countermodel is constructed.",
      "sourceRefIds": [
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        "finding:higgs-determinant-does-not-discharge-carrier-map",
        "finding:primitive-invariant-does-not-select-rank-three",
        "finding:fixed-background-source-does-not-fix-mixed-vertex",
        "finding:local-quarter-inner-variation-is-connection",
        "finding:calderon-enlargement-does-not-select-higgs",
        "finding:finite-sm-higgs-variation-retains-seed",
        "finding:operator-skeleton-does-not-identify-insertion-algebra",
        "finding:internal-even-car-hodge-is-not-coordinate-algebra",
        "finding:minimum-rank-unique-primitive-channel-does-not-select-32",
        "finding:joint-selfconsistency-presupposes-minimal-algebra-fiber-selection",
        "finding:process-composition-and-cyclicity-do-not-select-algebra",
        "finding:quartic-shape-selects-32-only-with-source-sign",
        "finding:quaternionic-sm-mass-winding-is-not-normal-determinant-clutch"
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-joint-ward-state-20261014",
      "titleEN": "seam-joint-ward-state-20261014",
      "questionEN": "Can one D8-containing even-unimodular extension preserve the source charge/clock class, determinant-only packet response, unchanged fold time, and original vacuum requirement at once?",
      "date": "2026-10-14",
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXCLUDED_MARKED_FOLD_COMPLETION",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "The verdict EXCLUDED_MARKED_FOLD_COMPLETION applies only to the historical unique-vacuum/unchanged-K/determinant-only comparison class. It does not exclude or downgrade the positive global even-sector factorization W4=U_s R_c proved relative to the stipulated E8 completion. The source-operator addendum starts from the retained original chiral CAR representation on its chosen source circle theta: multiplication by exp(i theta), its fourth power on the folded source-fermion realification V16_source, the folded boundary condition, normal-ordered Q and K_alpha, and the actual v988 finite-cylinder constructor. This source circle is not identified with the P1 seam-core circle; interpreting source winding four as core winding two additionally assumes a double cover. The addendum proves a genuine global charge-four CAR spectral flow, an affine label factorization, and—after the unitary integrable E8 level-one representation Ls is stipulated—a global neutral current-algebra lift R of the affine factor. On the original even D8 Fock sector relative to that stipulated E8 completion, an explicit extension of the ordered source cocycle and the torus factor Z_a prove the global identity W4=U_s R_c. It does not select either representation or the two kappa lift choices from raw P1/P2, identify R_c automatically with the fixed Tits R, extend the equality to an ordinary local odd-CAR/E8 field algebra, turn the global operators into local memory fields, or identify native f/b operators. D8-containing positive even-unimodular lattice extensions with the actual folded D8 currents; the unchanged K(p,N)=|p|^2/2+delta.p+N; the source cocharacter q=(1,...,1); the retained genuinely eight-periodic U(1)-dressed clock and its composition-preserving square C=g^2; and the original determinant-only packet formula in a common carrier/family frame. In Ls, lambda=q/2 is intrinsically a norm-two root, so every genuine E8 lattice isometry transports it as a root; this derives q=2 lambda and unit carrier/family projection norms in the same q frame, but does not select a physical axis, clutch, operator, coupling or statistics. The dressed clock and source-to-field dictionary remain selected premises, not raw P1/P2 derivations. The neutral SU2 statement additionally assumes the standard unitary level-one Ls lattice-current extension. The independent Ls C lift with pair (8,0) is a valid comparison but is not the square of the same unchanged g. The constructive residue bridge additionally retains the prior finite metric N and explicitly marked M3/U3 dictionary; native U3 is not identified with folded source g^2. The triplet-plus-singlet exclusion assumes the separate EXTRA parallel identification. The spectrum/CP corollary is restricted to the old one-A(h), 24-group single-C class (with common h and real coefficients for the CP statement). The six B_F objects are weight labels in a three-dimensional Cartan space; their rank-three h-map is not a complex-linear CCR-preserving isometry of the full native six-boson module. The family-time addendum projects the already retained fold cocharacter delta into the A3 factor of the assumed dressed-clock/E8 frame. Its action is representation-dependent rho_R(delta_F); it is not a P1 derivation, a native W insertion, an adjoint evolution of Cartan residue labels, or a proof of bilocal necessity.",
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        "finding:even-seam-global-operator-factorization",
        "finding:actual-j-covariant-source-transport",
        "finding:fixed-source-affine-j-obstruction",
        "finding:e8-current-dictionary-all-separated-responses"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-operator-synthesis-20261015",
      "titleEN": "seam-operator-synthesis-20261015",
      "questionEN": "Can typed operator programs and simultaneous inverse intertwiner synthesis generate and exactly check shared operator maps without supplying the desired map?",
      "date": "2026-10-15",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
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      "domain": null,
      "scopeEN": "Executable search infrastructure; known five-mode CAR recovery control and synthetic inverse control. No physical source selection.",
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        "source:a455a5c62fe0ae9a21c9",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:typed-operator-search-calibrated"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-partner-original-action-20261015",
      "titleEN": "seam-partner-original-action-20261015",
      "questionEN": "What does the original P2 carrier actually supply for the source-neutral partner, and which charge, state and time identifications remain distinct?",
      "date": "20261015",
      "kind": "contract",
      "status": null,
      "verdictRaw": "EXACT_TYPED_CARRIER_AND_FOLDED_TIME_AUDIT",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Original finite carrier representation and stipulated E8 fold, with all field/state/time identifications kept separate.",
      "sourceRefIds": [
        "source:189aedd3058f0b1b3250",
        "source:d8567546742e610f8c49",
        "source:3fde3c160d36ee63cd2e",
        "source:56f688ca53661521091e",
        "source:8e4b5ef79400fbe02c51",
        "source:91752ae50bbc9dfba47c",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:partner-carrier-charges-and-state-types",
        "finding:partner-fixed-quarter-time-splits-sm-multiplet",
        "finding:partner-original-carrier-cross-sheet-conjugation",
        "finding:partner-chiral-quarter-conjugation-state-time"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-positive-kernel-search-20261015",
      "titleEN": "seam-positive-kernel-search-20261015",
      "questionEN": "Can unknown positive word kernels be constructed, exactly completed and distinguished without supplying a target Hamiltonian or state?",
      "date": "2026-10-15",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Executable unknown noncommutative moment search; exact finite CAR/transfer realizations under declared search premises. No physical source-selection proof.",
      "sourceRefIds": [
        "source:409e7557c7c04b537f42",
        "source:762da63d2f06fc53d336",
        "source:b73366ef6fdcbae57486",
        "source:16b1e596a317250ab66d",
        "source:e5e537a0e667db8cd8ba",
        "source:05df9e733d35a5e1959c",
        "source:4d12d0dd8e1ef64fd6a1",
        "source:ad81b46b1a2e227f176e",
        "source:2a121873255e9a88d8ce",
        "source:9cc833eb2079e458c128",
        "source:56e3b529ba0dc94c094f",
        "source:13ccb51e1b159f9af18f",
        "source:4b56752f1168d78204b0",
        "source:f6e4bb48f9130fbcd264",
        "source:5eb8689b979a37230289",
        "source:cb6d3e90d7866a6f93fe",
        "source:5765c7974e54a1706b9e",
        "source:1132abf42371fe3320b6",
        "source:105ffbe504b1afbae321",
        "source:547ae4c4427f37cda9e3",
        "source:997f1c76ec096a9bf1b8",
        "source:ed8c0d89086247fd9d30",
        "source:3afed3a07a008b8818ed",
        "source:17f6eceb1cc7b74f3507",
        "source:c1e5bc88cf569b9cb2d6",
        "source:a397753d2e5218cd44c4",
        "source:1f496a5fb69680454eb4",
        "source:7982ab563935dac50687",
        "source:1f22cb567fbcae535590",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:positive-kernel-construction-with-exact-discriminator",
        "finding:faithful-gns-completion-closes-automated-source-query-feedback",
        "finding:declared-charged-pair-relation-leaves-five-word-ambiguity",
        "finding:full-creator-relations-close-fixed-free-two-mode-ambiguity",
        "finding:r098-withheld-response-search-has-exact-conditional-affine-certificates",
        "finding:r098-whole-finite-process-segment-preserves-2245-moments"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-readout-flow-deck-20261005",
      "titleEN": "seam-readout-flow-deck-20261005",
      "questionEN": "Do the existing original seam readout, transfer and NS deck lift select c3, phi_base and the carrier exponent as one physical mechanism, two fixed points or a compiler/process split?",
      "date": "20261005",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Native exact structural and conditional canonical current-algebra calculations. Not a derivation of the physical alpha, raw seam state, spacetime dynamics or compiler/process identity.",
      "sourceRefIds": [
        "source:48c59fc94e258d5e0f67",
        "source:fc9fdd48867c90bed8b3",
        "source:23ecf84107700ebbf4f4",
        "source:0a810385b5c7f25476ae",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-source-character-search-20261015",
      "titleEN": "seam-source-character-search-20261015",
      "questionEN": "Which order-four markings are generated by the retained source time and full charge, and do they supply a physical common source without an inserted P5?",
      "date": "2026-10-15",
      "kind": "contract",
      "status": null,
      "verdictRaw": "COMPLETE_INTERNAL_CHARACTER_CLASSIFICATION_PHYSICAL_SOURCE_OPEN",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "The rational source plane generated by the recorded folded chiral time and fully normalized U1 charge in the stipulated E8 extension; no classification of arbitrary P1/P2 sources.",
      "sourceRefIds": [
        "source:6be2eddd6aad5c3958b3",
        "source:b83b694db052d0b9c932",
        "source:d75e7d585e15dfb7672b",
        "source:216a10dec7eb412614ca",
        "source:197c451a1c62f5c958a6",
        "source:f02b9b92c6e54e6b9443",
        "source:c4954bb482c9ef67ba2b",
        "source:a5dfc171feb6b79742c8",
        "source:2e77e3ed09dce4fcc93a",
        "source:dda280f13b66779aa925",
        "source:61640bd0004b572bf8db",
        "source:711d5aae561daf4fbf70",
        "source:fe0eb5149cf3c9410abf",
        "source:a7de504fcb90ef735b85",
        "source:853aaceb638d0d3744cc",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:source-generated-marking-classification",
        "finding:source-marking-field-realization-boundary"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-source-operator-reconstruction-20261015",
      "titleEN": "seam-source-operator-reconstruction-20261015",
      "questionEN": "Does the actual P1/P2 seam determine a common field, state and time map with the quarter phase retained, and what exact operator conditions permit reconstruction?",
      "date": "2026-10-15",
      "kind": "contract",
      "status": null,
      "verdictRaw": "CONDITIONAL_SOURCE_RECONSTRUCTION_NO_P1_DERIVATION",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Original-source proof audit; abstract operator reconstruction under stated isometry, purity, minimal dilation and actual-time hypotheses; complete continuous scalar Hardy-symbol classification, exact rational diagnostics and conditional CAR sea transport. Same-source CAR excitation-energy identity and global minimizer in the H1 scalar-multiplier class; not uniqueness in the full restricted unitary group.",
      "sourceRefIds": [
        "source:c5bb76f35f44c4dff9e3",
        "source:0ffed8e72dc83416775f",
        "source:fb8061d4a657cf41b10c",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:minimal-defect-uniqueness-not-proved",
        "finding:conditional-seam-field-state-time-reconstruction",
        "finding:continuous-hardy-seam-classification",
        "finding:same-source-seam-energy-selection",
        "finding:master-functional-presupposes-source-selection"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-spectral-response-origin-20261013",
      "titleEN": "seam-spectral-response-origin-20261013",
      "questionEN": "Can one source-native double/lift, frozen reference and geometric/scalar dictionary produce the jointly asserted Einstein and Higgs residue coefficients and physical replica response?",
      "date": "20261013",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Conditional analytic completion of the given geometric Dirac datum plus exact standard-connection coefficient consistency test. Historical v4.5 source interface, not an active v5.4 full TOE countermodel or P1/P2 source selection. Additional Phi-dependent connection or different source trace must be explicitly derived before transferring the mismatch.",
      "sourceRefIds": [
        "source:80f33652de581a9d479c",
        "source:d6f4924449477e05e730",
        "source:00f8dd506e376682fef6",
        "source:d0a39d97399c965f5298",
        "source:50d94a07310752b06302",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-state-dynamics-injectivity-20260918",
      "titleEN": "seam-state-dynamics-injectivity-20260918",
      "questionEN": "Does [rho,C]=0 imply [rho,H]=0 for C=(I+sgn(H))/2, and does the state determine the positive magnitudes of H?",
      "date": "20260918",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite counterexample to the reverse sign-projector inference; positive-temperature KMS inversion retains magnitudes for known beta. No claim against fixed-standard-pair modular uniqueness, the forward mark-local route, or full TFPT source existence.",
      "sourceRefIds": [
        "source:daf3e6e28db68dc7afdc",
        "source:b370f7f1dbbc13f7c3a6",
        "source:f86a680aa838d30576c3",
        "source:2450e97de17e247bb263",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:sign-projector-does-not-determine-time-magnitude",
        "finding:full-faithful-kms-or-transfer-recovers-magnitudes"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seam-two-normalizations-origin-20261005",
      "titleEN": "seam-two-normalizations-origin-20261005",
      "questionEN": "Does one original seam operation select both 8pi/6pi responses, the deck lift and the actual alpha functional?",
      "date": "20261005",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact native lattice and finite contact-operator structure; canonical lattice-VOA interpretation conditional; no physical alpha or raw-source derivation.",
      "sourceRefIds": [
        "source:76ca2670150b50c0dab5",
        "source:8fa8965b438e10abb827",
        "source:4db346a4efa8c422999b",
        "source:b5c31244c7b46e72b8de",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:second-matter-round50",
      "titleEN": "second-matter-round50",
      "questionEN": "Round50: a second matter layer and exact source compilation",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "SECOND_MATTER_SUFFIX_EVALUATED_ON_FULL_CUBIC_BARE_COLUMN",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:1a6ecec927e37b704a2f",
        "source:aed55ab7aff6dbaac943",
        "source:173cce787d8038b499b1",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:second-source-round39",
      "titleEN": "second-source-round39",
      "questionEN": "Round39: evaluated second local source and phase-sensitive response",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "EVALUATED_SECOND_SOURCE_WITH_PHASE_SENSITIVE_RESPONSE_AND_UNIFORM_REMAINDER",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:2e24996a285ffae5af44",
        "source:fce61154713ca98c6336",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:session-reorientation-20260914",
      "titleEN": "session-reorientation-20260914",
      "questionEN": "Welche korrigierte Forschungspriorität und welcher einfache native Kopplungskern bleiben nach dem Abgleich mit sieben anderen Sessions und unabhängiger Gegenrechnung bestehen?",
      "date": "20260914",
      "kind": "contract",
      "status": null,
      "verdictRaw": "partial",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:6ac94b65307272a5e6d1",
        "source:d19a15b06f72d20f472e",
        "source:3330d7faf5098680a091",
        "source:1190aa6b3f0a54102abb",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seventh-frontier-bound",
      "titleEN": "seventh-frontier-bound",
      "questionEN": "Complete grade-seven source: conditional cubic ideal-error bound",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "CONDITIONAL_COMPLETE_GRADE7_SOURCE_BOUND_WITHOUT_COMBINED_READOUT",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:864daf5f70afa2825793",
        "source:f6646f44044dbe496a02",
        "source:2d43046d5403f07c6778",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:seventh-frontier-edge",
      "titleEN": "seventh-frontier-edge",
      "questionEN": "The complete weighted-grade-seven source on the original edge",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "COMPLETE_WEIGHTED_GRADE_SEVEN_SOURCE_ON_ORIGINAL_EDGE_ONLY",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:dd6f81ab26e7b3cdaff3",
        "source:edf4b468091d392acaba",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:sixth-source-round49",
      "titleEN": "sixth-source-round49",
      "questionEN": "Round49: sixth-order ideal source and a new cubic bare readout",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "SIXTH_IDEAL_SOURCE_COMPLETED_AND_CUBIC_BARE_READOUT_EXECUTED",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:0e9a017bd528043babda",
        "source:74f7a4e1c0dae6c727a7",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:soft-sector-round23",
      "titleEN": "soft-sector-round23",
      "questionEN": "soft-sector-round23",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:16ef3681dd55167daae0",
        "source:5781af285c6620c96bf7",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-boundary-lift-selection-20260922",
      "titleEN": "source-boundary-lift-selection-20260922",
      "questionEN": "Does the original boundary completion select a common charged lift, and which joint lifts preserve an independently fixed marked family connection?",
      "date": "20260922",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Archived source-interface audit and conditional common-lift theorem; existing algebraic flavor readout results not reopened",
      "sourceRefIds": [
        "source:39d51b3c66201af0e0b0",
        "source:d1041b87f6c2dfeb620b",
        "source:b5d96938705018af4e45",
        "source:f8e57b8f0468178ffc98",
        "source:8e3a2731b6c3fad1ca92",
        "source:08709460b99ccf1eee9d",
        "source:e065e88309b2744992ff",
        "source:d4a79e2600d5c225927f",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:joint-discrete-data-vs-connection",
        "finding:parallelity-excludes-2plus2-only-conditionally"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-boundary-selection-20260920",
      "titleEN": "source-boundary-selection-20260920",
      "questionEN": "Which declared source conditions select the local E8 boundary reconstruction, which hypercharge must its auxiliary vectorlike singlet pair carry, and can its complementary determinant generate a relative Down/lepton phase?",
      "date": "20260920",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:006cafc7b5c2a3c6c267",
        "source:5140fe49c3f1352ef516",
        "source:44fed40b4ffb6e40e0ec",
        "source:880287fcc4ede19c6224",
        "source:a1d72983700df4e5a41d",
        "source:989bf85561c10e00558b",
        "source:a7266213b19554ed6e03",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-charged-extension-selection-20260921",
      "titleEN": "source-charged-extension-selection-20260921",
      "questionEN": "Does restoring the precompression Clifford maps uniquely reconstruct the charged field dynamics and select the Maxwell bridge from the retained native data?",
      "date": "2026-09-21",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:934adac122037744a366",
        "source:eeb8e47d506e9fa61a27",
        "source:7d80939d7b7e2dc0c3ad",
        "source:55e4b90141e8a133cb6d",
        "source:d4cf77972ad8db8f05f2",
        "source:6e4686481683e4c446c2",
        "source:0281f224c387506e0c0d",
        "source:274773a129450bb20ce6",
        "source:9dae6d6f5191917f5563",
        "source:7c87a004914d4b874844",
        "source:67cd0b334ed2b7d18e48",
        "source:aeb966c37f438399436e",
        "source:483ca1b6d37b48a13d37",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-charged-lift-20260920",
      "titleEN": "source-charged-lift-20260920",
      "questionEN": "Can an integral additive section of the fixed neutral E8 quotient preserve the fixed charged-spinor action, and what minimal local lattice admits the full T(E8) lift?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
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        "source:41dd68a61c01d914c580",
        "source:e5435d1fbd03b8d624c4",
        "source:36f2ed38357601057e31",
        "source:55412ce8ce26c5a51c00",
        "source:66c1385514a1f1223aba",
        "source:f793b7ed2644ccd23f2f",
        "source:29bfa673d8ba06300bdf",
        "source:99d8de4e099a7bd4b0a3",
        "source:943ecb0b783553cc2bba",
        "source:aacf9a01814652f05501",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-charged-register-20260920",
      "titleEN": "source-charged-register-20260920",
      "questionEN": "Can the original static four-phase source retain charged CAR fields and the same time through a correlated register-number encoding, and what locality and interaction does that encoding actually preserve?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:c7ab9d4762ac8b0e6f19",
        "source:3c4eae9874e1f9a9491d",
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        "source:dbbee916835d6a6733ad",
        "source:175f88526d4da138233a",
        "source:a4cbd8b895ef96d1cfe1",
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        "source:5503d50434b54e0591aa",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-chiral-hierarchy-20260922",
      "titleEN": "source-chiral-hierarchy-20260922",
      "questionEN": "Can the actual native auxiliary source or single original clock vertex produce the requested regular chiral hierarchy with singular orders 2,3,5, and what exact source coefficients remain to be derived?",
      "date": "20260922",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:0bbfcf599c71237c4f45",
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-clifford-grade-20260920",
      "titleEN": "source-clifford-grade-20260920",
      "questionEN": "Does retaining the uncompressed Clifford source yield a correctly graded c-spinor field with the same time, and can the existing nonlinear boundary currents supply an explicit source seed instead?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:29bfa673d8ba06300bdf",
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        "source:3f857505a6194995ca19",
        "source:5a0d4e37f1b85004efcf",
        "source:ff9880949d92bc9c7531",
        "source:108f609706e8a4c0b473",
        "source:235b33db2e5fe1c8b500",
        "source:aaceb81735dd6929323e",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-conformal-kernel-selection-20260921",
      "titleEN": "source-conformal-kernel-selection-20260921",
      "questionEN": "Does scalar DtN geometry require a Flat-Away metric selector, and does the actual original v210 state prescription select the charged source?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Massless scalar DtN applicability and fixed-mode limit of original state prescription only; original clock commutator checks remain valid",
      "sourceRefIds": [
        "source:51a507487ee1204c0511",
        "source:3a8c1162fb3aee09e00d",
        "source:ee7faa2c90047ca3e5b5",
        "source:47e069e4a20539c48f72",
        "source:6dce8c8c688da0dee1d5",
        "source:34e7be0db4fde0c8d07b",
        "source:98830732ea619640aed6",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-continuous-marked-time-search-20260922",
      "titleEN": "source-continuous-marked-time-search-20260922",
      "questionEN": "Can any homogeneous Lindblad logarithm realize the supplied full marked source channel, and which continuous source-operator completions preserve the actual marked transfer words?",
      "date": "20260922",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:ee4d0bc06db6b485a0cd",
        "source:5038ede2322f31f899b7",
        "source:85595bd41e3a8b0f97dc",
        "source:41b3e8162b8f3e574512",
        "source:c5d89b903ef61f42755a",
        "source:2f18499f14abf7e82e76",
        "source:4a0482abf318437ceb19",
        "source:567f6e3d74b1ac1bbb89",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:marked-m4-channel-all-powers-homogeneous-gksl-excluded"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-critical-local-fields-20260920",
      "titleEN": "source-critical-local-fields-20260920",
      "questionEN": "Which actual local odd Spin10-family fields exist at the already chosen n/z critical diagnostic, and do their inherited grading, flavor tensor, clocks and source energy form a common physical derivation?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f7f5c929a70d90448ca9",
        "source:aacf9a01814652f05501",
        "source:3658432691218b298b8d",
        "source:1e439d7c162c1742927b",
        "source:787ad21bd39c1f53c113",
        "source:b3af7c351eedd6347f6d",
        "source:959eab6330d7ab138d95",
        "source:39b2ed1d512333ec4434",
        "source:e0629168201f3601e86e",
        "source:25194b22a49e940dd550",
        "source:4f40a0a494c40c1d92bc",
        "source:943ecb0b783553cc2bba",
        "source:9dae6d6f5191917f5563",
        "source:56a0b960fac483365485",
        "source:8bdcc00d10c1f72c45ec",
        "source:1b0d6c5f64f15d995ab5",
        "source:30d8154a5ccd14596a82",
        "source:505289ceb4d805a9cb4e",
        "source:f82a4ab7b22a449e54f7",
        "source:3f53e0c665028211e3e8",
        "source:99d8de4e099a7bd4b0a3",
        "source:1b5421738bbcfe5f455a",
        "source:842124fffe9446638e93",
        "source:34822936be88636e0c31",
        "source:6e4686481683e4c446c2",
        "source:8118da742955a3622195",
        "source:e751d6de69dcf4182277",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-current-operator-time-20260921",
      "titleEN": "source-current-operator-time-20260921",
      "questionEN": "UR.SOURCE.OPERATOR_TIME.01: Do the affine E8 current Ward/OPE data determine the RR/W Hamiltonian jets, and do the direct affine-grade-time or global linear RR-field identifications hold?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:6bd87ac6eca0ac44cfd7",
        "source:8ff3faa3351fed044b50",
        "source:a006af4eaaeaa1af10f6",
        "source:402152563d8e718a5a6b",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-current-symbol-match",
      "titleEN": "source-current-symbol-match",
      "questionEN": "Stimmt das energielinearisierte, gaußgefilterte Quellensymbol Φ_lin(J*B_aJ) auf dem J/J-Block uniform in a exakt mit dem halbzellenverschobenen endlichen Stromoperator T̄_a überein, und mit welcher...",
      "date": "",
      "kind": "contract",
      "status": null,
      "verdictRaw": "proved",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:d64c65647a0a8d669a46",
        "source:3066f6754286d85dc4f8",
        "source:dcc7b778293e536e91e6",
        "source:c8c31449dfb3be3ba06e",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-dressed-native-20260920",
      "titleEN": "source-dressed-native-20260920",
      "questionEN": "Does the existing F(E8) boundary with its odd pair component realize the native W, group action, CAR/CCR state space and original time simultaneously?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:5b827a96c7423545ede6",
        "source:41450371de73c7855325",
        "source:d1b4ef42de6f5f1eafdc",
        "source:0d3382ea897166ccd6e8",
        "source:cbeeeaa90f493635ffb1",
        "source:f199156436043a89fa35",
        "source:17896d312a964b84f10a",
        "source:e818d9510a1c94a516d7",
        "source:607cd39a7e01a9f8f456",
        "source:4e2a249f49e82409d22a",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-driven-carry-20260920",
      "titleEN": "source-driven-carry-20260920",
      "questionEN": "Does an actual unitary history of the unchanged free QWZ strip execute regional half-charge followed by integer carry without resetting the sea, including endpoint energy control?",
      "date": "20260920",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:bdafeebd2225da373e9a",
        "source:a4cbd8b895ef96d1cfe1",
        "source:b07474c5f97b08575078",
        "source:38bc369409ef36cd60c5",
        "source:5540133d30ec92f22dcf",
        "source:a40c3315bb67369a497c",
        "source:f79b0066a770be5ecfaa",
        "source:1d48be6e50787f82483b",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-dynamics-selection-20260920",
      "titleEN": "source-dynamics-selection-20260920",
      "questionEN": "Does faithful transport of the actual free source dynamics select the interacting E8 energy, and which neutral null operators compete along the direct connection between the existing energies?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:8bdcc00d10c1f72c45ec",
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        "source:e1c29d2cd6ef480fb079",
        "source:a154d05fd9b7b2229033",
        "source:1b0d6c5f64f15d995ab5",
        "source:af68c74991b03afe9938",
        "source:c95ce1d59ca525085be2",
        "source:9dae6d6f5191917f5563",
        "source:3e82251e7fbca1d57bc0",
        "source:99d8de4e099a7bd4b0a3",
        "source:5140fe49c3f1352ef516",
        "source:10ab1f4b897a1ffa69c0",
        "source:3c3f9aa20e0f57be47b4",
        "source:aeb966c37f438399436e",
        "source:0eaf3044aa10351e8e47",
        "source:75a6f6c5db2f4d40a7be",
        "source:4b60a8194db510326ff0",
        "source:5f72630975508566af50",
        "source:56a0b960fac483365485",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-edge-charge-transport",
      "titleEN": "source-edge-charge-transport",
      "questionEN": "Halb-Ladung aus der tatsächlichen Randdichte",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "GEOMETRIC_SOURCE_EDGE_CHARGE_WITH_COMMON_REFERENCE_HALF_SHIFT",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:c1680e49d3a16279ab67",
        "source:65c921ec15c1748a08de",
        "source:70d1f5ca41027cb8f812",
        "source:d8baba859733f680bf66",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-flavor-joint-dictionary-20260921",
      "titleEN": "source-flavor-joint-dictionary-20260921",
      "questionEN": "Does one marked D4 intertwiner carry the actual compiler Q, Sigma split, products and residue Gram jointly, and does the primitive source select its physical normalization and response?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Finite abstract D4 module dictionary subclaim only; no physical generation-space identification",
      "sourceRefIds": [
        "source:4107435d41cc599cb259",
        "source:c6a787151b86dbfd2674",
        "source:cf3cdcb68e22501729b4",
        "source:f49d44853652103a0361",
        "source:0adcd48bf9dada12aa4f",
        "source:b34dfd8337f258019135",
        "source:e63f9daafe78f1981266",
        "source:e858a16098000f1d175b",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-flavor-origin-20260920",
      "titleEN": "source-flavor-origin-20260920",
      "questionEN": "Do the original global carrier group and actual native cubic select a consistent source-level route to distinct Down/lepton masses and phases?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:be5004db766a700e0687",
        "source:3f53e0c665028211e3e8",
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        "source:39d1baf06f5f2be330e9",
        "source:e779bd2e12c6253776e8",
        "source:f02b9b92c6e54e6b9443",
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        "source:acad534dfc1f2a819138",
        "source:0420ebab0494f5de96c7",
        "source:4f40a0a494c40c1d92bc",
        "source:4835060df537815031e4",
        "source:26c4fadfb4014511fe11",
        "source:5140fe49c3f1352ef516",
        "source:ae3fc589a95433fd85c4",
        "source:505289ceb4d805a9cb4e",
        "source:c831c1bb311401a15b85",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:flavor-ratio-closed-absolute-anchor-open",
        "finding:alpha-equation-is-fixed-input-closure"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-flux-index-20260920",
      "titleEN": "source-flux-index-20260920",
      "questionEN": "Does preservation of original source markings select the gauge charge whose unit-flux index is n and whose full integral neutral quotient is E8?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:aceb54dc82ac9725c8a0",
        "source:63b15aa40088970e4d75",
        "source:aedc8757f5d5f5160ff7",
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        "source:c95ce1d59ca525085be2",
        "source:f43c67aaf569ae03ec99",
        "source:caaa70df13d6f7810b7f",
        "source:b9e790bd9d723cb4fc7f",
        "source:2e9d760e384734594a90",
        "source:117af94c29e6b38e8752",
        "source:dbbee916835d6a6733ad",
        "source:7c87a004914d4b874844",
        "source:f02b9b92c6e54e6b9443",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-graded-gns-matter-gate-20260922",
      "titleEN": "source-graded-gns-matter-gate-20260922",
      "questionEN": "Do the supplied graded GNS and cubic extensions select the original source and supply native Spin(10) spinor fields?",
      "date": "20260922",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:10ece8d43a8176c14637",
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        "source:cbb8b1853d9fc8be9e67",
        "source:b973a7d4560c553eb241",
        "source:7275ae8f8e7ec6053c47",
        "source:182e618f72f229125b2e",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:operational-seed-is-input"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-graded-locality-20260920",
      "titleEN": "source-graded-locality-20260920",
      "questionEN": "Does the existing E8 boundary plus massive complement contain the light graded fields required for a source-derived flavor mass map, and what exact locality information is lost by projection?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:ff0db429f61e3cf036c8",
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        "source:2aec9208e2df3216a866",
        "source:63dcd78603646c245721",
        "source:12570a4082496ade15b5",
        "source:4a0f2ddb373a569df985",
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        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-ground-response-20260920",
      "titleEN": "source-ground-response-20260920",
      "questionEN": "Can the original nonlinear dressed boundary fields realize the actual native N=64 charged ground response by choosing any true ground state of the existing quarter-shifted boundary, with the same adjoint and a common physical time?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:ac5d87bb06082d2be19b",
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        "source:68a4c97be33e6d8fc17c",
        "source:cc75af353e7b710c0401",
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        "source:361270c9be6b5f0decc9",
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        "source:77e2f7e9f69de0e218e5",
        "source:b199cac2f5f94a15a573",
        "source:8a6c5195c8ae7b833d5b",
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-half-sector-bridge",
      "titleEN": "source-half-sector-bridge",
      "questionEN": "Source sectors 1 and 3: half-shift, opposite-edge compensation and carry",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "SOURCE_HALF_SECTOR_REFERENCE_AND_ENERGY_BRIDGE",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:5b82ee428a2a0cb34476",
        "source:4bacc49b54757b96265b",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-joint-response-20260921",
      "titleEN": "source-joint-response-20260921",
      "questionEN": "UR.SOURCE.JOINT_RESPONSE.01: Does the existing source determine a complete joint pair/mediator response, and can the native Pauli coefficients and raw affine signed W bridge be verified without presupposing H+?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b3566a9c621d7d8bb594",
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        "source:edfe106cf2cec21ef9ae",
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        "source:7488f2ee220403a85945",
        "source:7edc8a5445de46f782a7",
        "source:00294450f024a1b6a5ab",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-joint-spin-family-lift-20260922",
      "titleEN": "source-joint-spin-family-lift-20260922",
      "questionEN": "Does the original coupled E8 quotient repair the odd-Chern Spin obstruction, and does the primitive source select its joint lift?",
      "date": "20260922",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Internal bundle and source-selection interface; no physical source equivalence or ledger promotion",
      "sourceRefIds": [
        "source:2af921167641f9084e23",
        "source:07385e27d89f4d82c531",
        "source:11dc1979de7c268f76af",
        "source:1d74941fae3ff792fffc",
        "source:e3c19f4a0050c25dc0d9",
        "source:95ba9ac8a1f72addb4bf",
        "source:747c16c43505d20b2112",
        "source:016464d48b5762d22ee5",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:joint-discrete-data-vs-connection",
        "finding:parallelity-excludes-2plus2-only-conditionally"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-local-line-20260920",
      "titleEN": "source-local-line-20260920",
      "questionEN": "Does the fixed-circle charged-time obstruction survive a genuine local growing-radius limit of the unchanged source, and can its original post-compression carrier restriction retain both polarization signs?",
      "date": "20260920",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:67c1c3665f38d5a2c99b",
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        "source:80fe820d0527c6d65025",
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        "source:92fcfdd21de1a628520c",
        "source:4b648793a8b3f0a4f4d4",
        "source:19751489cb9d4e33a965",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-local-time-origin-20260921",
      "titleEN": "source-local-time-origin-20260921",
      "questionEN": "Does the weighted scalar local-time classification select the original charged TFPT source, including its winding and same-space transfer?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Conditional scalar operator theorem and audits of prospective source identifications; no change to existing ledger verdicts",
      "sourceRefIds": [
        "source:421592e698e443e35ac2",
        "source:56f7b4b5773c0a9db78b",
        "source:0606a2fa1cb0c6a98122",
        "source:95708479494b162794ad",
        "source:be1e2ab8ff9dbeb1a8b6",
        "source:84d46ea3fe06c5db797f",
        "source:fb82e0b192d01b55844f",
        "source:b4d71e932b8391c43fcf",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-localized-spinor-20260919",
      "titleEN": "source-localized-spinor-20260919",
      "questionEN": "Can the existing microscopic CAR source realize the bounded observable responses of a localized spinor sector before constructing an unbounded intersector field?",
      "date": "2026-09-19",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Analytic L2 extension and bounded source-word responses of a known DHR spinor sector, conditional on existing source convergence, eight graded source copies, the even net, a fixed holonomy trivialization, and the cited sector theorem. Does not construct a microscopic charged field or preparation channel, prove FE-GEN/exhaustion, select the E8 extension, identify raw P1, or close a TOE gate.",
      "sourceRefIds": [
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        "source:03ae61cf34290c4cf197",
        "source:ae5dd487f0bbe0d570ef",
        "source:431c98ec09e35f7430b3",
        "source:e08fb982d9042e718e33",
        "source:292618b2076397d7a181",
        "source:d64e53814f0dedd8f069",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-maxwell-field-transfer-20260921",
      "titleEN": "source-maxwell-field-transfer-20260921",
      "questionEN": "Whether the Maxwell quotient is the full original field/time transfer and whether it closes TFPT.",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact finite algebra and conditional local Maxwell/Gauss statements; no physical closure claim.",
      "sourceRefIds": [
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        "source:6c5fb8bd0ff6da6baa14",
        "source:67cd0b334ed2b7d18e48",
        "source:438b60394c7313ecb761",
        "source:af0d636d7ec160dd05cb",
        "source:1e2af3ddd743c917cecf",
        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-mixed-response-reconstruction-20260921",
      "titleEN": "source-mixed-response-reconstruction-20260921",
      "questionEN": "[UR.SOURCE.MIXED_RESPONSE.01] Do canonical lower responses and a single filled-state transition defect reconstruct the complete native interaction, and is the corresponding primitive-source value available?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:815275f2b89d31eae593",
        "source:8daf4c75479c462443e6",
        "source:57d770128265906ce030",
        "source:35053273db3c55d352a2",
        "source:b32c5f75a8084c345416",
        "source:40559ac1f5456474ca20",
        "source:08446d3c3592127321a4",
        "source:7a27ab30185b4487e02f",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-native-clock-flavor-bridge-20260922",
      "titleEN": "source-native-clock-flavor-bridge-20260922",
      "questionEN": "Do original compiler and monodromy clocks admit one orientation-correct common dictionary, and can the existing symmetric source channel supply full-rank CP-breaking family vertices compatible with TFPT hierarchy constraints?",
      "date": "20260922",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:e634528ffdade16662df",
        "source:89bf0f98fe026b441ebe",
        "source:a9c5156d2c48c38eedc7",
        "source:fd9b3336af6c4a96de88",
        "source:16393ec76b10adfc8014",
        "source:b61930e9ea84de5c511b",
        "source:fd40bca55608b2ddd9df",
        "source:34a064bae3692568d373",
        "source:d4bd17c2c989afcf15f5",
        "source:200e998e81faeec94c34",
        "source:c43c1ed544a29620850b",
        "source:76e5a0cf358847781c4a",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-native-retarded-selection-20260922",
      "titleEN": "source-native-retarded-selection-20260922",
      "questionEN": "Does the existing native W interaction provide a source-derived current kernel and the nondegenerate family time response required by the existing Yukawa target?",
      "date": "20260922",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:9f61bd8eb9976328bdd0",
        "source:f8c268a1a43d479ef3cc",
        "source:5fce8f714c9ca9c79696",
        "source:ad7e506dcf3ec4479eec",
        "source:b39927325066fa946ff8",
        "source:563ac0da2106e3c791a6",
        "source:9350a5a36c63b0c84e4e",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-observation-identifiability-20261013",
      "titleEN": "source-observation-identifiability-20261013",
      "questionEN": "Can the common matter/modular future quotient determine geometric source normalization, and does tracing the family by itself isolate the fractional carrier response?",
      "date": "20261013",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Exact identifiability within an abstract observation class and conditional lattice-net dictionary. Not a countermodel to uniqueness of the specified original profile-free gravitational functional; no full physical source/net constructed.",
      "sourceRefIds": [
        "source:1887124fcae4b80de30f",
        "source:f13b928c165980bb76f3",
        "source:065da6ad161ddf8d781f",
        "source:07d69c590ca5ec41ce9f",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:matter-observations-do-not-fix-geometric-response"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-operator-origin-20260920",
      "titleEN": "source-operator-origin-20260920",
      "questionEN": "Can the unchanged native Fock or rotor source produce the common odd local boundary fields and select their critical interaction with the same group action, grading and physical time?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:90313161ac3d0c3a9983",
        "source:21fd337feebda22aed6d",
        "source:dbbee916835d6a6733ad",
        "source:cdbf5f0c226cac948aa4",
        "source:47df87824b335806e844",
        "source:eff9b71e72668d9d6009",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-oriented-polarization-20260921",
      "titleEN": "source-oriented-polarization-20260921",
      "questionEN": "Can the original oriented scalar seam kernel select a charged CAR polarization and its time response without a target covariance?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Scalar CR reconstruction, original source applicability, and conditional spin/CAR bridge only; original clock and Clifford identities preserved",
      "sourceRefIds": [
        "source:c650cf3d8993bb78312b",
        "source:ee8614e11e4c7cdd66e0",
        "source:b5078e6c72a50e8974d6",
        "source:a022d474f6ef6d73bc9e",
        "source:260ab5ef6ac51496b1c9",
        "source:ddf807b9a828a6ad19c9",
        "source:a0743cb562c750d9faf1",
        "source:337eb41c08eb790bf8a7",
        "source:a3a58c6cdb957e4a147f",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-pair-transfer-20260920",
      "titleEN": "source-pair-transfer-20260920",
      "questionEN": "Does the actual all-time response of the existing dressed F(E8) fields derive the native attractive pair interaction while retaining source state, energy and one-particle calibration?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:d8c41a5a28b4b6773f59",
        "source:27087f9c3e3840988fbb",
        "source:175f88526d4da138233a",
        "source:63b7cf84bfe6ec263fef",
        "source:928c95c0e88391017a80",
        "source:2cf246b22d633571a0c8",
        "source:b832318e3ae32b53ef38",
        "source:41c9ee3ce8906fbfe72c",
        "source:b7374656ae2c01108e0d",
        "source:6d0f91e82029aae8f92c",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-probe-carry-20260920",
      "titleEN": "source-probe-carry-20260920",
      "questionEN": "Does the new QWZ/carry/probe report hold, and does the full operator-valued spinor transition measure give exact projected controlled dynamics?",
      "date": "20260920",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:c9f6f2463a46d40a5cbd",
        "source:6f55479c23adeeff02c7",
        "source:c9555a834d4ab6f6c836",
        "source:f63d29e13db47f90b0d1",
        "source:087f429b119c1ad166a7",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-register-response-20260920",
      "titleEN": "source-register-response-20260920",
      "questionEN": "What charged and disorder response follows from the original v1033 source, its actual finite ground, and the correlated completed CAR encoding, with one common Hamiltonian and time?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-rg-clock-bridge-20260920",
      "titleEN": "source-rg-clock-bridge-20260920",
      "questionEN": "Can the unchanged one-copy QWZ source hide the missing bounded-energy channels, and can chiral fixed-point stability and Coxeter covariance select common physical kinetics?",
      "date": "20260920",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
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      "stage": null,
      "evidenceClass": null,
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-rotor-gauss-20260920",
      "titleEN": "source-rotor-gauss-20260920",
      "questionEN": "What exact Gauss-physical reduction and source-charge constraints does the existing compact-U(1) rotor provide, and can they support a finite-local E8 current map?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-rule-search-20260930",
      "titleEN": "source-rule-search-20260930",
      "questionEN": "Do the original P1 normal-spin/winding types and actual SM/clock constraints select a joint source operator? Test the explicit Bott/basic-E8 class map and its actual operator normalization before further response optimization.",
      "date": "20260930",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:normal-clutch-orbit-index-equivariantly-recovers-given-weak-module"
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-sector-reconstruction-20260920",
      "titleEN": "source-sector-reconstruction-20260920",
      "questionEN": "Can the original charged fermionic Gamma NS/R sectors and their odd-field response be reconstructed from the fixed even neighbor L_h with inherited charges, parity, and assigned time?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:unchanged-ns-vector-generators-cannot-create-d5-spinor-fields"
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-stable-low-charge-reconstruction-20260921",
      "titleEN": "source-stable-low-charge-reconstruction-20260921",
      "questionEN": "UR.SOURCE.LOWQ.01: Rekonstruieren globale Operatorantworten, volle irreduzible Fockdarstellung und globale uniforme Semibeschraenktheit den stabilen Generator bereits aus Q<=4, und sind seine Quelljets tatsaechlich aus P1/P2 hergeleitet?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-static-register-20260920",
      "titleEN": "source-static-register-20260920",
      "questionEN": "Can tracing the existing static four-phase source register produce a deterministic interacting matter evolution, and how can true reduced four-point non-Gaussianity be distinguished from a coherent quartic Hamiltonian?",
      "date": "2026-09-20",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-three-route-closure-20260922",
      "titleEN": "source-three-route-closure-20260922",
      "questionEN": "Do original source selection, native current response, and the existing flat family connection close into one source-derived process?",
      "date": "20260922",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-variation-origin-gate-20260922",
      "titleEN": "source-variation-origin-gate-20260922",
      "questionEN": "Do the actual scalar source and natural determinant lift generate the proposed GN/Berry mechanism, and does the original minimal-bordism or spectral-action selection fill the missing charged operator map?",
      "date": "20260922",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-yukawa-forward-gate-20260921",
      "titleEN": "source-yukawa-forward-gate-20260921",
      "questionEN": "Does the actual fixed microscopic seam-mode covariance yield a finite source-induced Dirac block without target Yukawas, and can pure covariance compression preserve physical time?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:source-z8-parity-descent-20260921",
      "titleEN": "source-z8-parity-descent-20260921",
      "questionEN": "Can the existing gauge parity complete the internal quarter operation without an additional parent and restore the required fermionic matter?",
      "date": "2026-09-21",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:spectator-clock-round16",
      "titleEN": "spectator-clock-round16",
      "questionEN": "spectator-clock-round16",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:spectator-normalization-separation-20261013",
      "titleEN": "spectator-normalization-separation-20261013",
      "questionEN": "Does the finite seam-generated/no-spectator repair also fix absolute source normalization, and is its commutant helper invariant under equivalent complex bases?",
      "date": "20261013",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": "Finite linear-algebra cross-check of the existing model and abstract normalization criterion; no proof that scalar shifts are admissible original TFPT source deformations, no fixed-Fermi-level covariance equivalence, no 4D reconstruction.",
      "sourceRefIds": [
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        "source:9172d51c671f87b8e0ee",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:symmetric-source-car-interface-20260921",
      "titleEN": "symmetric-source-car-interface-20260921",
      "questionEN": "Can the complete 820 symmetric E8 product image be carried into the existing Majorana CAR with the same products, vacuum, Cartan charges and charged time, and yield the required physical scalar coupling?",
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:bd2a768b9bb71fe56fcc",
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:symmetric-source-product-audit-20260921",
      "titleEN": "symmetric-source-product-audit-20260921",
      "questionEN": null,
      "date": "20260921",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:systematic-origin-audit-20260912",
      "titleEN": "systematic-origin-audit-20260912",
      "questionEN": "Liefern die ursprünglichen endlichen Regeln gemeinsam Ursprung (Clock), Wechselwirkung und Ladung mit physikalischen Identifikationen, die eines der acht TOE-Tore T1–T8 schließen?",
      "date": "20260912",
      "kind": "contract",
      "status": null,
      "verdictRaw": "all_replays_pass; physical_completion_proved=false; physical_gates_closed=[]",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:f75e017104c2b0c5da2d"
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:tfpt-full-process-20261002",
      "titleEN": "tfpt-full-process-20261002",
      "questionEN": "Is there ONE parameter vector Theta and ONE state |Omega_Theta> from which chiral light matter, flavor, charges, the E8 readouts, alpha, mass relations, dynamical gauge fields, the space-time cone and gravity follow simultaneously?",
      "date": "20261002",
      "kind": "contract",
      "status": null,
      "verdictRaw": "FAIL",
      "verdictClass": "fail",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:tfpt-unified-source-derivation-20261029",
      "titleEN": "tfpt-unified-source-derivation-20261029",
      "questionEN": "Combine the actual TFPT source derivation into one scoped chain and reduce neutral source word matching to structural current, state, time and reflection conditions.",
      "date": "2026-10-29",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIAL",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
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        "source:b1415931b6d09a70be47",
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        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [
        "finding:whole-quarter-channels-identified-by-exact-internal-kernel",
        "finding:actual-joint-insertion-hull-resolves-eight-coefficient-directions",
        "finding:e8-bare-trilinear-and-single-anchor-weyl-class-insufficient",
        "finding:complete-family-four-cycle-class-separates-native-clock-from-sm-preservation",
        "finding:native-clock-word-transpose-has-static-rank-four-counterexample",
        "finding:whole-constant-coupled-source-is-implementable-despite-isolated-insertion-domain",
        "finding:fixed-quarter-jloc-pfaffian-closure-fails-local-skew-test",
        "finding:same-collar-has-canonical-selfdual-kinetic-pairing-and-charged-determinant",
        "finding:quarter-cover-pairing-does-not-supply-local-normal-or-select-scale-measure",
        "finding:fixed-aps-source-has-whole-inverse-and-finite-boundary-correction",
        "finding:mass-only-deck-relative-heat-action-fails-free-infinite-trace",
        "finding:finite-antiperiodic-scalar-wall-has-no-exact-massless-normal-mode",
        "finding:spectral-heat-covariance-positivity-does-not-imply-time-rp",
        "finding:quaternionic-sm-mass-winding-is-not-normal-determinant-clutch",
        "finding:bounded-relative-trace-obstruction-and-whole-genuine-pair-heat-reader",
        "finding:normal-clutch-orbit-index-equivariantly-recovers-given-weak-module",
        "finding:normal-orbit-spin-family-index-and-signed-charge-balance",
        "finding:fixed-flavor-cartan-sign-cover-and-root-lift-parity",
        "finding:original-family-vector-action-is-not-cartan-rotation-or-spinlift-selection",
        "finding:actual-genus-two-sign-family-closes-common-parallel-k-connection",
        "finding:actual-q-quarter-extends-common-k-connection-and-real-coefficient-lifts",
        "finding:real-source-reflection-is-not-linear-duality-or-compact-clock-inversion",
        "finding:source-selected-spin-and-q-signs-have-three-explicit-global-kernels",
        "finding:source-s0-szego-point-legs-generate-q-kernels-with-typed-products",
        "finding:actual-spin-kernel-determinant-has-inverse-q-norm-character",
        "finding:closed-source-flavor-spin-has-functorial-pfaffline-with-charged-type-limit",
        "finding:original-relative-seam-has-explicit-whole-graph-fredholm-mismatch",
        "finding:whole-constant-coupled-clutch-defects-are-exact-internal-kernels",
        "finding:old-complex-scalar-clutch-separates-c0-and-product-reflection",
        "finding:scalar-defect-circle-character-does-not-select-projector-holonomy",
        "finding:source-spin-is-canonical-ramified-base-spin-pullback",
        "finding:original-v117-has-explicit-algebraic-q-cover-fundamental-frame",
        "finding:double-circle-reflection-does-not-fix-entire-cubic-cable-seam",
        "finding:actual-fuchs-real-map-transports-whole-given-finite-source-state-and-time",
        "finding:actual-e0-compensator-extends-whole-k-e8-with-transported-quarter",
        "finding:actual-v252-entire-real-basis-has-signed-p2-dual-dictionary",
        "finding:chiral-fuchs-source-transport-has-distinct-majorana-phase-and-torus-absorption",
        "finding:native-theta-composition-retains-conjugate-source-and-parity-square",
        "finding:single-graph-range-isometry-does-not-give-local-whole-seed-map",
        "finding:hard-holonomy-selfduality-leg-and-finite-character-phase-separation",
        "finding:original-z6-positive-structural-kernel-does-not-supply-oriented-phase-observable",
        "finding:original-genus-two-hexagonal-rotation-has-concrete-rho-hodge-line",
        "finding:original-mixed-spin-products-realize-positive-u6-cycle",
        "finding:actual-spin-quadratics-reach-original-hexagonal-hodge-line",
        "finding:spin-pair-car-transport-retains-parity-and-whole-source-types",
        "finding:real-total-trace-does-not-exclude-coherent-phase-reader",
        "finding:geometric-six-spin-clock-differs-from-marked-native-clock",
        "finding:whole-q-to-p-pullback-transports-given-source-state-and-time",
        "finding:actual-fixpoint-evaluation-keeps-coefficient-signs-and-source-type",
        "finding:original-source-naturality-needs-no-second-p-image-background",
        "finding:canonical-spin2-lift-carries-whole-annulus-source-with-reversed-time",
        "finding:geometric-spin-collar-map-closes-weighted-image-domain-with-total-deck-action",
        "finding:claude33-annulus-map-is-valid-distinct-type-not-unique-geometric-spin-selection",
        "finding:original-mixed-spin-products-already-have-complete-dual-hom-coefficients",
        "finding:whole-f5-graph-supplies-canonical-reverse-qp-hom-kernel",
        "finding:actual-spin-product-weight-has-canonical-trace-class-form-pairing",
        "finding:fully-descended-covariant-reverse-kernel-removes-rho-form-channel",
        "finding:original-a4-linear-quarter-does-not-supply-proposed-scalar-mu3-repair",
        "finding:offdiagonal-hom-matches-a4-family-six-but-not-two-triplet-e8-product",
        "finding:compact-e8-adjoint-completes-family-six-with-carrier-rank-retained",
        "finding:three-family-cx-recursion-closes-exact-d8-with-minimal-original-escape",
        "finding:original-weak-current-coefficient-has-explicit-finite-oneform-consumer",
        "finding:original-d5-zero-mode-closes-triplet-carrier-and-fixed-glue-is-minimal-escape",
        "finding:mixed-spin-full-deck-has-no-rank-three-projector",
        "finding:actual-reverse-hom-diagonal-supplies-global-q-hodge-response",
        "finding:bare-c3-kernel-diagonal-yukawas-have-common-real-frame",
        "finding:original-primitive-action-is-present-highpass-is-not-finite-selector",
        "finding:atlas-detail-retrieval-recovers-existing-d4-solution",
        "finding:original-poisson-normal-trace-fixes-whole-calderon-graph",
        "finding:induced-original-hardy-defect-gives-finite-whole-source-reader",
        "finding:original-weak-quartic-action-has-nonzero-nonlinear-response",
        "finding:all-common-leading-distance-clutches-fail-original-flavor-lengths",
        "finding:actual-hardy-response-has-weak-clifford-odd-and-ko-real-completion",
        "finding:two-entry-hardy-adjoint-hierarchy-fails-full-ko-and-su2",
        "finding:actual-fuchs-halfpath-has-canonical-g-metric-c6-kernel-map",
        "finding:original-real-delta-jet-reads-same-marked-hardy-open-word",
        "finding:four-actual-fuchs-spine-edges-recover-marked-meridians-and-nonzero-open-word",
        "finding:native-adjoint-quarter-clock-cannot-compensate-hardypair-odd-character",
        "finding:whole-cubic-gram-differential-retains-hardy-phase-and-cross-resonance",
        "finding:complete-original-mu01-hardy-reader-has-two-calibrated-entries",
        "finding:whole-six-original-hardy-inputs-generate-full-family-coefficient-algebra",
        "finding:actual-whole-hardy-alphabet-has-finite-particle-hole-wick-block",
        "finding:bare-unsmeared-mu-crossface-quadratic-fails-vacuum-domain",
        "finding:linear-spectral-centralization-does-not-replace-full-marked-hardy-source",
        "finding:original-admissibility-projector-is-explicit-penalties-do-not-read-retained-amplitudes",
        "finding:actual-original-inner-fluctuation-has-whole-noncommuting-two-face-response",
        "finding:fiber-only-primitive-split-and-frozen-gap-miss-original-action",
        "finding:oriented-resolvent-weights-do-not-identify-original-reflection-producer",
        "finding:current-odd-carrier-reader-is-lossless-on-whole-coupled-source",
        "finding:ap-spectral-formulas-do-not-force-normal-domain-or-complete-source",
        "finding:actual-weak-connection-transmits-family-orientation-to-both-faces",
        "finding:original-higgs-variation-is-not-independent-yukawa-stationarity",
        "finding:actual-weak-cap-converges-on-whole-quarter-circle",
        "finding:canonical-clifford-double-derives-normal-ap-and-typed-deck",
        "finding:universal-graded-source-reducing-images-do-not-fix-carrier-frame",
        "finding:whole-two-face-compression-projector-defect-detects-hidden-source-loss",
        "finding:actual-v252-quark-lepton-split-prevents-weak-grading-uniqueness-inference",
        "finding:actual-graded-hypercharge-trace-rejects-quark-lepton-sign-intertwiner",
        "finding:separable-normal-real-maps-compose-to-given-deck-and-quarter-image",
        "finding:actual-gauge-real-frames-leave-carrier-phase-as-coordinate-freedom",
        "finding:original-higgs-family-has-one-complex-kk-class-but-different-whole-sources",
        "finding:signed-one-particle-modular-weight-is-not-the-positive-even-heat-operator",
        "finding:three-moments-select-one-exponential-exactly-in-positive-laplace-class",
        "finding:existing-ap-positive-source-factor-has-oriented-poisson-heat-bridge",
        "finding:actual-v252-entire-compatibility-family-has-generic31-dimensional-quotient",
        "finding:full-memory-schur-reconstruction-preserves-every-ordered-word-under-nesting",
        "finding:original-return-and-native-j-have-minimal68-dimensional-all-word-memory",
        "finding:original-full-source-regulator-flow-retains-normalized-kernel-and-vacuum-factor",
        "finding:full-reflected-quadratic-regulator-cone-preserves-every-rp-source",
        "finding:original-shared-higgs-source-induces-fixed-yukawa-mixed-matter-words",
        "finding:local-even-yukawa-sewing-preserves-given-joint-graded-rp",
        "finding:whole-original-constant-higgs-orbit-has-reduced-majorana-spectral-response",
        "finding:archived-geometric-higgs-residue-bulk-needs-coefficient-identification-repair",
        "finding:original-local-higgs-residue-linear-coefficients-fail-same-trace-heat-ratio",
        "finding:whole-original-higgs-moments-fix-conditional-local-kinetic-mass-quartic",
        "finding:whole-variable-original-higgs-bound-reference-response-and-forced-clifford-factor",
        "finding:original-symmetric-scale-map-fails-simultaneous-higgs-einstein-repair",
        "finding:whole-original-higgs-inner-scale-and-affine-full-source-transport",
        "finding:normal-higgs-mode-type-and-exact-kernel-metric-require-actual-relative-operator-map",
        "finding:original-superconnection-grades-and-weighted-heat-retain-higgs-kinetic-excursions",
        "finding:whole-normal-reduction-preserves-relative-spectral-reader-and-higgs-jets",
        "finding:original-admissibility-own-spectral-reader-has-no-free-low-mode-residue-repair",
        "finding:whole-total-chiral-positive-spectrum-retains-higgs-kinetics-and-common-half-trace",
        "finding:whole-scale-energy-response-uniquely-reconstructs-normal-profile",
        "finding:original-relative-scale-flow-separates-residue-finite-part-and-local-anomaly",
        "finding:original-whole-green-produces-energy-response-with-correct-orthogonal-trace",
        "finding:whole-mixed-scale-source-reads-bosonic-insertion-before-higgs-average",
        "finding:current-original-spectral-action-triplet-fails-positive-laplace-class-unless-leading-relative-term-cancels",
        "finding:correct-current-argument-weights-link-whole-higgs-threshold-and-same-einstein-response",
        "finding:whole-original-spinor-curvature-a4-has-no-independent-scalaron-r-squared",
        "finding:whole-original-entropic-curvature-corrects-max-symmetric-scalar-scale",
        "finding:given-whole-higgs-source-fixes-radial-curvature-susceptibility-without-extra-scalar",
        "finding:actual-original-four-ghost-complex-preserves-base-selector-with-full-cohomology-and-distinct-traces",
        "finding:whole-original-admissibility-energy-source-recovers-constraints-but-cannot-replace-geometric-operator",
        "finding:original-moving-normal-kernel-fixes-induced-connection-and-full-scale-covariance",
        "finding:fixed-original-o1-source-rejects-nonconstant-normal-multiplier-and-fixes-placement-test",
        "finding:original-master-variation-keeps-spin-weight-and-active-source-route-typed",
        "finding:shared-original-higgs-mixture-has-invariant-color-fourpoint-wick-defect",
        "finding:bounded-fixed-rank-spectral-action-does-not-normalize-noncompact-higgs-volume",
        "finding:whole-original-quarter-source-bounds-higgs-weight-uniformly-through-joint-mode-ir-limits",
        "finding:original-o1-covariance-leaves-full-radial-higgs-law-and-exact-fourier-source-readout",
        "finding:whole-process-reconstruction-priority-and-original-locality-geometry-input-audit",
        "finding:actual-disjoint-local-weyls-acquire-spurious-commutator-under-bare-native-compression",
        "finding:actual-quarter-current-state-excludes-nontrivial-geometric-local-point-time",
        "finding:actual-elliptic-interval-car-source-produces-local-modular-generator",
        "finding:actual-proper-two-face-regions-do-not-contain-pure-local-source-double",
        "finding:actual-elliptic-whole-environment-fixes-regional-car-partner",
        "finding:actual-original-color-triplet-has-spectator-dependent-modular-field-law",
        "finding:actual-color-marginal-has-complete-finite-source-reader-and-mixture-criterion",
        "finding:two-and-four-field-words-do-not-complete-original-color-triplet-source",
        "finding:whole-original-quarter-occupation-tower-uniquely-reconstructs-common-radial-higgs-law",
        "finding:finite-original-tower-reader-and-existing-weak-symmetry-fix-shared-matter-responses",
        "finding:unchanged-free-quarter-source-cannot-be-nontrivial-integrated-higgs-mixture",
        "finding:actual-e8-record-doily-action-is-signed-p-plus-compatible-point-with-typed-sym2-lift",
        "finding:actual-e8-record-words-distinguish-order-and-retain-phase-beyond-fifteen-labels",
        "finding:literal-doily-incidence-output-and-strict-causal-order-on-fifteen-source-labels-excluded",
        "finding:actual-doily-context-record-characters-have-ranks-four-two-two-two",
        "finding:canonical-standard-split-localizes-original-source-record-words-with-full-descendant-companion",
        "finding:unchanged-global-sixty-event-source-fails-local-exterior-current-test",
        "finding:canonical-source-localization-changes-exterior-state-and-does-not-select-event-origin",
        "finding:original-elliptic-fixed-holonomy-insertion-gives-local-operation-on-unchanged-source",
        "finding:original-quarter-pair-fixes-square-charge-law-half-response-and-real-quillen-norm",
        "finding:actual-elliptic-source-determines-all-path-normalized-causal-current-response",
        "finding:original-higgs-quark-source-has-exact-whole-su3-counting-response",
        "finding:single-original-color-parity-separates-free-quillen-from-positive-higgs-integrated-source",
        "finding:whole-original-quarter-graph-color-response-is-relative-and-diagonal-singlet",
        "finding:original-center-selector-requires-typed-state-field-and-face-transport",
        "finding:original-color-center-fixes-whole-e6-a2-source-and-charged-ward-word-action",
        "finding:original-color-neutral-lattice-class-cannot-supply-odd-fields-by-inherited-superlattice-extension",
        "finding:original-color-center-extends-to-folded-ns-but-full-current-action-needs-spin-sector-transport",
        "finding:actual-color-spin-car-mixed-word-has-complete-thermal-source-and-cyclic-sewing",
        "finding:exact-original-ns-ramond-heat-equality-does-not-identify-fixed-color-restricted-source",
        "finding:original-scalar-cover-profile-cannot-implement-fixed-spin-cartan-loop",
        "finding:actual-spin-cartan-composite-source-retains-multi-arc-support-and-fails-additive-even-locality",
        "finding:actual-color-selector-admits-exactly-eighth-periodic-original-density-variations",
        "finding:actual-color-is-internal-exactly-on-eightfold-coordinate-source-regions",
        "finding:original-whole-two-face-multiplier-reduction-is-only-constant-residue-diagonal",
        "finding:original-two-face-local-fock-implementation-and-exact-source-variation-differ-from-reduction",
        "finding:whole-undecorated-transfer-does-not-determine-original-marked-field-source",
        "finding:volume-wise-injective-positive-transfer-does-not-prove-uniform-parent-gap",
        "finding:original-c6-half-power-has-exact-entire-positive-ordered-word-expansion",
        "finding:original-c6-whole-word-sewing-retains-source-amplitude-and-controlled-infinite-tail",
        "finding:historical-parent-and-actual-field-time-bridges-must-be-reused-before-new-source-models",
        "finding:actual-native-v990-full-timed-words-recover-kubo-response-distinct-from-instantaneous-variance",
        "finding:actual-original-higgs-force-has-complete-ordered-fermionic-determinant-source",
        "finding:finite-covariant-higgs-composites-have-no-nontrivial-positive-instantaneous-classical-law",
        "finding:actual-original-collective-mean-has-exact-ball-domain-and-relative-entropy-action",
        "finding:original-uniform-allmode-force-clt-is-nonzero-only-before-fixed-time-smearing",
        "finding:original-unscaled-time-smeared-force-has-selfadjoint-whole-ordered-source",
        "finding:original-local-higgs-force-has-whole-centered-hilbert-schmidt-determinant-source",
        "finding:given-original-circle-force-source-generates-an-exact-causal-local-net",
        "finding:literal-archived-global-rg-kernel-does-not-preserve-finite-measures",
        "finding:native-higgs-marginal-retains-induced-vertex-and-noether-response",
        "finding:isospectral-noether-orbit-does-not-supply-original-metric-higgs-variation",
        "finding:metric-dtn-form-bound-needs-transfer-comparison-for-gap",
        "finding:conditional-higgs-pair-winding-protection-in-common-circle-carrier",
        "finding:natural-five-clock-carrier-excludes-invariant-three-transfer-compression",
        "finding:shared-scalar-shift-whole-retained-higgs-sector-has-index-minus-eighteen",
        "finding:whole-coupled-quark-circle-common-shift-cancels-relative-winding",
        "finding:one-sided-shift-full-higgs-pair-is-hilbert-schmidt-not-trace-class",
        "finding:selective-coupled-higgs-reader-has-well-defined-det2",
        "finding:v311-population-reader-does-not-identify-quantum-channel",
        "finding:comoving-diagnostic-clock-exact-response-but-nonlocal-mode-transport",
        "finding:free-quarter-two-face-response-strip-with-relative-zero-mode-defect",
        "finding:comoving-clock-dynamic-higgs-connection-and-charged-flow",
        "finding:r064-sixty-record-channel-exact-distance-and-continuous-record-parent",
        "finding:two-syntheses-shared-source-priorities-and-typed-limits",
        "finding:weighted-index-trace-and-selfdual-theta-require-original-selection",
        "finding:ordered-quarter-fourfield-e8-record-and-charge-filters",
        "finding:r091-recovered-native-hodge-sewing-and-full96-quarter-complement",
        "finding:r092-fold-ward-target-neutral-source-and-smaller-creation-branch",
        "finding:r093-original-kink-time-response-distinguishes-quarter-states",
        "finding:r093-ordered-current-kink-and-eight-arc-locality",
        "finding:r094-original-five-excitations-distinct-from-clustering-vacuum",
        "finding:r096-joint-higgs-twoface-source-constraint",
        "finding:r096-positive-twoface-fourword-defect-bound",
        "finding:r096-unnormalized-mixed-source-linear-identity",
        "finding:r096-original-quark-crossing-negative-covariance",
        "finding:recovered-e6-closed-81-current-module-and-unique-source-cubic",
        "finding:e-series-operational-role-review-and-source-time-centralizer",
        "finding:actual-folded-current-ward-and-state-determine-all-neutral-words",
        "finding:mixed-vector-axial-current-is-existing-full-car-subalgebra",
        "finding:constant-product-time-stable-current-level-is-kernel-index",
        "finding:paired-quarter-source-candidate-needs-original-filter-and-oriented-conjugation",
        "finding:graded-boundary-clifford-typing-transports-full-scalar-and-finite-coupled-source",
        "finding:actual-charge-j-transport-retains-full-dirac-and-distinct-pairings",
        "finding:fixed-graded-chart-transports-normal-dependent-source-and-given-mixed-moments",
        "finding:neutral-many-body-source-time-is-not-finite-summable-geometric-dirac",
        "finding:actual-product-reflection-and-same-time-have-full-positive-clifford-source-intertwiner",
        "finding:actual-v252-positive-grade-has-global-p2-wedge-dictionary",
        "finding:old-quarter-full-source-embeds-locally-exactly-on-decoupled-channel"
      ],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:theta1-universality-class-20261005",
      "titleEN": "theta1-universality-class-20261005",
      "questionEN": "If Gate B holds at the frozen point P0 = (b, theta, gamma) = (0, 120 deg, 0), does the symmetric-gapped chiral phase persist on an open neighbourhood in (b, theta, gamma), so that P1/P2 only need to select a region?",
      "date": "20261005",
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      "titleEN": "third-electric-cubic",
      "questionEN": "Third electric source: full cubic census and both new boundary terms",
      "date": null,
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      "verdictRaw": "FULL_CUBIC_MEEE_CENSUS_AND_ISOLATED_SOURCE_EVALUATED",
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      "reviewState": "inventoried-not-reviewed",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:three-routes-source-bridge-20260920",
      "titleEN": "three-routes-source-bridge-20260920",
      "questionEN": "Which source-selected bridges can the native a0 phase family, C/J E8 reconstruction and exact local compiler-complement dynamics jointly supply, and what remains unproved?",
      "date": "20260920",
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      "scopeEN": "Algebraic results within pinned existing source models; no new physical choice of Yukawa connection, extra edge pair, energy symmetry, globally dressed chain or spacetime derived.",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:toe-bridge-round30",
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      "kind": "contract",
      "status": null,
      "verdictRaw": "QUANTUM_GAUGE_BRIDGE_AND_RESIDUAL_FLAVOR_SELECTION",
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      "id": "contract:translation-completion-round22",
      "titleEN": "translation-completion-round22",
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      "kind": "contract",
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      "id": "contract:translation-locality-round23",
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      "kind": "contract",
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:two-edge-spacetime-field",
      "titleEN": "two-edge-spacetime-field",
      "questionEN": "Two-edge half-transfer: a sharp spatial obstruction and a spacetime construction",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "CONDITIONAL_TWO_EDGE_SPACETIME_CURRENT_FIELD",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:universalraum-carrier-hand-20260915",
      "titleEN": "universalraum-carrier-hand-20260915",
      "questionEN": "Der übersehene Träger-Zeiger: die Fünf im Vier-Bank-Modell (2026-09-15)",
      "date": "20260915",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:universalraum-clock-origin-20260915",
      "titleEN": "universalraum-clock-origin-20260915",
      "questionEN": "TFPT Universalraum: Clock und gemeinsame Quelle, v1.6.6",
      "date": "20260915",
      "kind": "contract",
      "status": null,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:universalraum-closure-20260914",
      "titleEN": "universalraum-closure-20260914",
      "questionEN": "Lassen sich die vom paired-release-Audit und der Universalraum-Konsolidierung offen gelassenen endlichen Fragen — exakte Multiplizitätsschranke, vollständiger Nicht-Singulett-Vergleich, native Phas...",
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      "kind": "contract",
      "status": null,
      "verdictRaw": "4 von 5 Fragen geschlossen; higher_order_bound offen (quantifiziert)",
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      "stage": null,
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:universalraum-closure-round-20260914",
      "titleEN": "universalraum-closure-round-20260914",
      "questionEN": "Sind die im Universalraum-Gesamtkonstrukt vom 14.09.2026 behaupteten exakten endlichen Strukturen (Vertex-Kohärenz, Clebsch-Labels, T1-Auswahlprinzip, L*-Weil-Brücke, SU(4)-Sektorzerlegung) unabhän...",
      "date": "20260914",
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      "status": null,
      "verdictRaw": "coherence 16/16, dressed_star 16/16, selection 15/15, weil_bridge 12/12, sectors 64/64 — alle Checks bestanden",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:universalraum-common-process-20260915",
      "titleEN": "universalraum-common-process-20260915",
      "questionEN": "Gemeinsamer Prozess, v1.6.8",
      "date": "20260915",
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      "verdictRaw": "PASS",
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "id": "contract:universalraum-d4-torsor-seam-20260917",
      "titleEN": "universalraum-d4-torsor-seam-20260917",
      "questionEN": "D4-Torsor statt ausgezeichneter Seam-Markierung — Präregistrierung",
      "date": "20260917",
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      "status": null,
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      "stage": null,
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:universalraum-fable-kernfragen-20260910",
      "titleEN": "universalraum-fable-kernfragen-20260910",
      "questionEN": "universalraum-fable-kernfragen-20260910",
      "date": "20260910",
      "kind": "contract",
      "status": null,
      "verdictRaw": "UNKNOWN",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:universalraum-five-reports-native-clock-20260915",
      "titleEN": "universalraum-five-reports-native-clock-20260915",
      "questionEN": "universalraum-five-reports-native-clock-20260915",
      "date": "20260915",
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:universalraum-five-source-frontier-20260914",
      "titleEN": "universalraum-five-source-frontier-20260914",
      "questionEN": "Liefern die fünf geprüften Quellen N9–N13 und die eigenen Nachrechnungen neue rigorose Resultate zu Bandtrennung, F4-Positivität, CAR-Adapter und Zeitfilter, ohne die T1–T8-Tore zu schließen?",
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      "verdictRaw": "modellresultate_bewiesen_tore_offen",
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      "historical": true,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:universalraum-followup-solutions-20260914",
      "titleEN": "universalraum-followup-solutions-20260914",
      "questionEN": "Wie lauten die Antworten auf die sechs Follow-up-Fragen der Universalraum-Revision v1.4 (Kontroll-Ledger, vorgeschriebene Bauweise, Vierfachstruktur, Fehlerbudgets/Größe, gemeinsame Welt, Parameter...",
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      "verdictRaw": "gemischt: Q1–Q4 positiv beantwortet (Q3 exakt bewiesen), Q5/Q6 ehrliche Negative, kein T1–T8-Abschluss",
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      "stage": null,
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "titleEN": "universalraum-followups-closure-20260914",
      "questionEN": "Universalraum v1.4 — Abarbeitung der sechs Follow-ups",
      "date": "20260914",
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      "verdictRaw": "EXPERIMENT_ONLY_SHARED_TRUNCATED_OPERATOR",
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
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      "titleEN": "universalraum-fugen-20260914",
      "questionEN": "Lassen sich die fünf im Universalraum-Manuskript als gesetzt markierten Fugen (λ, Kopplungsgraph, Cross-Register-Kopplung, Präparation, Zeitskala) auf den gepinnten Quellobjekten exakt und numerisc...",
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      "verdictClass": "other",
      "stage": null,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:universalraum-fundamental-20260915",
      "titleEN": "universalraum-fundamental-20260915",
      "questionEN": "Universalraum-Fundamental — opset- und GS-Repro-Sanity-Sonden",
      "date": "20260915",
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      "status": null,
      "verdictRaw": "UNKNOWN",
      "verdictClass": "unknown",
      "stage": null,
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:universalraum-inversion-20260914",
      "titleEN": "universalraum-inversion-20260914",
      "questionEN": "Universalraum-Inversion: Hypothese bestätigt als Richtung, Rekonstruktion mit fünf offenen Gattern",
      "date": "20260914",
      "kind": "contract",
      "status": null,
      "verdictRaw": "consistent_partial",
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
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      "id": "contract:universalraum-keyA-multiplicity-space-20260915",
      "titleEN": "universalraum-keyA-multiplicity-space-20260915",
      "questionEN": "Key-A: Multiplizitätsraum des nativen Blocks — 15. September 2026",
      "date": "20260915",
      "kind": "contract",
      "status": null,
      "verdictRaw": "UNKNOWN",
      "verdictClass": "unknown",
      "stage": null,
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:universalraum-keyB-clock-gluing-20260915",
      "titleEN": "universalraum-keyB-clock-gluing-20260915",
      "questionEN": "Clock als Verklebungsanweisung — exakter Test (keyB, 2026-09-15)",
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      "kind": "contract",
      "status": null,
      "verdictRaw": "PARTIELL",
      "verdictClass": "partial",
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      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:universalraum-keyC-condensate-state-20260915",
      "titleEN": "universalraum-keyC-condensate-state-20260915",
      "questionEN": "KeyC: Kondensat- vs. Zustandsfrage (Theory Contract)",
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      "kind": "contract",
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      "verdictRaw": "PASS",
      "verdictClass": "pass",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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      "questionEN": "universalraum-six-new-audit-20260914",
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      "id": "contract:universalraum-six-source-audit-20260914",
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      "questionEN": "Welche Behauptungen der sechs eingesandten Universalraum-Quellen (History-Kanal, unitäre Reparatur, Relaxation, Zweizellenlücke, Entropieauswahl, Sternfilter) bestehen eine exakte lokale Nachprüfun...",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:universalraum-source-composition-20260915",
      "titleEN": "universalraum-source-composition-20260915",
      "questionEN": "TFPT / Universalraum — Quellenkomposition v1.6.9",
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      "id": "contract:universalraum-source-equivalence-decision-20260915",
      "titleEN": "universalraum-source-equivalence-decision-20260915",
      "questionEN": "Can a linear/Bogoliubov state-preserving Gaussian raw-seam CAR map realize the existing native 64-CAR/60-CCR interacting model? Parity and W-bright-sector obstruction.",
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      "id": "contract:universalraum-spin-lift-basics-20260915",
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      "id": "contract:universalraum-two-bank-transfer-20260915",
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      "questionEN": "Kontrollierter Zwei-Banken-Transfer · v1.6.5",
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      "id": "contract:universalraum-v14-F1-primitive-20260914",
      "titleEN": "universalraum-v14-F1-primitive-20260914",
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    {
      "id": "contract:universalraum-v14-F1-primitives-20260914",
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      "questionEN": "F1 — Laborgriffe auf eingefrorene Compiler-Primitive",
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      "id": "contract:universalraum-v14-F2-architektur-20260914",
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      "questionEN": "F2: Zellbank gegen Kantenmoden — quellenbasierte Auswahl",
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      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
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    {
      "id": "contract:universalraum-v14-F3-quartett-20260914",
      "titleEN": "universalraum-v14-F3-quartett-20260914",
      "questionEN": "F3: Vierfachstruktur — exakte Projektoren, bedingter Sektorvergleich",
      "date": "20260914",
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      "id": "contract:universalraum-v14-F4-fehler-skalierung-20260914",
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      "questionEN": "F4: Fehler und wachsende, gekoppelte Zellen",
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      "id": "contract:universalraum-v14-F5-gemeinsame-welt-20260914",
      "titleEN": "universalraum-v14-F5-gemeinsame-welt-20260914",
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      "id": "contract:universalraum-v14-F6-transfer-20260914",
      "titleEN": "universalraum-v14-F6-transfer-20260914",
      "questionEN": "F6 gemeinsamer Transfer: Amplitude, Neigung, Tensor, Flavour",
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      "verdictRaw": "tension",
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      "id": "contract:universalraum-v16-integrated-20260915",
      "titleEN": "universalraum-v16-integrated-20260915",
      "questionEN": "universalraum-v16-integrated-20260915",
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      "titleEN": "universalraum-v169-controller-20260915",
      "questionEN": "v1.6.9-Controller: autonomer Zb-Eingriff im selben System — 15. September 2026",
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      "questionEN": "v1.6.9 Lift-Typisierung — getypte Quell-Träger-Audit · 15. September 2026",
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    {
      "id": "contract:universalraum-v169-state-time-20260915",
      "titleEN": "universalraum-v169-state-time-20260915",
      "questionEN": "TFPT / Universalraum v1.6.9 — Zustand und Zeit ohne Zirkularität",
      "date": "20260915",
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      "verdictRaw": "The proper-subalgebra escape from the full-factor centralizer argument is exact, but none of the three added non-circular candidates is both faithful on an H-invariant tested subalgebra and dynamically matching. The earlier bounded exclusion therefore survives with an explicitly enlarged, still finite scope.",
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      "questionEN": "Unreduced finite quantum Hamiltonian: measurable extension existence",
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      "kind": "contract",
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      "questionEN": "Can the original charged packet and the proposed Mobius clock fold provide an explicit V16 operator-action dictionary without adding channel copies?",
      "date": "2026-10-14",
      "kind": "contract",
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      "verdictRaw": "PARTIAL",
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      "stage": null,
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      "scopeEN": "Exact connection/action inverse within the supplied original E/F lift; original marked current witness; unitary finite-cover source pushforward on a stipulated eightfold quotient localization; exact periodic E8 root-action conjugacy and separate quarter-holonomy audit. Not a derivation of the primitive source localization, E8 extension, raw Xi or full TFPT.",
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        "source:84b2053b8a2fb33a87e6",
        "source:b032b80af600d2f58434",
        "source:ce6aca843ad751ff8582",
        "source:c4954bb482c9ef67ba2b",
        "source:d08e346c030ddc4c0278",
        "source:3c978bb85ad76c53e584",
        "source:a5dfc171feb6b79742c8",
        "source:e374544be2dc71152a37",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:vertex-preserving-round15",
      "titleEN": "vertex-preserving-round15",
      "questionEN": "vertex-preserving-round15",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:a3cae3a3622d3d39f896",
        "source:755dfe98350ad7272c35",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:virtual-readout-round32",
      "titleEN": "virtual-readout-round32",
      "questionEN": "Round32: virtual readouts and the missing local-energy premise",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "CONDITIONAL_DRESSED_READOUT_AND_LOCAL_ENERGY_OBSTRUCTION",
      "verdictClass": "partial",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:23a1fb96902d08e9911f",
        "source:690b25e63584bf82c6d8",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:weak-constraints-round13",
      "titleEN": "weak-constraints-round13",
      "questionEN": "weak-constraints-round13",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:aab01fb0f59fcdf8ad06",
        "source:fe1d07eab7038d899144",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:weak-local-construction-round13",
      "titleEN": "weak-local-construction-round13",
      "questionEN": "weak-local-construction-round13",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "PASS",
      "verdictClass": "pass",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:2c96486a1b88de66f1cb",
        "source:f86d561c8f72266a10bc",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:weylcoin-origin-20261005",
      "titleEN": "weylcoin-origin-20261005",
      "questionEN": "Does the existing source contain a local, family- and gauge-neutral two-dimensional factor (an M_2(C) block of the parity-even neutral commutant) on which the spatial process acts nontrivially?",
      "date": "20261005",
      "kind": "contract",
      "status": null,
      "verdictRaw": "NO_NEUTRAL_COIN_IN_SOURCE",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b15437d888a3a418eea9",
        "source:dac763be8d0fec79187e",
        "source:1b7d7f5b97c0ecea7122",
        "source:2395c053a7769dbb5d3b",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "contract:word-resummation-round46",
      "titleEN": "word-resummation-round46",
      "questionEN": "Round46: fixed-word resummation with a separate electric-leakage bound",
      "date": null,
      "kind": "contract",
      "status": null,
      "verdictRaw": "FIXED_WORD_SUFFIX_RESUMMED_ON_EDGE_WITH_VOLUME_UNIFORM_LEAKAGE_BOUND",
      "verdictClass": "other",
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:a4721fb8a3b932edfa3a",
        "source:1ccefbe6a7579e61c255",
        "source:f75e017104c2b0c5da2d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:bbn-lithium-watchdog",
      "titleEN": "bbn-lithium-watchdog",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "consistent",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:021dc90247f2459b4dbb",
        "source:7cee73908cc1502a5d2f"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:ccbh-dark-energy",
      "titleEN": "ccbh-dark-energy",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "CONSISTENT-BUT-CONTESTED (data_limited): TFPT k=3 matches Farrah+2023 (k=3.11+/-0.79) at -0.14 sigma, and the SMBH population can source Omega_Lambda at order level -- BUT the CCBH-as-dark-energy interpretation is disputed (Lacy/Amendola/Andrae&El-Badry/Mistele). A downstream bridge, not a TFPT confirmation; the discriminating decision is DESI w(z).",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:34be2162697737035a58",
        "source:ae609c268f01ea65eec3"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:ccc-crossover-disc",
      "titleEN": "ccc-crossover-disc",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "null (SMICA pass): no top-hat disc excess above the Gaussian LCDM null battery; well-powered at the frozen radius band; replication legs not needed for a null",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:411fda8955ec2feb2de7",
        "source:6cb4217055075ac5897f"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:cmb-birefringence-seed",
      "titleEN": "cmb-birefringence-seed",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "consistent with the seed line: one frozen phi0 fits beta and Omega_b and the line Omega_b/beta_rad = 4pi-1 holds within errors (NOT validated -- beta errors are wide and the joint covariance is unmodelled)",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:ae85f3cb0ee4461e0105",
        "source:e5a8942fb91c7d049a88"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:cmb-eb-logcomb",
      "titleEN": "cmb-eb-logcomb",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "null",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:1e4bef0ce1f234a0426a",
        "source:754085ed2da035c06780"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:cmb-inflation-scalaron",
      "titleEN": "cmb-inflation-scalaron",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "n_s point 0.9611: consistent with Planck, tension with the DESI-combined value; r point 0.0045 below BK18 (sharp future falsifier at CMB-S4); A_s point is -11.3 sigma -> the measured A_s requires faster reheating (N_star ~ 56.1). All [C]: N_star is an input, M_scal and R+R^2 are [E].",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:14482f791c92ddd5ceed",
        "source:cbec97a10ff8354bc07b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:cmb-primordial-logcomb",
      "titleEN": "cmb-primordial-logcomb",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "data_limited",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:255076ebc352967d5ac9",
        "source:98b72411faafdfb5e3d1"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:comb-meta-limit",
      "titleEN": "comb-meta-limit",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:86f59ab0fd0f310642e5",
        "source:c2e2ca8f0149e44dd87d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:cosmic-dipole-watchdog",
      "titleEN": "cosmic-dipole-watchdog",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "data_limited",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:3674462b27b6b944337a",
        "source:1d057f175c0820de820b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:cosmic-handedness",
      "titleEN": "cosmic-handedness",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "FRONTIER WATCHDOG (data_limited): the JADES excess is a ~3.3 sigma MONOPOLE, but it is most likely a Milky-Way-rotation aberration (a DIPOLE), and Galaxy Zoo found isotropy. TFPT allows only a tiny boundary remnant, so it does NOT predict a ~20% asymmetry: approximate parity is the prediction. A robust global parity monopole surviving MW-aberration + selection systematics across surveys would become a frontier parent-spin candidate -- not yet, and never the compiler core. A pure dipole is a systematic, not a signal.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:498d400a56789808bfe2",
        "source:0ae92f9e42fa8bd5ee74"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:crust-cooling-comb",
      "titleEN": "crust-cooling-comb",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "8 crust-cooling episodes across 6 quasi-persistent transients (KS 1731-260, MXB 1659-29 x2, XTE J1701-462, EXO 0748-676, MAXI J0556-332 x2, Aql X-1). Every single cooling curve is RANGE-BLIND for the (3/2)^6 comb (best = 2.46 < 2.8 periods), so the phase-incoherent kernel stack has n_used=0 and cannot test omega=2.583. The superposed-epoch pooled stack (3.08 periods) CAN: omega=2.583 is NOT special in the superposed-epoch pooled stack (p=0.4539, 3.08 pooled comb periods). The TFPT lambda-battery is a clean NULL after look-elsewhere (Bonferroni global p=1.0); 7/8 episodes show a significant nonzero core-equilibrium floor (consistent with the TFPT protected floor, but generic crust physics). Injection on the REAL sampling: a strong comb (eps=15%) is recovered 100% and the null false-alarm is 5%, BUT the PREDICTED eps~2% is detected only 2% -> the stack is UNDERPOWERED on the intrinsic amplitude (density-poor). VERDICT: data_limited -- crust cooling has the right FLOOR-TERMINATED character but is range/density-limited for the discriminating ~2% omega=2.583 comb; it serves as an honest 2nd world only via the (low-specificity) lambda-battery NULL. FIREWALL: surface heat diffusion, not a horizon recovery -> no hit here could ever be TFPT confirmation. No claim; nothing [E].",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:8facc8b0dde7c43ee0b7",
        "source:f13d760b0bc8a80dd9bf"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:dark-energy-w-watchdog",
      "titleEN": "dark-energy-w-watchdog",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "WATCHDOG ARMED (data_limited): strongest overlap-aware exclusion of w=-1 is 4.4 sigma (< 5.0) on the frozen 2025 baseline. 2026 status: that headline is known to be calibration-inflated (DES-Dovekie: 4.2 -> 3.2 sigma; Bayesian DESI+CMB-only ln B = -0.57) -- the preference is dissolving, as TFPT's w=-1 fixed point requires; Union3-driven frequentist pulls (~3.8 sigma) remain. Not a TFPT kill.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:4e4f108c0e27dab939c0",
        "source:9d6707b2827da34026ba"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:double-cover-rh-audit-2026-09-08",
      "titleEN": "double-cover-rh-audit-2026-09-08",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:dsi-false-positive-control",
      "titleEN": "dsi-false-positive-control",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "8 real control sequences (4 aftershock cascades from USGS ComCat incl. Landers/Tohoku/Ridgecrest; 4 solar-flare sequences after large X-flares, NGDC GOES XRS), 4 clear the >= 2.8-period gate. Kernel omega=2.583 false-positive rate: frozen 0/4 (Wilson95 [0.0, 0.4899]), strict 0/4. the detector is QUIET at the kernel on every gated control (FP 0/4, Wilson95 upper 0.4899), consistent with the nominal ~5% threshold rate -> the existing TFPT-channel nulls are SPECIFIC: the kernel frequency does not fire on generic Omori/DSI-type cascades. CONTROL 1 (Efimov ladder, exactly-derived non-TFPT DSI lambda=e^(pi/s0)=22.69): measured cold-atom ratios (Cs/7Li/39K) combine to 21.331+-1.12 — Efimov-consistent (-1.22 sigma) and 8.88 sigma from the TFPT lambda=11.39 (Cs alone 7.39 sigma); the frozen detector on the gated Efimov comb fired at the kernel 0/25 seeds while detecting omega_Efimov=2.01 at 100% -> PASSED. CONTROL 2 (glass/MCT exponent spread, structural): gamma across 7 systems spans [2.2, 2.8] (std 0.2023, 4.0x the median per-system error) — the TFPT bend 2.7095 sits inside the spread but a LOCKED universal bend is rejected at chi2=43.36/7 dof (~4.87 sigma): boundary-less two-step relaxation shows no frozen bend -> PASSED. COMBINED over all 5 gated DSI controls (4 gated cascade sequences + Efimov ladder (EF.02)): kernel fired 0/5 (Wilson95 [0.0, 0.4345]). FIREWALL: controls have no TFPT mapping by construction; this calibrates detector specificity only and is NOT evidence for TFPT. No claim; nothing [E].",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:479f11baf14b24362e4f",
        "source:73c088239a358f2348cf"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:e8-ladder-bed",
      "titleEN": "e8-ladder-bed",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "validated",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:2f22debada16560eb5f0",
        "source:5f106ce8a10df4413c0f"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:eht-achromatic-residual",
      "titleEN": "eht-achromatic-residual",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:4298d5d7eaea2b61a25b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:extended-signatures",
      "titleEN": "extended-signatures",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:813750f1ccd79ee11c95",
        "source:ed8e336da5f68c5e8d8b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:fixed-point-watchdog",
      "titleEN": "fixed-point-watchdog",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:3b9772ff97f6cc1893f6",
        "source:85702b80784f6cf77164"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:frb-kernel-couplings",
      "titleEN": "frb-kernel-couplings",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "8/8 axis-runs NULL. KC.05/KC.06 add the non-tooth operator-proxy searches: mu4 block leakage and S2a multivariate spectrum. Firewall: search targets, surface-leakage only, never TFPT confirmation.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b7183b49d0b4cca1a653",
        "source:fdf3a06c50b5c94dd6ce"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:frb-ontology",
      "titleEN": "frb-ontology",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:2f9e997ef17b7af92779",
        "source:e5152eb093548ad9638c"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:frb-parity-comb",
      "titleEN": "frb-parity-comb",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b012e6cbb592711970e0",
        "source:955735067a07b8e5e471"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:frb-tfpt-signatures",
      "titleEN": "frb-tfpt-signatures",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "not_confirmed_not_refuted",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b5c5618b72b1d1b07a35",
        "source:9f9b06565b7ed92a212c"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:ftransfer",
      "titleEN": "ftransfer",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:22d67b36d0b18faf22ef"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:ftransfer-clocks",
      "titleEN": "ftransfer-clocks",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:gauge-unification",
      "titleEN": "gauge-unification",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "sin^2 theta_W = 3/8 is the standard SU(5)/SO(10) GUT value (TFPT inherits it via the carrier 16). Running the measured SM couplings 1-loop: alpha1=alpha2 meet at Lambda~1.0e+13 GeV but alpha3 misses by 13% (the known SM non-unification). Imposing unification, the 3/8 boundary predicts sin^2 theta_W(M_Z)=0.2076 vs measured 0.23122 -- the classic ~10% GQW gap. CONSISTENT at GUT level, NOT a precision hit; closing the gap needs SUSY/thresholds (beyond TFPT's tree relation).",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:2b7d22781949e4277354",
        "source:b520b57962844881aa17"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:gravastar-compactness",
      "titleEN": "gravastar-compactness",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "SUGGESTIVE NORMAL-FORM MATCH ([C], data_limited): Nariai Q_geom and the Jampolski-Rezzolla max compactness are the SAME rational 3/8 with the SAME de Sitter endpoint 1/2 -- but no explicit C<->Q_geom map is proven, so it is a structural echo, not an identity. C=3/8 sits in 1/3<3/8<4/9<1/2: a HORIZONLESS light-trapping ECO. As a GW echo template it predicts an OBSERVED round-trip delay ~0.76 ms (GW150914: 62 Msun source frame x (1+z), z=0.09) with amplitude ratio <= (2/3)^6=0.0878; this is the (delay, amplitude) pair gw-ringdown-echo was missing. EHT shadow size (b_c=3 sqrt3 M) is DEGENERATE with Kerr -> echoes, not the shadow, are the discriminator.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:1a7687ce79f3cb29135d",
        "source:34ff9861d8eb3c186041"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:gw-ringdown-echo",
      "titleEN": "gw-ringdown-echo",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "catalog-feasibility: a maximal (2/3)^6 echo would be reachable by a stacked strain search (stacked rho_echo ~ 6.3 >= 5) -> the strain-level test is worth running; no echo claim is made at catalog level",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:5a6053c8e6b81caa8b1d",
        "source:0064f7c3efeb136f64a5"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:gw-ringdown-spectroscopy",
      "titleEN": "gw-ringdown-spectroscopy",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "structural: ln3 = ln N_fam exactly and the area quantum is 4 ln3 = ln 81 = ln(N_fam^4); but the asymptotic omega_R/T_H=ln3 lives in the high-overtone limit, while measured ringdowns see the n=0 fundamental -> the black-hole-direct family-count test is DATA-LIMITED (needs high-overtone spectroscopy). [C]/[P]: Hod's '3' is spin-dependent, the N_fam identification is suggestive, not forced.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:89f14984840ccbc4bc75",
        "source:e708bffb621ff364e9b9"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:gw-speed-multimessenger",
      "titleEN": "gw-speed-multimessenger",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "consistency (kill-test passed): the single-Lorentz-cone prediction (v_GW - c)/c = 0 sits inside the GW170817 bound; a measured v_GW != c would falsify the gravity closure. Not a detection (standard physics predicts the same).",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:e58765fba445c59d7b9e",
        "source:fd48e43d2e511429ab0b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:hfqpo-ladder",
      "titleEN": "hfqpo-ladder",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:7c40f5ee5c409b0d2fc8",
        "source:3979deb96035bbcf38ec"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:higgs-criticality",
      "titleEN": "higgs-criticality",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "SM lands at lambda(M_Pl) = -0.0143 +/- 0.0057, beta_lambda(M_Pl) = +1.92e-04 (1-loop): remarkably close to the double-critical surface (lambda=0, beta_lambda=0). lambda sits 2.5 sigma below 0 -> metastable vacuum (matches the published ~2.8 sigma). Consistent with the TFPT near-criticality bridge; the verdict is dominated by M_t -- a sharper top mass is the discriminating input. Downstream RGE bridge [C], not a compiler output.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:a4367fdaa3aab6d37168",
        "source:15956752a10b495bc1f6"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:inter-sheet-dynamics-audit-2026-09-08",
      "titleEN": "inter-sheet-dynamics-audit-2026-09-08",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:lab-residuals",
      "titleEN": "lab-residuals",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:12284ff59ef39c38e716",
        "source:a367803ce9fbd9fcf37a"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:lambda-h0-engine",
      "titleEN": "lambda-h0-engine",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "consistency: the EM fixed point alpha^-1 reproduces the measured Lambda hierarchy to 0.00 orders (122.95 predicted vs 122.94 measured) and H0/Mbar ~ e^-ainv/(2pi) to ~0.1 dex; the dimensionless identity S_dS rho_Lambda = 32 pi^4 is exact. One engine for Lambda, S_dS and H0 -- a consistency, not a parameter-free derivation of the absolute scale (the anchor).",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:8f298305f11b3f2e6195",
        "source:a0bdc8444ba1029ef4ef"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:lean4-carrier-rigidity",
      "titleEN": "lean4-carrier-rigidity",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:85c9accedac3ee5bbe53"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:neutrino-mixing",
      "titleEN": "neutrino-mixing",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "PMNS predictions of record: theta12 sharp ([-0.02, -0.28] sigma), theta13 mild ~2 sigma tension (NuFIT 0.02195 vs TFPT 0.0231), theta23 consistent with maximal (octant open); CKM delta consistent with the LHCb gamma. delta_PMNS = 240 deg = delta_CKM,lead + 180 (v231/v233 sheet relation) vs NuFIT 6.0 [1.08, 3.32] sigma -- consistent with the global best fit (CP-violating region; weak discriminative power until DUNE/HyperK). 2 sub-0.3-sigma hits, 1 >2 sigma.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:715515e70a5a9967611b",
        "source:63d69e0c00046e51e142"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:nu-scalaron-falsification",
      "titleEN": "nu-scalaron-falsification",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "consistent",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:067406ffa511d6ffb169",
        "source:ea2723a1285481f3f190"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:older_tests",
      "titleEN": "older_tests",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:p9-forecast",
      "titleEN": "p9-forecast",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "P9-FORECAST-GO",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:0f0a4548ed034f3b71e2",
        "source:9c9d6ccf279f8eb2aec4"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:pi-prime-event-log-2026-09-08",
      "titleEN": "pi-prime-event-log-2026-09-08",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:proton-decay",
      "titleEN": "proton-decay",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "Carrier-native Pati-Salam -> SO(10) proton decay (OPTIONAL gauged UV branch B; NOT the default boundary-only reading A). M_PS lands on the TFPT scalaron scale M_s=3.06e+13 GeV (x1.38-1.32), independent of the gauge running -- the TFPT-specific coincidence. GOLDEN CHANNEL p->e+pi0: (1) minimal 16-content M_GUT=2.40e+15 -> tau_p=4.19e+33 yr is EXCLUDED by Super-K (2.4e+34 yr) even at the optimistic band edge -> KILL. (2) The single E8-allowed 45 +(15,1,1) raises M_GUT to 5.80e+15 -> tau_p=1.46e+35 yr at 1-loop -> CONSISTENT and decisively probed by Hyper-Kamiokande (20 yr). (3) But at 2-loop M_GUT drops to 2.80e+15 -> tau_p=7.72e+33 yr < Super-K -> a latent TENSION (only the optimistic O(3) hadronic edge / GUT-threshold headroom saves it). So the whole PS branch is proton-safe ONLY with +(15,1,1) and ONLY marginally -- the E8 hull supplies just one 45 (v247), so this is a sharp, dated kill-test, not a knob. Second channel p->nubar K+ (DUNE/JUNO-optimised) is SUBDOMINANT in non-SUSY dim-6 gauge mediation: tau_p~4.6e+35 yr for +(15,1,1) sits above even the next-gen reach -> data_limited (R_nuK is an external nuisance, not a TFPT primitive). FIREWALL: tau_p is a downstream branch prediction, never [E]/\\veri{}; if only the minimal PS stage is gauged its leptoquarks mediate rare LFV, not p->e+pi0 (v385).",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:632e793c79dac7e46e79",
        "source:98090519cadecbaf53f4"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:pulsar-glitch-recovery",
      "titleEN": "pulsar-glitch-recovery",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "no TFPT recovery-kernel signature in pulsar glitches across all channels. (PG.01) glitch sizes show real log-periodic structure, but it is the known two-population BIMODALITY (vanishes under the population-controlled null) -- NOT a kernel comb; (PG.02/03) the decisive per-pulsar kernel ladders are null; (PG.04) the recovery fraction Q is not at phi0-multiples, and the multi-component tau_d ratios match neither the (3/2)^k ladder nor the det'-clean 2-mode bend 2.7095 (the correct v124 candidate) -- though the WALL holds (45/46 glitches need <=2 decay modes, consistent with the n=N_fam=3 pole). This mirrors the FRB energy-cascade result (generic discreteness, not kernel-specific) -- a clean cross-domain NULL. The exact clock is WALLED (2 modes + floor, not an infinite ladder), so sustained DSI needs a cascade; the open, more-sensitive probe is the fixed-ratio (2.7095) two-exponential recovery WAVEFORM template (matched filter), not summary Q/tau_d (see quantum-testbed QT.04).",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:e9c081d1dc75b242ef0f",
        "source:9e829d2b8253ee13dc1b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:pyrate",
      "titleEN": "pyrate",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:47f6cfbf8b26ae04e660"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:qc-recovery-kernel",
      "titleEN": "qc-recovery-kernel",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "consistent",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:e7338aed2f76e6d779ca",
        "source:93bc5bf1e311f95df246"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:qgeo-eit-soff",
      "titleEN": "qgeo-eit-soff",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "ANALOG CHANNEL VALIDATED on real measured hardware (H1+H2): the homogeneous tank realises a mu4-block-diagonal measured boundary operator at the instrument floor (S_off = 7.6e-05, clock commutator 1.5e-02, reciprocity 5.3e-03 -- the measured analog of the sigma~1e-3 dial in qgeo_soff_reconstruction.py); all 28 anisotropic (off-center) targets LEAK with the generic isotropic signature (forbidden fraction 0.87-1.00, expected ~0.8 = 12/15), and NONE fakes a mu4 positive (fraction -> 0); the 9 centered/annular targets are rotation-invariant-like and correctly sit near the floor (photo-verified refinement of the v1 H2 wording, on record). The decisive mu4-POSITIVE 4-inclusion configuration (large anisotropy, forbidden fraction -> floor) is NOT in the archive: preregistered as the future measurement (H3, data_limited). Firewall: instrument validation of the S_off observable, never TFPT evidence.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:e8168aa35d7fe8644548",
        "source:f6f2873731d0fc869816"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:qpe-recurrence",
      "titleEN": "qpe-recurrence",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:372271219f67c1a5de0a",
        "source:d3a753fb82b42ce0382a"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:quantum-recovery-analog",
      "titleEN": "quantum-recovery-analog",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:678d8eaac63e3d88d400"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:quantum-testbed",
      "titleEN": "quantum-testbed",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "the frozen kernel is carried by the QUANTUM dynamics, as a *dynamical* signature, not a static ratio: (QT.01) the entanglement spectrum reproduces the kernel exactly (surprisals 6 ln(3/2), 6 ln3; protected DFS mode; I_n=(2/3)^{6n}); (QT.02) a geometric ladder relaxes log-periodically at omega=2pi/ln lambda with exp(-pi^2/ln lambda)-suppressed amplitude (detectable only for the coarse (3/2)^6, p=0.002; invisible for 3/2, p=0.973); (QT.04) but the EXACT clock (v124) is WALLED -- a single recovery is two modes + a protected floor with the det'-clean bend rate ratio 2.7095=ln3/ln(3/2) and NO third mode (pole at n=3), so sustained DSI needs a cascade. The sharp, falsifiable waveform signature is therefore: a fixed-ratio (2.7095) two-exponential recovery template with a non-decaying floor -- a matched filter on recovery WAVEFORMS (FRB tails, pulsar nu(t), GW ringdown residuals), not size histograms. (QT.05) the discrete->dynamic completion (v241-243) adds a DIFFERENT signature class: discrete statistical phases -- spin in units of pi/4 (8th roots), braiding in pi/2, with a dominant m=2 fermion sector (theta=-1) and c=8 -- reinterpreting the FRB.08 'm=2' as the PREDICTED fermion mode. Internal-consistency, no data.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:b5aabb82f6edf9a90c04",
        "source:098324e050939336240d"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:rare-kaon-bridge",
      "titleEN": "rare-kaon-bridge",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "Flavour bridge geometry is internally consistent: BR(K+) -0.1s (NA62), delta_CKM/gamma +1.4s (LHCb), Jarlskog -0.1s (PDG); R_K=0.35238 respects Grossman-Nir and sits near the SM ratio 0.40. 3/5 legs are direct data hits; R_K and BR(KL) are data_limited (KOTO). This is a downstream BRIDGE [C] (external |Vcb|,|Vub| + short-distance), NOT a unique compiler fingerprint -- the real discriminator is KOTO measuring BR(KL) -> R_K.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:0b4103890628016a6899",
        "source:330bfec7d1892a40bcb3"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:recovery-channel",
      "titleEN": "recovery-channel",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "recovery kernel is a valid CPTP quantum channel (data-processing respected, protected 'law' code = decoherence-free subspace), and the TFPT Hawking law reproduces the unitary Page turnover at t_Page -- structural confirmation, not new data",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:01e8284925ff9f7d9b8d",
        "source:7c9c4a96b1908985b459"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:recovery-comb-domains",
      "titleEN": "recovery-comb-domains",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:6f9847f3b961fcbecd8c"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:repeater-cascade",
      "titleEN": "repeater-cascade",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:81c6eccae4b090b01cb5",
        "source:aecf4aa0ab4a0b92f95c"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:seam-emergence-probe",
      "titleEN": "seam-emergence-probe",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:1aff0830e534305cd153"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:seed-consistency",
      "titleEN": "seed-consistency",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "shared-seed block HOLDS (chi2/dof=1.23); dominant pull is theta13 at -1.80 sigma (< 3) -- a mild stress, no transfer correction triggered. Legs span CMB/BBN/reactor/CKM pipelines.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:f1ca83796d7b7e6b0a48",
        "source:d05f24b28793f9761cde"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:strange-metal-comb",
      "titleEN": "strange-metal-comb",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "LSCO x=0.24 sigma1(omega/T) master curve (Michon+ 2023 open data, 11227 points, T=40..300 K, 2.92 comb periods in u=ln(hw/kT) -> clears the 2.8 gate). omega=2.583 is NOT special in the LSCO x=0.24 master curve (primary p=0.2972, frozen-detector p=0.248, detrend-robust=True). Amplitude at the fixed kernel omega: eps_hat=0.0670, against a 0.1861 95% conservative-null floor (predicted TFPT eps=0.0173, i.e. the data's own systematics sit ABOVE the predicted ripple). Conservative null p=0.6843. TFPT lambda-battery Bonferroni global p=0.0632. Injection on the real master curve (best documented detrend variant): eps=5% detected 30% [spline], predicted eps=1.73% detected 25% [spline], max false-alarm 0% -> the search is UNDERPOWERED at the predicted amplitude. Drude negative controls (Au, Cu Ordal): quiet. Replication leg (Bi-2212 vdM 2003): data_limited (no public machine-readable table). VERDICT: null-at-detectable-amplitude / data_limited at the predicted 1.7%. FIREWALL: strange metals have no established boundary-recovery structure; even a hit would be universal-DSI coincidence, never TFPT confirmation. No claim; nothing [E].",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:f836a6a87e5e7952cd7a",
        "source:8e22f7068668ca84562e"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:tfpt-correspondence",
      "titleEN": "tfpt-correspondence",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "STRUCTURAL [C] CORRESPONDENCE (consistent, [O]-gated). The spacetime<->black-hole correspondence is a CHANGE OF BOOKKEEPING of one seam state (geometry channel = spacetime; boundary/information channel = the compiler), and its phase-boundary constants are ALL compiler atoms: the critical Bekenstein-saturation quotient q_Bek=1 has the atom coefficient 4 c3 = 1/(2 pi) with density 1/4=1/|mu4|; the geometric window runs over [3/8, 1/2] = [p2(a)/e1(a)^2, |Z2|/|mu4|]; the recovery reflectivity bound is (2/3)^6=(|Z2|/N_fam)^(2 N_fam). NOTHING here needs a free number, so the reading survives the numerology test -- but it is gated on the OPEN SEAM.EQUIV.01 (Seam-Horizon theorem) and stays [C]: NOT [E], NOT load-bearing. It is NOT Horowitz-Polchinski (TFPT has no Hagedorn/string scale); the shared content is only 'one state, two descriptions across a threshold'. The PHYSICAL phase transition (a measured order parameter) is data_limited.",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:77ab2df1ad6be2d886c3",
        "source:ebb641a8cc8ef48fed25"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:tfpt-discovery",
      "titleEN": "tfpt-discovery",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:uhecr-energy-dsi",
      "titleEN": "uhecr-energy-dsi",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": "null",
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:f99099f436ce44c467c4",
        "source:015d8dc5327f9752b739"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "experiment:watch-channels",
      "titleEN": "watch-channels",
      "questionEN": null,
      "date": null,
      "kind": "experiment",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [
        "source:5c0f03b5d708df331191"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.ARFSPINOR.01",
      "titleEN": "FAIL.ARFSPINOR.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.CARRIERGRAY.01",
      "titleEN": "FAIL.CARRIERGRAY.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.CLOCK.TORSIONECM.01",
      "titleEN": "FAIL.CLOCK.TORSIONECM.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.EVENT.LINDBLAD.01",
      "titleEN": "FAIL.EVENT.LINDBLAD.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.EXTRACTION.01",
      "titleEN": "FAIL.EXTRACTION.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.F4MODMUL.01",
      "titleEN": "FAIL.F4MODMUL.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.GEMEINSAMEWELT.01",
      "titleEN": "FAIL.GEMEINSAMEWELT.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.KERNEL.LOEWNER08.01",
      "titleEN": "FAIL.KERNEL.LOEWNER08.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.L2CASCADE.01",
      "titleEN": "FAIL.L2CASCADE.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.MOSCOSELECTION.01",
      "titleEN": "FAIL.MOSCOSELECTION.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.ORIENTIERUNG.T4C4.01",
      "titleEN": "FAIL.ORIENTIERUNG.T4C4.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.PLAKETTENGAP.01",
      "titleEN": "FAIL.PLAKETTENGAP.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.PNTGAMMA.01",
      "titleEN": "FAIL.PNTGAMMA.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.POLYGON.01",
      "titleEN": "FAIL.POLYGON.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.PRIME.CORNER.CHARACTER.01",
      "titleEN": "FAIL.PRIME.CORNER.CHARACTER.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.PRIME.EVOSEARCH.01",
      "titleEN": "FAIL.PRIME.EVOSEARCH.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.PRIME.FLOOR.ALIASMOMENT.01",
      "titleEN": "FAIL.PRIME.FLOOR.ALIASMOMENT.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.PRIME.LSTAR.CLOSED_FUNCTIONAL.01",
      "titleEN": "FAIL.PRIME.LSTAR.CLOSED_FUNCTIONAL.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.PRIME.MARGIN.LAW.01",
      "titleEN": "FAIL.PRIME.MARGIN.LAW.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.PRIME.PORT.TANGENT.SCHUR.01",
      "titleEN": "FAIL.PRIME.PORT.TANGENT.SCHUR.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.PRIMEFLOOR.01",
      "titleEN": "FAIL.PRIMEFLOOR.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.QUELLENABBILDUNG.GAUSS.01",
      "titleEN": "FAIL.QUELLENABBILDUNG.GAUSS.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.SECTOR.FLOORATTACK.01",
      "titleEN": "FAIL.SECTOR.FLOORATTACK.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.SHORTRANGE.01",
      "titleEN": "FAIL.SHORTRANGE.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "failure:FAIL.TAILMAP.01",
      "titleEN": "FAIL.TAILMAP.01",
      "questionEN": null,
      "date": null,
      "kind": "failure",
      "status": null,
      "verdictRaw": null,
      "verdictClass": null,
      "stage": null,
      "evidenceClass": null,
      "domain": null,
      "scopeEN": null,
      "sourceRefIds": [],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CKM:cabibbo-first-row-dissolution-watchdog-axis-e",
      "titleEN": "CKM: Cabibbo first-row dissolution watchdog (axis E)",
      "questionEN": "Cabibbo first-row dissolution watchdog (axis E)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CKM",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CKM:delta-ckm",
      "titleEN": "CKM: delta_CKM",
      "questionEN": "delta_CKM",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CKM",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CKM:r-d-lepton-universality-dissolution-watchdog",
      "titleEN": "CKM: R_D(*) lepton-universality dissolution watchdog",
      "questionEN": "R_D(*) lepton-universality dissolution watchdog",
      "date": null,
      "kind": "scorecard",
      "status": "tension",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CKM",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CKM:rare-kaon-ratio-r-k-kl-k",
      "titleEN": "CKM: rare kaon ratio R_K = KL/K+",
      "questionEN": "rare kaon ratio R_K = KL/K+",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "CKM",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:annulus-recovery-two-rate-cmi-obs-annulus-recovery-01",
      "titleEN": "CMB: annulus-recovery two-rate CMI (OBS.ANNULUS.RECOVERY.01)",
      "questionEN": "annulus-recovery two-rate CMI (OBS.ANNULUS.RECOVERY.01)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:baryon-fraction-omega-b",
      "titleEN": "CMB: baryon fraction Omega_b",
      "questionEN": "baryon fraction Omega_b",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:cosmic-birefringence-beta",
      "titleEN": "CMB: cosmic birefringence beta",
      "questionEN": "cosmic birefringence beta",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:cosmic-birefringence-rotation-fingerprint-beta-morphology-nu",
      "titleEN": "CMB: cosmic birefringence rotation fingerprint (beta morphology +",
      "questionEN": "cosmic birefringence rotation fingerprint (beta morphology + nulls)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:crossover-relic-top-hat-discs-ccc-disc-search-01",
      "titleEN": "CMB: crossover-relic top-hat discs (CCC.DISC.SEARCH.01)",
      "questionEN": "crossover-relic top-hat discs (CCC.DISC.SEARCH.01)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:eb-log-comb-at-the-frozen-omega-faithful-class-channel",
      "titleEN": "CMB: EB log-comb at the frozen omega_+ (faithful-class channel)",
      "questionEN": "EB log-comb at the frozen omega_+ (faithful-class channel)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:inflation-a-s-fixed-n-star-51-4-point",
      "titleEN": "CMB: inflation A_s (fixed N_star=51.4 point)",
      "questionEN": "inflation A_s (fixed N_star=51.4 point)",
      "date": null,
      "kind": "scorecard",
      "status": "tension",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:inflation-a-s-profiled-n-star",
      "titleEN": "CMB: inflation A_s (profiled N_star)",
      "questionEN": "inflation A_s (profiled N_star)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:inflation-alpha-s-running-of-n-s",
      "titleEN": "CMB: inflation alpha_s (running of n_s)",
      "questionEN": "inflation alpha_s (running of n_s)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:inflation-closure-invariant-c-inf-n-star-free",
      "titleEN": "CMB: inflation closure invariant C_inf (N_star-free)",
      "questionEN": "inflation closure invariant C_inf (N_star-free)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:inflation-mu-distortion-a-s-n-star-branch-discriminator",
      "titleEN": "CMB: inflation mu-distortion (A_s/N_star branch discriminator)",
      "questionEN": "inflation mu-distortion (A_s/N_star branch discriminator)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:inflation-n-s-starobinsky-scalaron",
      "titleEN": "CMB: inflation n_s (Starobinsky/scalaron)",
      "questionEN": "inflation n_s (Starobinsky/scalaron)",
      "date": null,
      "kind": "scorecard",
      "status": "tension",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:inflation-r-tensor-ratio",
      "titleEN": "CMB: inflation r (tensor ratio)",
      "questionEN": "inflation r (tensor ratio)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:primordial-log-comb-at-the-frozen-omega-planck-feature-searc",
      "titleEN": "CMB: primordial log-comb at the frozen omega (Planck feature sear",
      "questionEN": "primordial log-comb at the frozen omega (Planck feature search)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:CMB:seed-line-omega-b-beta-rad-4pi-1",
      "titleEN": "CMB: seed line Omega_b/beta_rad=4pi-1",
      "questionEN": "seed line Omega_b/beta_rad=4pi-1",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "CMB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:EHT:achromatic-dyonic-intercept-beta-bh-r",
      "titleEN": "EHT: achromatic dyonic intercept beta_BH(r)",
      "questionEN": "achromatic dyonic intercept beta_BH(r)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "EHT",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:EM:fine-structure-constant-alpha-1",
      "titleEN": "EM: fine-structure constant alpha^-1",
      "questionEN": "fine-structure constant alpha^-1",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "EM",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:EW:carrier-matter-one-anomaly-free-generation",
      "titleEN": "EW: carrier matter = one anomaly-free generation",
      "questionEN": "carrier matter = one anomaly-free generation",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "not_applicable",
      "evidenceClass": "internal_consistency",
      "domain": "EW",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:EW:higgs-near-criticality",
      "titleEN": "EW: Higgs near-criticality",
      "questionEN": "Higgs near-criticality",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "EW",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:EW:weinberg-angle-sin-2-th-w-spectral-scale",
      "titleEN": "EW: Weinberg angle sin^2 th_W (spectral scale)",
      "questionEN": "Weinberg angle sin^2 th_W (spectral scale)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "EW",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:activity-window-eigenwidths-frb-03",
      "titleEN": "FRB: activity-window eigenwidths (FRB.03)",
      "questionEN": "activity-window eigenwidths (FRB.03)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:anyon-pi-4-evpa-comb-ext-2",
      "titleEN": "FRB: anyon pi/4 EVPA comb (EXT.2)",
      "questionEN": "anyon pi/4 EVPA comb (EXT.2)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:dm-z-baryon-fraction-frb-05",
      "titleEN": "FRB: DM(z) baryon fraction (FRB.05)",
      "questionEN": "DM(z) baryon fraction (FRB.05)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:echo-ratios-frb-02",
      "titleEN": "FRB: echo ratios (FRB.02)",
      "questionEN": "echo ratios (FRB.02)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:episode-level-transfer-ladder-quiescence-gaps-episode-integr",
      "titleEN": "FRB: episode-level transfer ladder: quiescence gaps + episode-int",
      "questionEN": "episode-level transfer ladder: quiescence gaps + episode-integrated energies on the teeth (FO.05)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:free-quotient-null-frb-02b",
      "titleEN": "FRB: free-quotient null (FRB.02b)",
      "questionEN": "free-quotient null (FRB.02b)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:joint-echo-x-polarisation-ext-1",
      "titleEN": "FRB: joint echo x polarisation (EXT.1)",
      "questionEN": "joint echo x polarisation (EXT.1)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:kernel-couplings-joint-energy-time-tooth-v-handedness-size-s",
      "titleEN": "FRB: kernel couplings: joint energy-time tooth + V-handedness + s",
      "questionEN": "kernel couplings: joint energy-time tooth + V-handedness + size-space DSI + phase-time helix + operator proxies (KC.01-06)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:medium-state-common-two-rate-operator-fo-02-named-b-line-int",
      "titleEN": "FRB: medium-state common two-rate operator (FO.02, named-B line i",
      "questionEN": "medium-state common two-rate operator (FO.02, named-B line integrals)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:microshot-cascade-kernel-frb-20220912a-b1-b2",
      "titleEN": "FRB: microshot cascade kernel (FRB 20220912A B1/B2)",
      "questionEN": "microshot cascade kernel (FRB 20220912A B1/B2)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:no-native-dispersion-frb-01",
      "titleEN": "FRB: no native dispersion (FRB.01)",
      "questionEN": "no native dispersion (FRB.01)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:operator-structure-probes-covariance-blocks-polarimetric-nul",
      "titleEN": "FRB: operator-structure probes: covariance blocks + polarimetric",
      "questionEN": "operator-structure probes: covariance blocks + polarimetric null space + rank drop + time arrow (FO.07-10)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:pa-rm-markov-spectrum-frb-04",
      "titleEN": "FRB: PA/RM Markov spectrum (FRB.04)",
      "questionEN": "PA/RM Markov spectrum (FRB.04)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:parity-without-rate-diagnostic-no-mu4-pa-refinement-rate-fre",
      "titleEN": "FRB: parity-without-rate diagnostic: no mu4 PA refinement + rate-",
      "questionEN": "parity-without-rate diagnostic: no mu4 PA refinement + rate-free switches + persistent classes (FO.04)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:pol-fraction-quantisation-frb-06",
      "titleEN": "FRB: pol-fraction quantisation (FRB.06)",
      "questionEN": "pol-fraction quantisation (FRB.06)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:recovery-clock-dynamics-frb-09",
      "titleEN": "FRB: recovery-clock dynamics (FRB.09)",
      "questionEN": "recovery-clock dynamics (FRB.09)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:recovery-comb-in-chime-baseband-frb-tail-omega-2-58-stacked",
      "titleEN": "FRB: recovery comb in CHIME baseband FRB tail (omega=2.58, stacke",
      "questionEN": "recovery comb in CHIME baseband FRB tail (omega=2.58, stacked)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:recovery-comb-in-frb-burst-tail-omega-2-58-stacked",
      "titleEN": "FRB: recovery comb in FRB burst tail (omega=2.58, stacked)",
      "questionEN": "recovery comb in FRB burst tail (omega=2.58, stacked)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:repeater-burst-time-cascade-comb-walled-clock-rc-01-04",
      "titleEN": "FRB: repeater burst-time cascade comb + walled clock (RC.01-04)",
      "questionEN": "repeater burst-time cascade comb + walled clock (RC.01-04)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:repeater-one-off-leaf-classes-exact-two-mode-morphology-fo-0",
      "titleEN": "FRB: repeater/one-off leaf classes: exact two-mode morphology (FO",
      "questionEN": "repeater/one-off leaf classes: exact two-mode morphology (FO.06)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:state-clock-comb-in-tau-mod-cumulative-drm-fo-03-s14-named-c",
      "titleEN": "FRB: state-clock comb in tau_mod = cumulative |dRM| (FO.03, S14 n",
      "questionEN": "state-clock comb in tau_mod = cumulative |dRM| (FO.03, S14 named clock)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:static-pa-mu4-classes-frb-08",
      "titleEN": "FRB: static PA mu4 classes (FRB.08)",
      "questionEN": "static PA mu4 classes (FRB.08)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:v486-parity-resolved-combs-on-signed-circular-polarization-p",
      "titleEN": "FRB: v486 parity-resolved combs on signed circular polarization (",
      "questionEN": "v486 parity-resolved combs on signed circular polarization (PC.01-03)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:FRB:width-relaxation-echo-frb-07",
      "titleEN": "FRB: width-relaxation echo (FRB.07)",
      "questionEN": "width-relaxation echo (FRB.07)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "FRB",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:GW:area-quantum-spectral-comb-bm-lines",
      "titleEN": "GW: area-quantum spectral comb (BM lines)",
      "questionEN": "area-quantum spectral comb (BM lines)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "strain_level_test",
      "evidenceClass": "search_target",
      "domain": "GW",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:GW:dynamic-walled-clock-recovery-bend-stage-2",
      "titleEN": "GW: dynamic walled-clock recovery bend (Stage 2)",
      "questionEN": "dynamic walled-clock recovery bend (Stage 2)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "strain_level_test",
      "evidenceClass": "search_target",
      "domain": "GW",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:GW:eco-compactness-c-3-8-gravastar-echo",
      "titleEN": "GW: ECO compactness C=3/8 (gravastar echo)",
      "questionEN": "ECO compactness C=3/8 (gravastar echo)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "GW",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:GW:gravastar-joint-lag-ratio-ext-3",
      "titleEN": "GW: gravastar joint lag+ratio (EXT.3)",
      "questionEN": "gravastar joint lag+ratio (EXT.3)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "strain_level_test",
      "evidenceClass": "search_target",
      "domain": "GW",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:GW:qnm-family-count-omega-r-t-h-ln3",
      "titleEN": "GW: QNM family count omega_R/T_H -> ln3",
      "questionEN": "QNM family count omega_R/T_H -> ln3",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "GW",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:GW:ringdown-echo-amplitude-ratio",
      "titleEN": "GW: ringdown echo amplitude ratio",
      "questionEN": "ringdown echo amplitude ratio",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "strain_level_test",
      "evidenceClass": "search_target",
      "domain": "GW",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:GW:v-gw-c",
      "titleEN": "GW: v_GW = c",
      "questionEN": "v_GW = c",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "GW",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:X-ray:bh-hfqpo-3-2-pairs-geometric-ladder-discriminator-hfqpo-ladd",
      "titleEN": "X-ray: BH HFQPO 3:2 pairs + geometric-ladder discriminator (hfqpo-l",
      "questionEN": "BH HFQPO 3:2 pairs + geometric-ladder discriminator (hfqpo-ladder H1-H3)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "X-ray",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:X-ray:bh-hfqpo-third-tooth-extension-on-non-rxte-archives-nicer-ma",
      "titleEN": "X-ray: BH HFQPO third-tooth extension on non-RXTE archives (NICER/M",
      "questionEN": "BH HFQPO third-tooth extension on non-RXTE archives (NICER/MAXI J1820+070 + AstroSat/LAXPC; hfqpo-ladder ext)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "X-ray",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:X-ray:qpe-recurrence-kernel-search-qpe-01-03",
      "titleEN": "X-ray: QPE recurrence kernel search (QPE.01-03)",
      "questionEN": "QPE recurrence kernel search (QPE.01-03)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "X-ray",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:X-ray:recovery-comb-in-magnetar-outburst-relaxation-omega-2-58",
      "titleEN": "X-ray: recovery comb in magnetar outburst relaxation (omega=2.58)",
      "questionEN": "recovery comb in magnetar outburst relaxation (omega=2.58)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "X-ray",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:X-ray:recovery-comb-in-neutron-star-crust-cooling-omega-2-583-supe",
      "titleEN": "X-ray: recovery comb in neutron-star crust cooling (omega=2.583, su",
      "questionEN": "recovery comb in neutron-star crust cooling (omega=2.583, superposed-epoch)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "X-ray",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:channel:page-curve-turnover",
      "titleEN": "channel: Page curve turnover",
      "questionEN": "Page curve turnover",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "not_applicable",
      "evidenceClass": "internal_consistency",
      "domain": "channel",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:channel:petz-recovery-rank-one-baby-universe",
      "titleEN": "channel: Petz recovery + rank-one baby universe",
      "questionEN": "Petz recovery + rank-one baby universe",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "not_applicable",
      "evidenceClass": "internal_consistency",
      "domain": "channel",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:channel:recovery-kernel-as-cptp-map",
      "titleEN": "channel: recovery kernel as CPTP map",
      "questionEN": "recovery kernel as CPTP map",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "not_applicable",
      "evidenceClass": "internal_consistency",
      "domain": "channel",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:condensed matter:bosonic-e8-phase-thermal-hall-seam-edge-c-8",
      "titleEN": "condensed matter: bosonic E8 phase thermal Hall (seam edge c_-=8)",
      "questionEN": "bosonic E8 phase thermal Hall (seam edge c_-=8)",
      "date": null,
      "kind": "scorecard",
      "status": "parked",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "parked_analog",
      "evidenceClass": "parked",
      "domain": "condensed matter",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:condensed matter:comb-ripple-on-the-strange-metal-omega-t-master-curve-lsco-x",
      "titleEN": "condensed matter: comb ripple on the strange-metal omega/T master curve (LSCO",
      "questionEN": "comb ripple on the strange-metal omega/T master curve (LSCO x=0.24)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "condensed matter",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:condensed matter:e8-mass-ladder-blind-recovery-bed-conb2o6-baco2v2o8",
      "titleEN": "condensed matter: E8 mass-ladder blind recovery bed (CoNb2O6 / BaCo2V2O8)",
      "questionEN": "E8 mass-ladder blind recovery bed (CoNb2O6 / BaCo2V2O8)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "not_applicable",
      "evidenceClass": "internal_consistency",
      "domain": "condensed matter",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmic-ray:uhecr-energy-spectrum-size-space-dsi-auger-open-data",
      "titleEN": "cosmic-ray: UHECR energy-spectrum size-space DSI (Auger Open Data)",
      "questionEN": "UHECR energy-spectrum size-space DSI (Auger Open Data)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "cosmic-ray",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmo:ccbh-cosmological-coupling-k-3-w-1",
      "titleEN": "cosmo: CCBH cosmological coupling k=3 (w=-1)",
      "questionEN": "CCBH cosmological coupling k=3 (w=-1)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "cosmo",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmo:cosmic-number-count-dipole-ellis-baldwin-watchdog",
      "titleEN": "cosmo: cosmic number-count dipole (Ellis-Baldwin) watchdog",
      "questionEN": "cosmic number-count dipole (Ellis-Baldwin) watchdog",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "cosmo",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmo:cosmic-spin-handedness-parity",
      "titleEN": "cosmo: cosmic spin handedness (parity)",
      "questionEN": "cosmic spin handedness (parity)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "cosmo",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmo:dark-energy-equation-of-state-w",
      "titleEN": "cosmo: dark-energy equation of state w",
      "questionEN": "dark-energy equation of state w",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "cosmo",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmo:flat-lambdacdm-budget-closure-h0-omega-m-t0",
      "titleEN": "cosmo: flat LambdaCDM budget closure (H0, Omega_m, t0)",
      "questionEN": "flat LambdaCDM budget closure (H0, Omega_m, t0)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "cosmo",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmo:joint-fixed-point-w-sigma-m-nu-pincer",
      "titleEN": "cosmo: joint fixed point (w, Sigma m_nu) pincer",
      "questionEN": "joint fixed point (w, Sigma m_nu) pincer",
      "date": null,
      "kind": "scorecard",
      "status": "tension",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "cosmo",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmo:lambda-hierarchy-rho-lambda-m-pl-4",
      "titleEN": "cosmo: Lambda hierarchy rho_Lambda/M_pl^4",
      "questionEN": "Lambda hierarchy rho_Lambda/M_pl^4",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "cosmo",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmo:primordial-7li-at-the-frozen-eta-lithium-watchdog",
      "titleEN": "cosmo: primordial 7Li at the frozen eta (lithium watchdog)",
      "questionEN": "primordial 7Li at the frozen eta (lithium watchdog)",
      "date": null,
      "kind": "scorecard",
      "status": "tension",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "cosmo",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmo:s-ds-rho-lambda-32-pi-4",
      "titleEN": "cosmo: S_dS rho_Lambda = 32 pi^4",
      "questionEN": "S_dS rho_Lambda = 32 pi^4",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "not_applicable",
      "evidenceClass": "internal_consistency",
      "domain": "cosmo",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cosmo:s8-forecast-from-the-flat-budget-structure-side",
      "titleEN": "cosmo: S8 forecast from the flat budget (structure side)",
      "questionEN": "S8 forecast from the flat budget (structure side)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "cosmo",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cross-domain:dsi-false-positive-control-frozen-comb-textbook-negative-con",
      "titleEN": "cross-domain: DSI false-positive control: frozen comb + textbook negative",
      "questionEN": "DSI false-positive control: frozen comb + textbook negative controls (Efimov, glass/MCT)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "cross-domain",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cross-domain:meta-analytic-ul-on-recovery-comb-amplitude-eps-omega-2-583",
      "titleEN": "cross-domain: meta-analytic UL on recovery-comb amplitude eps (omega=2.583",
      "questionEN": "meta-analytic UL on recovery-comb amplitude eps (omega=2.583)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "cross-domain",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:cross-domain:z2-moebius-double-cover-readings-of-the-recovery-comb-3-2-3",
      "titleEN": "cross-domain: Z2/Moebius double-cover readings of the recovery comb ((3/2)",
      "questionEN": "Z2/Moebius double-cover readings of the recovery comb ((3/2)^3, (3/2)^4, (3/2)^12)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "cross-domain",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:horizon:compiler-fingerprint-catalog-ext-4",
      "titleEN": "horizon: compiler fingerprint catalog (EXT.4)",
      "questionEN": "compiler fingerprint catalog (EXT.4)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "horizon",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:alpha-lambda-drift-lock-alpha-dot-alpha-0",
      "titleEN": "lab: alpha-Lambda drift lock (alpha_dot/alpha = 0)",
      "questionEN": "alpha-Lambda drift lock (alpha_dot/alpha = 0)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:axion-haloscope-marker",
      "titleEN": "lab: axion haloscope marker",
      "questionEN": "axion haloscope marker",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:axion-relic-dm-axion-hilltop-01",
      "titleEN": "lab: axion relic DM.AXION.HILLTOP.01",
      "questionEN": "axion relic DM.AXION.HILLTOP.01",
      "date": null,
      "kind": "scorecard",
      "status": "tension",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:axion-relic-dm-axion-spine-01-theta-i-3pi-5",
      "titleEN": "lab: axion relic DM.AXION.SPINE.01 (theta_i=3pi/5)",
      "questionEN": "axion relic DM.AXION.SPINE.01 (theta_i=3pi/5)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:charged-lepton-koide-ratio-q-f-pole",
      "titleEN": "lab: charged-lepton Koide ratio Q (F_pole)",
      "questionEN": "charged-lepton Koide ratio Q (F_pole)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:electron-edm-theta-eff-0",
      "titleEN": "lab: electron EDM (theta_eff=0)",
      "questionEN": "electron EDM (theta_eff=0)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:koide-q-2-3-tau-mass-kill-window",
      "titleEN": "lab: Koide Q=2/3 tau-mass kill window",
      "questionEN": "Koide Q=2/3 tau-mass kill window",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:leptogenesis-eta-b-scalaron-decuple",
      "titleEN": "lab: leptogenesis eta_B (scalaron-decuple)",
      "questionEN": "leptogenesis eta_B (scalaron-decuple)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:muon-g-2-delta-a-mu-wp2020-dispersive",
      "titleEN": "lab: muon g-2 Delta a_mu (WP2020 dispersive)",
      "questionEN": "muon g-2 Delta a_mu (WP2020 dispersive)",
      "date": null,
      "kind": "scorecard",
      "status": "parked",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:muon-g-2-delta-a-mu-wp2025-lattice",
      "titleEN": "lab: muon g-2 Delta a_mu (WP2025 lattice)",
      "questionEN": "muon g-2 Delta a_mu (WP2025 lattice)",
      "date": null,
      "kind": "scorecard",
      "status": "kill_channel",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:neutron-edm-theta-eff-0",
      "titleEN": "lab: neutron EDM (theta_eff=0)",
      "questionEN": "neutron EDM (theta_eff=0)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:neutron-lifetime-tau-n-parameter-free-beam-bottle-side",
      "titleEN": "lab: neutron lifetime tau_n (parameter-free, beam-bottle side)",
      "questionEN": "neutron lifetime tau_n (parameter-free, beam-bottle side)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:proton-electron-mass-ratio-m-p-m-e-f-qcd",
      "titleEN": "lab: proton/electron mass ratio m_p/m_e (F_QCD)",
      "questionEN": "proton/electron mass ratio m_p/m_e (F_QCD)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:rare-kaon-br-k-pi-nu-nu",
      "titleEN": "lab: rare kaon BR(K+ -> pi+ nu nu)",
      "questionEN": "rare kaon BR(K+ -> pi+ nu nu)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:rare-kaon-br-kl-pi0-nu-nu",
      "titleEN": "lab: rare kaon BR(KL -> pi0 nu nu)",
      "questionEN": "rare kaon BR(KL -> pi0 nu nu)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:sterile-neutrino-dissolution-watchdog-n-fam-3",
      "titleEN": "lab: sterile-neutrino dissolution watchdog (N_fam=3)",
      "questionEN": "sterile-neutrino dissolution watchdog (N_fam=3)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:lab:x17-dissolution-watchdog-no-e8-slot",
      "titleEN": "lab: X17 dissolution watchdog (no E8 slot)",
      "questionEN": "X17 dissolution watchdog (no E8 slot)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "lab",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:neutrino:delta-nu-cp",
      "titleEN": "neutrino: delta_nu_CP",
      "questionEN": "delta_nu_CP",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "neutrino",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:neutrino:j-pmns-derived-cp-strength-ext-5",
      "titleEN": "neutrino: J_PMNS derived CP strength (EXT.5)",
      "questionEN": "J_PMNS derived CP strength (EXT.5)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "neutrino",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:neutrino:m-betabeta-0vbb",
      "titleEN": "neutrino: m_betabeta (0vbb)",
      "questionEN": "m_betabeta (0vbb)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "neutrino",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:neutrino:m-r-scalaron-trace-rung-nusf-01",
      "titleEN": "neutrino: M_R scalaron-trace rung (NUSF.01)",
      "questionEN": "M_R scalaron-trace rung (NUSF.01)",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "neutrino",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:neutrino:sin-2-theta12",
      "titleEN": "neutrino: sin^2 theta12",
      "questionEN": "sin^2 theta12",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "neutrino",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:neutrino:sin-2-theta13",
      "titleEN": "neutrino: sin^2 theta13",
      "questionEN": "sin^2 theta13",
      "date": null,
      "kind": "scorecard",
      "status": "tension",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "neutrino",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:neutrino:sin-2-theta23",
      "titleEN": "neutrino: sin^2 theta23",
      "questionEN": "sin^2 theta23",
      "date": null,
      "kind": "scorecard",
      "status": "consistent",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "neutrino",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:neutrino:sum-m-nu",
      "titleEN": "neutrino: sum m_nu",
      "questionEN": "sum m_nu",
      "date": null,
      "kind": "scorecard",
      "status": "tension",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "prediction_of_record",
      "evidenceClass": "external_data",
      "domain": "neutrino",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:proton decay:proton-lifetime-tau-p-p-e-pi0-carrier-ps-so-10-branch-b",
      "titleEN": "proton decay: proton lifetime tau_p (p->e+pi0), carrier-PS->SO(10) branch",
      "questionEN": "proton lifetime tau_p (p->e+pi0), carrier-PS->SO(10) branch B",
      "date": null,
      "kind": "scorecard",
      "status": "tension",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "downstream_bridge",
      "evidenceClass": "downstream_bridge",
      "domain": "proton decay",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:pulsar:dense-j0537-stacked-recovery-comb-range-finding-pg-06",
      "titleEN": "pulsar: dense J0537 stacked recovery comb + range finding (PG.06)",
      "questionEN": "dense J0537 stacked recovery comb + range finding (PG.06)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "strain_level_test",
      "evidenceClass": "search_target",
      "domain": "pulsar",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:pulsar:dynamic-crab-mf-frb-gap-clock-ext-7",
      "titleEN": "pulsar: dynamic Crab MF + FRB gap clock (EXT.7)",
      "questionEN": "dynamic Crab MF + FRB gap clock (EXT.7)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "pulsar",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:pulsar:dynamic-recovery-comb-on-real-nu-t-pg-05",
      "titleEN": "pulsar: dynamic recovery comb on real nu(t) (PG.05)",
      "questionEN": "dynamic recovery comb on real nu(t) (PG.05)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "strain_level_test",
      "evidenceClass": "search_target",
      "domain": "pulsar",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:pulsar:dynamic-recovery-comb-on-the-2024-vela-giant-glitch-pg-07",
      "titleEN": "pulsar: dynamic recovery comb on the 2024 Vela giant glitch (PG.07)",
      "questionEN": "dynamic recovery comb on the 2024 Vela giant glitch (PG.07)",
      "date": null,
      "kind": "scorecard",
      "status": "data_limited",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "strain_level_test",
      "evidenceClass": "search_target",
      "domain": "pulsar",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:pulsar:glitch-size-log-periodicity-pg-01",
      "titleEN": "pulsar: glitch-size log-periodicity (PG.01)",
      "questionEN": "glitch-size log-periodicity (PG.01)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "pulsar",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
      "id": "scorecard:pulsar:per-pulsar-size-waiting-kernel-ladder-pg-02-03",
      "titleEN": "pulsar: per-pulsar size/waiting kernel ladder (PG.02/03)",
      "questionEN": "per-pulsar size/waiting kernel ladder (PG.02/03)",
      "date": null,
      "kind": "scorecard",
      "status": "null",
      "verdictRaw": null,
      "verdictClass": null,
      "stage": "search_target",
      "evidenceClass": "search_target",
      "domain": "pulsar",
      "scopeEN": null,
      "sourceRefIds": [
        "source:d54cd6ae6be56d9cff2b"
      ],
      "historical": true,
      "reviewState": "inventoried-not-reviewed",
      "reviewedFindingIds": [],
      "notice": "Original historical attempt metadata. A reported PASS is not a reviewed theorem, a fresh run or physical completion."
    },
    {
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      "kind": "scorecard",
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    {
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      "reviewState": "inventoried-not-reviewed",
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      "reviewState": "inventoried-not-reviewed",
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      "titleEN": "quantum: Efimov DSI tuned to the kernel lambda=(3/2)^6 (heteronuclear",
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      "date": null,
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      "titleEN": "quantum: QGEO S_off on a real measured boundary operator (EIT analog",
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      "kind": "scorecard",
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      "questionEN": "recovery kernel as a quantum circuit (Kraus dilation)",
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      "historical": true,
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      "historical": true,
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      "id": "edge:f088c0d294230e6b7a8e",
      "from": "scorecard:quantum:qgeo-s-off-on-a-real-measured-boundary-operator-eit-analog-c",
      "to": "claim:QGEO.SYM.01",
      "type": "tests",
      "reviewState": "inventoried-not-reviewed",
      "fromState": "included",
      "toState": "external-reference"
    },
    {
      "id": "edge:5749179dd6f9839b4443",
      "from": "scorecard:quantum:quench-discrete-scale-invariance-qt-02",
      "to": "experiment:quantum-testbed",
      "type": "sourced_from",
      "reviewState": "inventoried-not-reviewed",
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "edge:22135afe017332e461a1",
      "from": "scorecard:quantum:recovery-kernel-as-a-quantum-circuit-kraus-dilation",
      "to": "experiment:qc-recovery-kernel",
      "type": "sourced_from",
      "reviewState": "inventoried-not-reviewed",
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "edge:8677e861ed5307e8cf21",
      "from": "scorecard:quantum:walled-clock-matched-filter-discriminator-qt-04",
      "to": "experiment:quantum-testbed",
      "type": "sourced_from",
      "reviewState": "inventoried-not-reviewed",
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "edge:855d674f6d6fb8f3b6ca",
      "from": "scorecard:seed:extended-seed-xi-bbn-shadows-ext-6",
      "to": "experiment:extended-signatures",
      "type": "sourced_from",
      "reviewState": "inventoried-not-reviewed",
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "edge:2f722f04590a752d24d3",
      "from": "scorecard:seed:shared-seed-phi0",
      "to": "experiment:cmb-birefringence-seed",
      "type": "sourced_from",
      "reviewState": "inventoried-not-reviewed",
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "edge:dc91e8b5b5fed66ccdff",
      "from": "scorecard:seed:shared-seed-phi0",
      "to": "experiment:seed-consistency",
      "type": "sourced_from",
      "reviewState": "inventoried-not-reviewed",
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:c2a1b95e3fa01d20963c903f",
      "from": "structure:p1-p2",
      "to": "structure:anchor",
      "type": "conditional_bridge",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Ankerrelationen verdichten P1/P2 in der gewählten geometrisch-algebraischen Struktur; die Rücklesung beweist nicht voraussetzungslos die Auswahl.",
      "conditionsDE": [
        "Anker a=(1,1,2)",
        "Naht- und Trägerinterpretation gelten als Eingangsdaten"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:51927fd02bb953503b4b5204",
      "from": "structure:anchor",
      "to": "structure:carrier-family",
      "type": "compiler_step",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "e2=5 und die vier Marken/Familienzählung werden als interne Träger- und Familienansicht verwendet.",
      "conditionsDE": [
        "benannte Riemann–Roch- und Markenroute"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:e1981e7f2ceaf826401c0077",
      "from": "structure:carrier-family",
      "to": "structure:e8-glue",
      "type": "compiler_step",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "D5-Träger und A3-Familienseite werden über gemeinsame Z4-Glue-Daten zum E8-Abschluss verbunden.",
      "conditionsDE": [
        "konkrete Gruppenwirkungen und passende Glue-Klassen"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:fd2f2acceebe13746a7551ed",
      "from": "structure:e8-glue",
      "to": "structure:sm-readout",
      "type": "conditional_bridge",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "E8-Abschluss lässt bestimmte Darstellungs-/Verzweigungsansichten zu; E8 selbst ist dadurch nicht als beobachtete Eichgruppe identifiziert.",
      "conditionsDE": [
        "gewählte 3+2-Markierung",
        "explizite Ladungs-/Gruppenabbildung"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:432f6e14984694a8088aba79",
      "from": "structure:carrier-family",
      "to": "structure:shared-seed",
      "type": "compiler_step",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Familienoperatoren, Deckung und diskrete Residuen liefern Eingaben der Flavor-Auslesung.",
      "conditionsDE": [
        "benannter Operator-/Windungsvertrag"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:74037e38e01d01d32b06363c",
      "from": "structure:shared-seed",
      "to": "structure:alpha-root",
      "type": "shares_seed",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Flavor- und Alpha-Formeln verwenden gemeinsam Seed- und Budgetgrößen; daraus entstehende Übereinstimmungen sind korreliert.",
      "conditionsDE": [
        "gleiches φ0 und gemeinsame Naht-/Budgetinputs"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:beced4d17232192ef64d9333",
      "from": "structure:e8-glue",
      "to": "structure:clock-network",
      "type": "consistency_check",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Coxeterordnung und Teilungsstruktur prüfen dieselbe E8-/Trägerarchitektur; sie sind keine unabhängigen Bestätigungen.",
      "conditionsDE": [
        "festgelegte Coxeter- und Clockdarstellung"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:5a860194ada26a64eb586306",
      "from": "structure:clock-network",
      "to": "structure:transfer-attractor",
      "type": "not_independent_evidence",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Periodische algebraische Aktionen und kontrahierende Transfermoden sind verschiedene Clocktypen, obwohl sich gemeinsame Zahlen wie 6 zeigen.",
      "conditionsDE": [
        "Clock- und Transferoperatoren bleiben getrennt typisiert"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:e0453c716e34ff1d591baa76",
      "from": "structure:msc",
      "to": "structure:finite-parents",
      "type": "conditional_bridge",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "MSC und endliche Parents sind bereits Anschlussobjekte, aber ihre Parameter-/Quellwahl ist nicht durch ihre bloße gemeinsame Darstellung abgeleitet.",
      "conditionsDE": [
        "gemeinsame Kovarianz, Zustands- und Operatorabbildung aus derselben Quelle"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:4fcbf20a72f2ff50903a502b",
      "from": "structure:finite-parents",
      "to": "structure:record-closure",
      "type": "consistency_check",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Wiederholung, Instrumentzweige und Recordantworten unterscheiden den Einzelkanal von einem vollständigen Prozessgesetz.",
      "conditionsDE": [
        "konkretes Interventionsmenü und Umgebung"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:3f992babc58bb463224441ce",
      "from": "structure:future-equivalence",
      "to": "structure:record-closure",
      "type": "conditional_bridge",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Zukunftsäquivalenz muss Antworten auf alle erlaubten Zweige und Records einschließen.",
      "conditionsDE": [
        "Operationsmenü enthält die tatsächlichen Messprotokolle"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:0288a600962508856ee75a85",
      "from": "structure:coupled-sufficiency",
      "to": "structure:future-equivalence",
      "type": "consistency_check",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Erweiterte Kopplungen können Unterschiede sichtbar machen, die im lokalen Antwortmenü unsichtbar waren; die Äquivalenzklasse muss dann neu berechnet werden.",
      "conditionsDE": [
        "Kopplung ist ein erlaubter zukünftiger Eingriff"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:0d0e44b8033695e95bbba3b9",
      "from": "structure:modular-state",
      "to": "structure:msc",
      "type": "conditional_bridge",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Modularer Zustand und Spektraldaten sind Teile des MSC-Anschlussbilds; benötigter Referenzzustand und physische Quellenwahl bleiben offen.",
      "conditionsDE": [
        "tatsächlicher treuer Zustand und kompatible Algebra"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:f74e2d1efac4c716c05664a6",
      "from": "structure:gravity-outputs",
      "to": "structure:T1-T8",
      "type": "conditional_bridge",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Gravitations- und Raumzeitanschlüsse decken Teilanforderungen von T3/T5/T7 ab, schließen aber keinen dieser gemeinsamen Gesamtverträge allein.",
      "conditionsDE": [
        "gemeinsamer Parent mit dynamischer Materie und universeller Kopplung"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:cb074a89a53b4a87b3214229",
      "from": "structure:arithmetic-e8",
      "to": "structure:e8-glue",
      "type": "consistency_check",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Theta-/Hecke-Daten bilden eine arithmetische Ansicht des E8-Gitters. Sie liefern weder automatisch eine RH-Herleitung noch neue Physikbelege.",
      "conditionsDE": [
        "benannte Gitterzählung und arithmetischer Geltungsbereich"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:0234e9620bfedeff535dc7a9",
      "from": "structure:p1-p2",
      "to": "structure:T1-T8",
      "type": "seeks_origin",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "T1 fordert Herkunft der Strukturprämissen, Markierungen und physischen Dimensionsannahmen.",
      "conditionsDE": [
        "Ledgerstatus des Gesamtvertrags bleibt maßgeblich"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:835640f6873d9dcc6e72ea88"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:d262cc956e7fc5780c9f76b8",
      "from": "structure:e8-glue",
      "to": "structure:T1-T8",
      "type": "seeks_origin",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "T2 fordert die tatsächliche mikroskopische Erzeugung und Randnetzidentifikation des algebraischen E8-Abschlusses.",
      "conditionsDE": [
        "gemeinsame geladene Naht und kontrollierter Grenzwert"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:4f98197613fed96709f08c93"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:fbba88b6ea5a4e325021aabf",
      "from": "structure:finite-parents",
      "to": "structure:T1-T8",
      "type": "seeks_origin",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "T3–T8 verlangen, dass Parent, chirale Materie, IR, Kopplungen, Gravitation und Anfangszustand gemeinsam erzeugt werden.",
      "conditionsDE": [
        "keine Addition getrennter Teilmodelle ohne gemeinsame Herkunft"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71",
        "semantic-source:835640f6873d9dcc6e72ea88"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:996ea68b54c8564bb67a872b",
      "from": "structure:future-equivalence",
      "to": "structure:T1-T8",
      "type": "seeks_origin",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Der Universalraum-Auftrag verlangt, dass dieselbe Quelle die tatsächlich erlaubten Zukunftsversuche und Antworten festlegt.",
      "conditionsDE": [
        "Operationsmenü wird aus der gemeinsamen Quelle bestimmt"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:18693ee9d77af4e7fcc691cc",
      "from": "structure:shared-seed",
      "to": "structure:alpha-root",
      "type": "not_independent_evidence",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Gemeinsame Seeds und gemeinsame Budgets machen Alpha-/Flavor-Ausgaben abhängig; Treffer dürfen nicht als unabhängige Erfolge gezählt werden.",
      "conditionsDE": [
        "gleiche Eingaben werden in mehreren Readouts wiederverwendet"
      ],
      "sourceRefIds": [
        "semantic-source:33b21c3a9e92e88b5cca5e71"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:01ca32c3395cf370f2e42038",
      "from": "structure:gravity-normalization",
      "to": "goal:T7",
      "type": "conditional_bridge",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "v73 fixes k=c3/2 only after the declared c3 and S² seam normalization; v358 assembles linearized Einstein coefficients under first-law and entropy-density premises. T7 still needs the microscopic normalization/replica selection and nonlinear universal spin-2 coupling from the common parent.",
      "conditionsDE": [
        "P1 c3 input and compactified S² seam convention",
        "v358 entropy-density/area-law premises",
        "T7 shared-parent and nonlinear-coupling requirements remain unmet"
      ],
      "sourceRefIds": [
        "semantic-source:e033fa8a6aca1c06927d3e1c",
        "semantic-source:c6aff0505cc5d4f8c8913119",
        "semantic-source:b8f39b8e95ee0cc35bfb08c8"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:9c9cec2d0a431872955c5493",
      "from": "structure:gravity-energy-flow",
      "to": "goal:T7",
      "type": "conditional_bridge",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "The matter boost-flux term needs an already-local 4D QFT with suitable vacuum/geometric modular action. The finite v323 symmetry helper does not derive that action. The current source diagnostic leaves open the same-region metric functional, conical-entropy match, local horizon action and area response; even these would remain upstream of the T7 nonlinear spin-2/emergence contract.",
      "conditionsDE": [
        "Local Poincare-covariant 4D net, locality, suitable vacuum and spectrum condition for BW/CHM",
        "Actual (E8)_1 collar/net and vacuum-preserving expectation for the conditional Cartan-current bridge",
        "Same state, algebra, normalization, regulator for metric variation and horizon relative entropy",
        "No promotion: bounded contract verdict PARTIAL and GRAV.SPIN2.EMERGENCE.01 remains Open"
      ],
      "sourceRefIds": [
        "semantic-source:74fe55f52ecae3c977649cc9",
        "semantic-source:facd2950a7db5a19f8dea646",
        "semantic-source:b8f39b8e95ee0cc35bfb08c8",
        "semantic-source:c6aff0505cc5d4f8c8913119"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:cae482e687e9e335364c21ea",
      "from": "structure:p1-p2",
      "to": "structure:gravity-normalization",
      "type": "shares_seed",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "The gravitational coefficient calculations reuse the P1 c3 normalization; reusing it across gravitational readouts does not independently derive or validate its physical origin.",
      "conditionsDE": [
        "P1 remains a declared input"
      ],
      "sourceRefIds": [
        "semantic-source:944346a48634c19b8b8a2bc8"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:3fe86f55cc4588048194c0a3",
      "from": "structure:clock-network",
      "to": "structure:gravity-normalization",
      "type": "shares_seed",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "The entropy density η=1/|μ4| shares the same fourth-root/mark structure used by the clock network; the common atom creates a linked readout, not independent evidence.",
      "conditionsDE": [
        "v358 entropy-density premise is used as declared"
      ],
      "sourceRefIds": [
        "semantic-source:6e38ed0d2e00444edcd1bf3a"
      ],
      "fromState": "included",
      "toState": "included"
    },
    {
      "id": "semantic-edge:156095d6e210887e2453e279",
      "from": "structure:carrier-family",
      "to": "structure:shared-seed",
      "type": "shares_seed",
      "reviewState": "authored-navigation",
      "explanationEN": null,
      "explanationDE": "Family count and carrier data feed the same seed/budget used by more than one output; such shared-input outputs are correlated and should not count as independent confirmation.",
      "conditionsDE": [
        "common φ0 and family/deck budget are reused"
      ],
      "sourceRefIds": [
        "semantic-source:835640f6873d9dcc6e72ea88",
        "semantic-source:33b21c3a9e92e88b5cca5e71"
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      "fromState": "included",
      "toState": "included"
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