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The original technical record remains available here. For explanations, reviewed conclusions and the history of research questions, start with the knowledge atlas.

Research snapshot 2026-11-02 · 783 active ledger claims · 706 scientific findings · 707 registered scripts. These are different inventories, not counts of independent physical confirmations.

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What does this inventory cover?

Every one of the 783 active ledger IDs is included. All 788 ledger rows, including superseded rows, remain in the download. The reviewed research corpus contains 707 findings; 1 administrative record is excluded from public scientific content, with the omission recorded in the coverage file.

The scientific findings include 515 established scoped results, 63 conditional results and 128 scoped exclusions. These labels describe the recorded finding. They do not upgrade its parent physical goal or overwrite the original ledger.

Sources were matched to their recorded hashes and line ranges at this snapshot. Bounded text excerpts make sources available even when a source is not in the earlier public release. Any omitted administrative lines are explicitly marked. This is source coverage, not a new execution of Python, Lean or Wolfram proofs.

Atlas revision 4d8fcdb3587f8e4cc0898e5c · snapshot SHA256 7c23438352ba021cef5aa0999c31e5c242fbc6ed12b172e4d35fb6a68f65dbb4

3 matching records · page 1 of 1

Original ledger status

QGEO.COVER.01

QGEO.COVER.01

Strategy I/II, first executed step -- the mu3-cover of P^1 branched at mu4 (the curve y^3 = x^4 - 1) carries FOUR independent compiler fingerprints (one module, 6 checks, <1 s; discovery probe mu4_cover_model_probe.py 6/6, verdict FINGERPRINTS-HIT): (1) genus 3 with five cusps (mu4 + infinity; monodromies (w,w,w,w,w^2) multiplying to 1) and Chevalley-Weil H^{1,0} = (1,2) per character -- H_1 is a RANK-3 module over the Eisenstein integers, the compiler's 3-dimensional integral frame; (2) the D4 rotation closes PROJECTIVELY VIA THE DECK: in the reduced Burau model at t = omega (braid relations machine-verified) the rotation braid satisfies r^4 = omega x identity and r^12 = 1; (3) THE TORSION: the cusp-class group is (Z/3)^5 modulo one global relation = (Z/3)^4 of order 81 = 3^4 -- the v566 saturation index with exactly the per-mark Z/3 mechanism the self-code program asked for (four free local classes); det_Z(1 - deck) = 27 complementarily; (4) THE SIGNATURE: the invariant hermitian form of the Burau module is unique up to scale with eigenvalues {-2, 2-2sqrt2, 2+2sqrt2} -- LORENTZ SIGNATURE (1,2), matching the Chevalley-Weil Hodge numbers AND the rank-3 polarization signature of Paper II: Strategy II's first prediction (RP positivity as Hodge/Riemann positivity) confirmed at the form level. First operator pass: the single-cusp Gram has all-integer spectrum {0,0,2}; the compiler V-spectrum {0,1,2} is not yet located -- the operator dictionary (which canonical homology operator is Q/V) and the real-structure/RP map to the v572 Gram data are the NAMED NEXT STEPS. Kill criteria live (Smith/spectral mismatch for I; signature mismatch for II -- not triggered). GATE.QGEO does NOT move; no marker changes. [2026-08-01 XI, the dictionary's first entry: U IS LOCATED -- the cusp Gram (1-T2)(1-T2)^dagger has characteristic polynomial x^2(x-3) = char(U) exactly (the winding operator as a cusp Gram; fifth fingerprint); additional exact structure: opposite-twist products (1-T1)(1-T3) are NILPOTENT (char x^3), and G1+G3 has spectrum {0,1,3}; V/H/Q not located in the scanned canonical ranges (products/sums/omega-twists of length <= 2) -- the V-dictionary likely requires the parabolic flag (the seam-cusp filtration), named as the next step.] [2026-08-01 XIII: dictionary round 2 -- v598: THREE entries now exact (U ~ G2; Q_- ~ G1-G3, the sheet coupling as the diamond-diagonal Gram difference; the binary ladder ~ 1+G1+G3); the grading half absent from 7296 canonical combinations; see QGEO.DICT.01.] [2026-08-01 XV: the real structure is constructed and the invariant form is pinned -- v599: R unique with R^2 = +1, det J = 8 (a sheet-diamond determinant list member), Lorentz (1,2) confirmed exactly; see QGEO.REAL.01.] [2026-08-01 XVI: the operator dictionary lands at ALGEBRA level -- v600: the compiler pair (U, V) realized on the cover with the exact v566 saturation structure (index 81, divisors (1,1,1,3,3,3,3)); the [P]-model of GATE.QGEO has an explicit construction; canonicity and the two-demand derivation stay open; see QGEO.EMBED.01.] [2026-08-01 XXI: the torsion picture completes -- v604: 81 = 3^4 localizes at the finite marks (divisor classes; per-frame word order) and 27 = 3^3 at infinity (monodromy-defect cokernel = equivariant-order cokernel = det(1-deck)); see QGEO.EQORDER.01.] [2026-08-01 XXVIII: the curve's wider landscape is mapped -- v610: the Jacobian splits into a Q(zeta_12)-CM surface (the field of deck AND marks) times the Q(omega)-CM elliptic quotient, point-count-confirmed; the integer-spectrum census honestly relativizes single-char hits (the anchor class is the most frequent nontrivial family; the joint structure is the distinction); see QGEO.LANDSCAPE.01.] [2026-08-01 XXXV: the bedrock direction reverses -- v617: the conformal seam axioms FORCE the mu3-cover (Z4-Mobius rigidity, uniform weights j in {1,2}, genus 3, seam reflections = the v599 pattern); the QGEO.SYM.01 residue narrows to the cyclic-3 choice and the physical<->conformal seam identification; see QGEO.SEAMFORCE.01.]

Recorded status: Exact [E] fingerprints + typed candidate [C] (Burau convention validated; Q-identification open)

Dependencies, status detail and source

Canonical status: FINGERPRINTS-HIT: rank-3 Eisenstein module; projective D4 via deck (r^4 = omega); cusp-class group (Z/3)^4 = 81 with the per-mark mechanism; Lorentz (1,2) polarization (Chevalley-Weil + Paper II simultaneously); single-cusp Gram {0,0,2}; Q/V dictionary and RP map named open; 6/6 checks

Dependencies: QGEO.INVOL.01; QGEO.WINDING.SELF.01; DIAMOND.PARA.SELFCODE.01; GATE.QGEO.01; v566; v574; v590

Scripts: v597_mu4_cover_model.py

Location: tfpt_1;tfpt_2;tfpt_3

Original CSV, line 615

Original ledger status

QGEO.DICT.01

QGEO.DICT.01

The cover dictionary, round 2 -- THREE compiler objects located as canonical cusp-Gram combinations on the mu3-cover (one module, 4 checks, <1 s; discovery probe cover_dictionary_probe.py 4/4, verdict DICT-THREE-ENTRIES): with T_1..T_4 the D4-conjugate cusp twists and G_k their Grams -- U ~ G_2 (char x^2(x-3), the winding operator as a single-cusp Gram; v597 entry); Q_- ~ G_1 - G_3 (char x(x^2-3)): THE MU4 SHEET COUPLING IS THE DIFFERENCE OF THE OPPOSITE CUSP GRAMS -- the diamond diagonal; ladder ~ 1 + G_1 + G_3 (char (x-1)(x-2)(x-4)): the binary AnchorLadder (1,2,4) = (2^0,2^1,2^2) of v568 is identity plus the diagonal sum. Supporting exact structure: opposite-twist products (1-T_1)(1-T_3) are nilpotent (cube zero), Q_-^2 has char x(x-3)^2. THE NEGATIVES QUANTIFIED: Q_+ ({1,2,3}), V ({0,1,2}), H ({1,1,2}) and Q itself are NOT contained in 7296 scanned canonical combinations (the integer Gram lattice a + bG_1 + cG_2 + dG_3 + eG_4 and its non-hermitian (1-T_i)(1-T_j) extension; numeric prefilter, exact confirmation; 0 matches) -- the grading half needs a generator outside the finite-cusp twist algebra, with the anti-holomorphic D4 reflections (the real structure) as the named suspect. The Strategy-I kill criterion is NOT triggered (the canonical space is not exhausted). GATE.QGEO does not move; no marker changes. [2026-08-01 XV: the named suspect is CONSTRUCTED -- v599: the real structure exists and is unique up to scale (R^2 = +1); its grading functor closes all three gaps at char level (V, H with the anchor spectrum, Q_+); the joint algebra embedding stays open (quantified negative); see QGEO.REAL.01.] [2026-08-01 XVI: the dictionary completes at algebra level -- v600: a Gamma-even degree-2 pair realizes (U, V) jointly (conjugation exact, index 81); canonicity open; see QGEO.EMBED.01.] [2026-08-01 XXVIII: retroactive typing confirmed -- v610's census shows single integer spectra are common on the cover; this module's char-level entries were correctly typed candidates, upgraded to the joint embedding only by v600; see QGEO.LANDSCAPE.01.]

Recorded status: Exact [E] entries + quantified negatives (numeric prefilter, symbolic confirmation)

Dependencies, status detail and source

Canonical status: DICT-THREE-ENTRIES: U ~ G2, Q_- ~ G1-G3 (diamond diagonal), ladder ~ 1+G1+G3 -- all exact; grading half absent from 7296 canonical combinations (kill not triggered; real structure the named suspect); 4/4 checks

Dependencies: QGEO.COVER.01; QGEO.INVOL.01; DIAMOND.PARA.SELFCODE.01; v566; v568; v597

Scripts: v598_cover_dictionary.py

Location: tfpt_1;tfpt_2;tfpt_3

Original CSV, line 616

Original ledger status

QGEO.LANDSCAPE.01

QGEO.LANDSCAPE.01

The curve landscape round -- what else the mu3-cover carries (one module, 9 checks, ~1 s; discovery probe curve_landscape_probe.py 9/9, verdict LANDSCAPE-MAPPED). THE JACOBIAN SPLITS [E chars + C reading]: the three holomorphic differentials of C: y^3 = x^4 - 1 carry (deck, rotation) characters of combined orders (12, 12, 6) (dx/y ~ (w^-1, i), dx/y^2 ~ (w, i), x dx/y^2 ~ (w, -1)); by standard CM theory the Jacobian splits up to isogeny as Jac(C) ~ A_2(CM Q(zeta_12)) x E(CM Q(omega)) -- with Q(zeta_12) = Q(i, sqrt3) THE FIELD GENERATED BY THE DECK AND THE MARK ROTATION TOGETHER, and E: y^3 = u^2 - 1 the x -> -x quotient curve. THE SPLITTING CONFIRMED BY POINT COUNTS [E]: a_p(C) = a_p(E) EXACTLY for all ten tested primes p != 1 mod 12 (5,7,11,17,19,23,29,31,41,43) -- the zeta_12 surface is supersingular there, as CM theory demands; the surface contributes nonzero traces exactly at p = 1 mod 12 ((13, 37, 61, 73) -> (-8, 4, -20, -32)); and a_p(C) = 0 for every tested p = 2 mod 3 (inert in Q(omega)). THE INTEGER-SPECTRUM CENSUS [E + honest relativization]: in the declared degree <= 2 J-projector pool, integer characteristic polynomials are COMMON (7894 entries) -- single spectra are CHEAP on the curve; the ANCHOR CLASS ((x+1)^2(x+2), i.e. {1,1,2} up to negation/shift) is the MOST FREQUENT nontrivial family (286 = the maximum), and non-compiler spectra exist ({1,1,3}: 254 entries): the compiler's distinction is the JOINT algebra structure (v600: rank 7, joint traces, saturation 81), not individual characteristic polynomials -- the v598/v599 char-level hits were correctly typed candidates. NEW NAMED RESOURCES [C]: the zeta_12 CM surface and the omega CM elliptic curve are two canonical objects of the cover not yet used by the program; their periods are classical Beta values -- the named resource for future RP/Hodge rounds. GATE.QGEO does not move; no marker changes. [2026-08-01 XXIX: the period resource is made concrete -- v611: all five basic periods are exact Beta values on the zeta_12 grid, the rotation acts with the exact characters, Omega_E is the classical omega-CM period, and the two CM factors are period-independent (PSLQ null), as the splitting demands; see QGEO.PERIODS.01.]

Recorded status: Exact [E] characters/point-counts/census + [C] CM-theory reading and named resources (deterministic integer computations; no floats beyond the census prefilter)

Dependencies, status detail and source

Canonical status: LANDSCAPE-MAPPED: differential characters (12,12,6); Jac ~ A_2(zeta_12) x E(omega) point-count-confirmed (10 exact zero-differences; surface traces only at p = 1 mod 12); anchor class most frequent nontrivial integer family (286); single spectra cheap, joint structure the distinction; periods named; 9/9 checks

Dependencies: QGEO.COVER.01; QGEO.DICT.01; QGEO.EMBED.01; v597; v598; v600

Scripts: v610_curve_landscape.py

Location: tfpt_1;tfpt_2;tfpt_3

Original CSV, line 628

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 closure for fixed inputs

Which closure equation follows for a fixed seam projector, and which inputs still need justification?

  • Resolved in scope: Separate root calculation from source selectionRead result
  • open: Derive alpha inputs and Thomson transfer
  • 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 response search with original-source decision

Which additional joint response actually follows from original source equations, and which entire finite process family remains undecided without it?