Established within the stated premises
finding:r094-original-five-excitations-distinct-from-clustering-vacuum
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.
Scope: 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.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:r096-joint-higgs-twoface-source-constraint
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.
Scope: 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.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures - Same constant Higgs and two-face carrier
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.
premise:r096-same-constant-higgs-twoface-carrier
Established within the stated premises
finding:r096-positive-twoface-fourword-defect-bound
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.
Scope: Only the specified R096 branch under its jointly required premises. No derived physical Higgs measure, general H(x) field theory or P1 source completion.
Required premises and original source excerpts
- Same constant Higgs and two-face carrier
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.
premise:r096-same-constant-higgs-twoface-carrier - Positive normalized mixture of covariance contractions
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.
premise:r096-positive-normalized-contraction-mixture - Actual R054 color-symmetric quasifree fibers
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.
premise:r096-conditional-r054-color-wick-fibers
Established within the stated premises
finding:r096-unnormalized-mixed-source-linear-identity
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.
Scope: Only the specified R096 branch under its jointly required premises. No derived physical Higgs measure, general H(x) field theory or P1 source completion.
Required premises and original source excerpts
- Same constant Higgs and two-face carrier
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.
premise:r096-same-constant-higgs-twoface-carrier - Actual R054 color-symmetric quasifree fibers
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.
premise:r096-conditional-r054-color-wick-fibers - Identical integrable unnormalized weights and insertions
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.
premise:r096-same-integrable-unnormalized-weights
Established within the stated premises
finding:r096-original-quark-crossing-negative-covariance
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.
Scope: Only the specified R096 branch under its jointly required premises. No derived physical Higgs measure, general H(x) field theory or P1 source completion.
Required premises and original source excerpts
- Same constant Higgs and two-face carrier
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.
premise:r096-same-constant-higgs-twoface-carrier - Real face frame and positive nonconstant radial law
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.
premise:r096-real-face-quark-crossing-positive-radial-law
Established within the stated premises
finding:known-fourmark-system-has-three-and-five-canonical-views
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.
Scope: 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.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:reverse-bootstrap-retained-operator-scope
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.
Scope: Source audit of the specified reverse chain. No retraction of numerical self-consistency and no independent derivation of the framework.
Required premises and original source excerpts
- Reverse selection in the discrete closure framework
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.
premise:reverse-bootstrap-e8-closure-framework - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:e8-current-dictionary-all-separated-responses
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.
Scope: 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.
Required premises and original source excerpts
- Reverse selection in the discrete closure framework
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.
premise:reverse-bootstrap-e8-closure-framework - Given local E8_1 vacuum representation and explicit cocycle
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.
premise:local-e8-current-response-realization - Quarter phase is retained
Comparisons retain the original charged quarter phase; switching to another phase branch is not an admissible solution to the selection problem.
premise:quarter-phase-retained - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:charged-scaling-microscopic-map-still-unspecified
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.
Scope: 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.
Required premises and original source excerpts
- Literal charged scaling contract and original Slater case
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.
premise:literal-microscopic-charged-scaling-and-v988-slater-data - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Excluded in the stated class
finding:original-slater-proxy-fitted-bound-fails-actual-norm
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.
Scope: 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.
Required premises and original source excerpts
- Literal charged scaling contract and original Slater case
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.
premise:literal-microscopic-charged-scaling-and-v988-slater-data
Established within the stated premises
finding:periodic-microscopic-zero-modes-distinguish-source-state
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.
Scope: 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.
Required premises and original source excerpts
- Actual periodic v988 state and occupied frame
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.
premise:original-v988-periodic-zero-mode-state-comparison - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:r097-original-q-twins-are-integrally-conjugate-before-fixed-source-form
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.
Scope: 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.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:replicated-deterministic-consistency-iff-influence-dag
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.
Scope: 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.
Required premises and original source excerpts
- Finite deterministic processes with full joint replica control
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.
premise:finite-deterministic-joint-replication-control
Established within the stated premises
finding:three-binary-processes-two-copy-reversible-classification
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.
Scope: Complete bounded classification of three binary interfaces; no particle/generation/dimension interpretation. One-shot consistency does not force a fixed order.
Required premises and original source excerpts
- Finite deterministic processes with full joint replica control
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.
premise:finite-deterministic-joint-replication-control
Established within the stated premises
finding:independent-poset-information-composition-consequences
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.
Scope: 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.
Required premises and original source excerpts
- Finite event order as starting data
A finite strict partial order is supplied as event/precedence structure without metric, space, rates or probability. Order is an input in this class.
premise:finite-event-poset - Supplied finite update, observation and errors
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.
premise:finite-update-observation-errors - Supplied finite operational action and effects
A transformation monoid acts on finite X; effects define operational distinguishability. Composition, action, effects and any selected time generator are separate starting data.
premise:finite-operational-composition-action
Established within the stated premises
finding:reset-diagnosis-not-global-tfpt-underdetermination
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.
Scope: Refinement of already reviewed diagnosis and explicit counterworld comparison of new classes; no refutation of all TFPT and no closure of a physical goal.
Required premises and original source excerpts
- TFPT for later comparison only
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.
premise:foundational-reset-no-target-input
Established within the stated premises
finding:three-inequivalent-repeatable-observation-countermodels
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.
Scope: 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.
Required premises and original source excerpts
- Explicit repeatable-distinction benchmark
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.
premise:repeatable-distinction-benchmark - Three explicit operational countermodels
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.
premise:three-explicit-observability-countermodels
Established within the stated premises
finding:repeatable-reports-do-not-imply-full-state-stability
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.
Scope: 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.
Required premises and original source excerpts
- Explicit repeatable-distinction benchmark
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.
premise:repeatable-distinction-benchmark
Established within the stated premises
finding:finite-sequential-data-admit-classical-history-realization
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.
Scope: 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.
Required premises and original source excerpts
- Finite prefix-consistent sequential response tables
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.
premise:finite-prefix-consistent-sequential-data
Established within the stated premises
finding:pascal-carrier-rank-unique-unbounded-source-proof
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.
Scope: 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.
Required premises and original source excerpts
Open questions preserve their achieved subresults
Each research problem has its own scope. A resolved task does not close its whole physical parent. Historical tasks remain explicitly historical in the source record.
Future quotient and positive GNS reconstruction
What is determined by complete future behavior, and what additional positive word-kernel source is needed to reconstruct a cyclic operator realization?
- Resolved in scope: Future quotient from complete rRead result
- Resolved in scope: Conditional GNS reconstruction from supplied KRead result
- open: Select complete K from the original source
Historical: common source, state and event selection
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?
Seam connection and family action
Does the joint discrete theorem determine a concrete connection and a family coupling compatible with the determinant seam action?
- Resolved in scope: Separate classes from actual transportRead result
- open: Derive the common connection from the original source
Physical time and complete transfer
Do the original reflection/projector structures determine the full physical time generator and required field transfer?
- Resolved in scope: Reuse the sign-projector counterexampleRead result
- Resolved in scope: Reuse conditional full-transfer reconstructionRead result
- open: Identify the physical complete TFPT transfer
- Resolved in scope: Reuse complete collar reconstructionRead result
- Resolved in scope: Classify homogeneous GKLS embedding of the shared register familyRead result
- Resolved in scope: Decide every homogeneous GKSL logarithm of the fixed M4 channelRead result
Flavor ratio and absolute amplitude scale
Which flavor quantity is fixed on the derived discrete stratum, and which requires the continuous holonomy anchor?
- Resolved in scope: Reuse the derived flavor ratioRead result
- open: Determine the absolute holonomy amplitude
Alpha: derived terms, unique root and physical EM identification
Where do the factors and closed alpha equation come from, which provenance steps are proved, and which precise physical EM identification remains open?
- Resolved in scope: Separate root calculation from source selectionRead result
- open: Derive the actual EM functional variation and Thomson identification
- Resolved in scope: Establish the unique global positive rootRead result
Geometric flow and gravity normalization
Do common matter-only observations derive geometric horizon flow and the area response from the original gravity source?
- Resolved in scope: Record scope of fixed original functionalRead result
- open: Derive geometric modular response and area coefficient
Clocks and complete neutral source response
Which complete quadratic response can the actual clock images reconstruct?
- Resolved in scope: Reconstruct all neutral quadratic matrix directionsRead result
- open: Derive physically admissible probe access
Clock action on charge, time and quarter transition
How does the actual Gaussian J act on the complete marked source?
- Resolved in scope: Construct original J lift with complete time/charge actionRead result
- open: Derive physical meaning of the frame orbit
Which responses distinguish charged time action?
Which data separate sources with identical complete neutral vacuum response?
- Resolved in scope: Determine twist blindness completelyRead result
- Resolved in scope: Reconstruct twist from charged responsesRead result
- open: Derive actual charged source probes
Which seam action distinguishes native opposite charges?
Can existing native charge fields produce the quarter-twist time response of the seam?
- Resolved in scope: Check native fields and response discriminatorRead result
- open: Derive actual marked seam/state action
Constructive seam search: operators, state and source compatibility
What does the complete phase search decide, and which additional state information prevents a false source solution?
- Resolved in scope: Finite search closed, actual winding and parity equivalenceRead result
- Resolved in scope: Positive finite-word state extensionRead result
- Resolved in scope: E8 current group conditionally determines the P signRead result
- Resolved in scope: The same shift functional hides distinct ground statesRead result
- Resolved in scope: No phase hit realizes the unchanged sourceRead result
Which partner actually belongs to the original seam?
Which charge, state type and time action belong to the root partner and original sheet pairing?
- Resolved in scope: Concrete pair operator; source neutrality is not hypercharge neutralityRead result
- Resolved in scope: Fixed quarter time splits the color/weak multipletRead result
- Resolved in scope: Explicit conjugation for the existing sheet pairingRead result
- Resolved in scope: Actual partner map between quarter domainsRead result
- Resolved in scope: Bilinear sheet pairing is not Hermitian kernel selectionRead result
- Resolved in scope: Actual quarter conjugation transports the supplied markingRead result
- Resolved in scope: No time-stabilizing orthogonal repair of the fixed markingRead result
- Resolved in scope: Spinor16 is a state sector, not a 16-real one-particle fieldRead result
Automated construction of operator maps and sources
Which tools generate operator maps, learn counterexamples, and can search for the full positive source?
- Resolved in scope: Calibrate new search without supplying the target mapRead result
- open: Synthesize a joint field, marking and transfer dictionary
- open: Search for the positive common source kernel itself
- Resolved in scope: Automatically construct, certify and distinguish finite kernelsRead result
- Resolved in scope: Repair search conditions against source types and collar controlsRead result
- Resolved in scope: Reconstruct multi-field sewing of the canonically identified boundary sourceRead result
- Resolved in scope: Retain absolute reference amplitude in searchRead result
- Resolved in scope: Integrate supplied free source including boundary response and scalarRead result
- Resolved in scope: Convert the full finite CAR kernel into a link functionalRead result
- Resolved in scope: Close original recursive word reconstruction with memoryRead resultRead result
- Resolved in scope: Retain whole original caller through scale and readoutRead resultRead result
- Resolved in scope: Execute actual shared Higgs source with full matter words and local RPRead resultRead result
- Resolved in scope: Reduce whole constant original Higgs spectral fiberRead result
- open: Resolve original geometric Higgs residue sign and field map
- Resolved in scope: Evaluate local original Higgs heat identification and whole finite consumerRead resultRead result
- Resolved in scope: Execute whole variable bound Higgs reference and original scale mapRead resultRead result
- Resolved in scope: Execute whole inner Higgs scale/source and normal kernel transportRead resultRead result
- Resolved in scope: Execute given whole superconnection and normal spectral readerRead resultRead result
- Resolved in scope: Determine own-admissibility and whole total-chiral spectral readersRead resultRead result
- Resolved in scope: Derive whole scale-energy map,normal profile and relative flowRead resultRead result
- Resolved in scope: Execute original Green energy producer and mixed scale readoutRead resultRead result
- Resolved in scope: Match current action argument and common Higgs/gravity weightsRead resultRead result
- Resolved in scope: Execute whole original curvature consumers and Higgs radial sourceRead resultRead resultRead result
- Resolved in scope: Execute original whole four-ghost source and geometric type testRead resultRead result
- Resolved in scope: Execute original moving normal kernel derivative and whole source responseRead result
- Resolved in scope: Decide fixed original O1 source and normal operator placementRead result
- Resolved in scope: Compare whole Higgs mixture and covariance reader on invariant four-field witnessRead result
- Resolved in scope: Test exact bounded cutoff on whole ordinary Higgs volumeRead result
- Resolved in scope: Test whole original circle joint mode and IR Higgs normalizationRead result
- Resolved in scope: Test original O1 mode covariance against whole Higgs-law classRead result
- open: Reconstruct original localization from the whole process
- Resolved in scope: Test bare native-code word compression against actual localityRead result
- Resolved in scope: Decide original geometric local-time class and execute actual interval readerRead resultRead result
- Resolved in scope: Execute actual regional two-face partner and supported charged wordRead resultRead result
- Resolved in scope: Execute original color marginal, modular field law and complete class readerRead resultRead resultRead result
- Resolved in scope: Reconstruct common Higgs law from whole original quarter source towerRead resultRead resultRead result
- Resolved in scope: Execute original record action on Doily and ordered whole source responseRead resultRead resultRead resultRead result
- Resolved in scope: Locally implement original record process and test unchanged exterior sourceRead resultRead resultRead result
- Resolved in scope: Execute original elliptic insertion,whole source and causal responseRead resultRead resultRead result
- Resolved in scope: Evaluate actual joint Higgs and color group sourceRead resultRead result
- Resolved in scope: Execute whole original graph color reader with typed original center selectorRead resultRead result
- Resolved in scope: Execute original color fixed source and first inherited grading testRead resultRead result
- Resolved in scope: Execute actual original color-spinor CAR four-word and complete spin-sector sewingRead resultRead result
- Resolved in scope: Decide actual color admissibility of density operations and coordinate regionsRead resultRead result
- Resolved in scope: Execute actual whole seam-operation class and two-face responseRead resultRead result
- Resolved in scope: Execute entire original C6 word expansion with source amplitudeRead resultRead result
- Resolved in scope: Execute original collective Higgs force source and entire mean dualRead resultRead resultRead result
- Resolved in scope: Execute original all-mode force with actual time and whole sourceRead resultRead result
- Resolved in scope: Execute original local space/time force source and causal liftRead resultRead result
Origin reverse selection, field dictionary and original P1 kernel
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?
Observable reality: minimal conditions and counterworlds
Which operational conditions are independently required, which inequivalent models satisfy them, and which observable distinctions remain for selection?
Formal carrier core: unbounded Pascal uniqueness and finite glue
Which carrier and glue statements are already present in the papers and Lean sources, and which physical selection does not follow?
- Resolved in scope: Classify the unbounded Pascal proofRead result
- Resolved in scope: Classify the formal finite glue scopeRead result
Active mathematical program: marked seam monodromies and lattice lifts
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.
- Resolved in scope: Define marked seam category and factor formulaRead result
- Resolved in scope: Completely classify quarter-clock four-puncture liftsRead result
- Resolved in scope: Determine central class and all subgroup restrictionsRead result
- Resolved in scope: Determine full G0 cocycle and classRead result
- Resolved in scope: Determine native4/5/6local cohomologyRead result
- Resolved in scope: Classify unrestricted G31 reflection monodromiesRead resultRead result
- Resolved in scope: Determine lift class beyond G0Read result
- open: Classify additional reflection/clock equivariance and mapping-class quotients
- Resolved in scope: Equivariant lifting and divisibility by eightRead result
- Resolved in scope: All62clock obstructions and central transport variantsRead result
- Resolved in scope: Actual group comparison and central pushout exclusionRead result
- Resolved in scope: Complete invariants and explicit collisionsRead result
- Resolved in scope: Compare E6 and E7 slices with the actual quarter clockRead resultRead resultRead resultRead result
- Resolved in scope: Classify original character-valued G31monodromy liftsRead resultRead result
- Resolved in scope: Determine E7-pair action on all original lattice fieldsRead result
- Resolved in scope: Completely connect E6/E7 cuts to the original compilerRead result
- Resolved in scope: Compare common covers and actual clock carriersRead result
- Resolved in scope: Prove shared representation consequence for48,4/3 and5/4Read result
- Resolved in scope: Completely decide joint compiler-field-cover constructionRead resultRead resultRead resultRead result
- Resolved in scope: Reconstruct canonical local compiler field source from C4Read resultRead result
- Resolved in scope: Eliminate redundant sector and multiplicity assumptionsRead result
- Resolved in scope: Classify native equivariant markingsRead result
- Resolved in scope: Classify pure quarter clock mapping class quotientRead result
- Resolved in scope: Determine complete cut algebra and lossless tetrahedron transformRead resultRead resultRead resultRead result
- Resolved in scope: Completely compare scalar glue and actual native compiler classRead resultRead resultRead resultRead result
Common clock sectors, quartic geometry and operational reconstruction
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?
Automatic joint origin hypotheses and source responses
Which simple joint rules connect the existing P1 source chain,double cover,information and compiler,and which whole candidate classes can be decided automatically using actual source consequences?
- Resolved in scope: Decide even-matter word class and check actual AI operator expressionsRead resultRead result
Existing TFPT derivations and correction of repeated gap diagnoses
Which common source/reconstruction chain already exists in the old original papers, and which purported global gaps arose from reducing P1 or choosing an optional CAR route?
Complete physical Hamiltonian source with Gauss sector and thermal word limit
Which whole source is constructed on the original local Hamiltonian route, how do physical constraints and thermal words follow, and how is its actual IR response distinguished from the original covariant geometric source branch?
Original TFPT source versus DET16 mirror vertex
Does the same original TFPT source produce the concrete DET16 generator and whole responses,or is a computable parent supplied as extra input?
Whole original source and canonical vacuum attachment
Which vacuum joins are already in the whole original source,and how do H ground source and R104 field/Gauss source join completely without second state choice or parent change?
Craig chiral measure and the original whole TFPT source
Which concrete operator and Berezin measure map preserves the original TFPT source when connecting Craig overlap measure?
- open: Compare original4D fermion Hessian and measure line with Craig
Cyclic quantum universe and original Genesis connection
Does original TFPT dynamics yield the exact cyclic quantum return in the September/October press lead and a geometric Genesis transition?
- open: Test periodicity and Genesis response on the same whole source
Physical constants as joint constraints on the TFPT source
Which independent constants constrain the original common source, and can one relative heat product supply gravity and vacuum energy together?
- open: Evaluate original volume, curvature and gauge responses together