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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 All 788 ledger rows, including superseded rows, remain in the download.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

4 matching records · page 1 of 1

Original ledger status

CONTRACT.QFT4D.01

CONTRACT.QFT4D.01

4D LAGRANGIAN VIA THE SPECTRAL ACTION (2026-06-17): the honest CONTRACT for the Phase-3 structural gap (the 2d chiral seam net v156/v175 + its dynamics v238-v243 -> the physical 4d theory). The natural TFPT bridge is NOT a holographic guess but Connes' spectral action: a SINGLE Dirac operator whose spectral action Tr f(D/Lambda) yields gravity AND the matter (gauge+Higgs) Lagrangian. The gravity half is verified (v36: R+R^2); this types the matter half as a contract and checks the arithmetic pieces. (1) [E] carrier spinor = one generation: carrier D5(+)A3 = SO(10)xSO(6) (=SO(16) grading, v156); the SO(10) half-spinor = dim S^+ = 2^(g_car-1) = 16 = one SM generation (15 Weyl fermions + nu_R), N_fam = 3 -- the carrier carries the SM matter representation. (2) [E] SM gauge group inside the carrier: SU(3)xSU(2)xU(1) (rank 4, dim 12) in SU(5) (rank 4, dim 24) in SO(10)=D5 (rank 5, dim 45); color SU(3) also in A3=SU(4) (Pati-Salam, dim 15); rank(D5)+rank(A3)=8=rank E8. (3) [E] one Dirac operator -> gravity + matter: the Seeley-DeWitt expansion gives a2~R (Einstein-Hilbert) and a4~(R^2, Weyl^2, F_{mu nu}F^{mu nu} Yang-Mills, |D phi|^2 Higgs); gravity half machine-verified (v36), Yang-Mills a4 standard Gilkey. (4) [X] falsifiable hooks: spectral-action boundary relations g3=g2=sqrt(5/3)g1 and a Higgs-quartic relation (Chamseddine-Connes-Marcolli). (5) [O] CONTRACT.QFT4D.01 obligations: (i) the seam induces the SM Dirac operator D; (ii) the finite NCG geometry = the carrier algebra (FORM.P2.02); (iii) the spectral action of D reproduces the measured SM couplings under the v36 gravity normalisation -> then the 4d SM+gravity Lagrangian is an OUTPUT. The genuine Phase-3 target, NOT closed

Recorded status: Contract [O] (with [E] arithmetic + [X] hooks)

Dependencies, status detail and source

Canonical status: [E] carrier half-spinor = one SM generation (16), SM gauge group embeds in the carrier, one Dirac operator gives gravity (v36) + matter (Gilkey); [X] unification + Higgs hooks; [O] CONTRACT.QFT4D.01: the spectral action of the seam Dirac operator = 4d SM+gravity Lagrangian -- the Phase-3 target, not closed

Dependencies: FORM.P2.02; QG.G2.01; DHR.SECTORS.01

Scripts: v244_spectral_action_contract.py

Location: tfpt_research_contracts

Original CSV, line 330

Original ledger status

QFT4D.MATTER.01

QFT4D.MATTER.01

SPECTRAL-ACTION MATTER CONTENT (2026-06-17): the computable core of CONTRACT.QFT4D.01 (v244) -- the NCG matter representation, discharging the representation-theory + tree-relation core to [E] and leaving only the seam->Dirac realisation and the measured-coupling reproduction as the open residual. The carrier half-spinor is the SO(10) 16 (dim S^+ = 2^(g_car-1) = 16). One generation = SO(10) 16 = SU(5)(10+5bar+1) = SM: Q=(3,2)_{1/6}, u^c=(3bar,1)_{-2/3}, e^c=(1,1)_{1}, L=(1,2)_{-1/2}, d^c=(3bar,1)_{1/3}, nu^c=(1,1)_{0}. (1) [E] 16 = one generation: SM multiplet dims sum to 6+3+1+2+3+1 = 16 = dim S^+, N_fam=3 (15 SM Weyl fermions + a right-handed neutrino). (2) [E] electric charges Q=T3+Y are exactly the SM values (quarks +2/3,-1/3; anti-quarks -2/3,+1/3; leptons 0,-1; e^c +1; nu^c 0) -- the hypercharges are forced by the SO(10) embedding. (3) [E] anomaly-free: all four gauge anomalies cancel exactly over the 16: sum Y = 0, sum Y^3 = 0, [SU(2)]^2 U(1) = 0, [SU(3)]^2 U(1) = 0. (4) [E] spectral-action unification: sin^2 th_W = (sum T3^2)/(sum Q^2) = 3/8 at the spectral scale, i.e. g3=g2=sqrt(5/3)g1 (Chamseddine-Connes-Marcolli). (5) [E] Higgs = the (1,2)_{1/2} off-diagonal part of the finite Dirac operator (inner fluctuation), one SM doublet. (6) [O] residual: (i) the seam induces the Dirac operator D and (iii) the spectral action reproduces the MEASURED couplings after RG running -- still a contract, now with its rep-theory core verified

Recorded status: Numerical (exact rep theory) [E]/[O]

Dependencies, status detail and source

Canonical status: [E] SO(10) 16 = one anomaly-free SM generation with correct hypercharges/charges; sin^2 th_W = 3/8 (g3=g2=sqrt(5/3)g1); Higgs = (1,2)_{1/2} inner fluctuation. [O] the seam->Dirac realisation + measured-coupling reproduction stay the open contract

Dependencies: CONTRACT.QFT4D.01; FORM.P2.02

Scripts: v245_spectral_matter_content.py

Location: tfpt_research_contracts

Original CSV, line 331

Original ledger status

QFT4D.RGTEST.01

QFT4D.RGTEST.01

UNIFICATION DATA CROSS-CHECK (2026-06-17): the honest data-confrontation kill-test for the spectral-action prediction (CONTRACT.QFT4D.01, v244/v245). Does the boundary condition g1=g2=g3, sin^2 th_W=3/8 at the unification scale survive contact with the MEASURED Standard-Model couplings? Answer: NOT in the plain SM. Inputs (PDG, GUT-normalised, at M_Z; consistent with the PyR@TE cross-check v159): alpha_i^-1 = (59.01, 29.59, 8.47), SM 1-loop betas b=(41/10,-19/6,-7), sin^2 th_W(M_Z)=0.23122. (1) [E] the prediction: at Lambda, alpha1=alpha2=alpha3 and sin^2 th_W=3/8. (2) [X] tension: running the measured couplings up 1-loop, the three do NOT meet at one scale -- pairwise crossings a1=a2 ~1.0e13, a1=a3 ~2.4e14, a2=a3 ~9.9e16 GeV (~4 decades spread), residual spread at 2e16 GeV Delta(alpha^-1) ~ 8.8. (3) [X] sin^2 th_W: predicted 3/8 vs measured 0.23122 (the known few-percent non-SUSY shortfall). (4) [X] two-loop also misses: an RK4 2-loop run gives minimal spread Delta(alpha^-1) ~ 3.2 at mu ~ 1.7e14 GeV (never a common point), ~8.7 at 2e16. (5) [O] NO rescue in the current theory: TFPT has SM gauge content and no new states (tfpt_3 'Dark matter = no new state'), and the E8 cascade is an arithmetic spine (D_n=60-2n, v5), NOT a threshold tower -- there is no admissible gauge-threshold source; closing the spread would require EITHER new gauge-charged matter (a new postulate, contradicting 'no new state') OR a non-GUT/boundary reading of the spectral-action cutoff. The spectral-action 4d-GUT route is in genuine tension -- the SAME status as the Connes-Chamseddine NCG Standard Model -- likely falsified unless the theory is extended (the AQFT skeleton + DHR + SM rep-core survive as an emergent boundary QFT). Typed [X]/[O], NEVER [E]-as-success; the tension IS the result

Recorded status: Data confrontation (kill-test) [X]/[O]

Dependencies, status detail and source

Canonical status: [X] plain-SM run misses unification at 1- and 2-loop (1-loop spread ~9; 2-loop min spread ~3.2 at 1.7e14) and sin^2 th_W 3/8 vs 0.231; [O] no admissible threshold source (SM content, no new state; the E8 spine is arithmetic, not a tower) -- spectral-action 4d-GUT route in tension like NCG-SM, likely falsified unless extended; not a confirmation

Dependencies: QFT4D.MATTER.01; CONTRACT.QFT4D.01

Scripts: v246_unification_data_crosscheck.py

Location: tfpt_research_contracts

Original CSV, line 332

Original ledger status

QGAMB.NODEP.01

QGAMB.NODEP.01

The No-Ambient-Dependency certificate (2026-06-25): no frozen TFPT readout is COMPUTED from the ambient QG measure QG.AMB.01 -- sharpening the v369/v384 prose redundancy ('QG.AMB.01 is a [C] redundancy, not dynamics') into a machine-checked DAG+script fact, told HONESTLY. [E] GAP-DECOUPLING MARGIN: 2 dim(E8) c3^2 = 31/(4 pi^2) (31=2^g_car-1) ~ 0.785, Delta = 6 ln(3/2) ~ 2.433, so Delta_eff ~ 1.648 > 0 (v76/v337); chi = 1/(1-(2/3)^6) = 729/665 finite (negative control: gap->0 => chi->inf, the ambient re-enters). [E] CERTIFICATION SINK: every claim that lists QG.AMB.01 as a dependency is a gravity-gate/QG-certification row (GATE.METRIC.01, GRAVITY.COMPLETE.01, the QGAMB.* cluster, SEAM.S3.RP.01, ...), NONE a frozen physical prediction -- QG.AMB.01 has no predictive direct dependent. [E] NOT A VALUE SOURCE: QG.AMB.01 has no producing script (ledger script='-'); every frozen prediction of record is computed by a compiler script (alpha^-1<-v3, sin^2 th12<-v9, sin^2 th13<-v268, cosmology<-v7), none of which is an ambient-measure script (v76/v330/v332/v334/v335) -- so no readout VALUE is produced by the ambient measure. [E] ARCHITECTURAL-ONLY LINK (honest): of the frozen readouts only theta13 transitively references QG.AMB.01, and the path runs through the 4D-QFT CONTRACT spine (PS.DIRAC.02 -> CONTRACT.QFT4D.01 -> QG.G2.01 -> GATE.METRIC.01) -- the readout lives INSIDE the unified spectral-action construction, a coherence edge, not a numerical input (its value sin^2 th13 = phi0 e^{-5/6}, v268, takes no ambient-measure input); alpha, theta12 and all of cosmology have NO route to QG.AMB.01 at all. [C] VERDICT: QG.AMB.01 is a gap-decoupled certification object -- no readout VALUE is computed from it, its only predictive link is the architectural 4D-QFT contract, and the gap margin (1.648>0) suppresses its back-reaction -- v369 as a DAG/script fact. HONEST: this does NOT prove SEAM.EQUIV.01 (the readouts depend on the seam being the (E8)_1 net, the one open keystone); QG.AMB.01 specifically is dead.

Recorded status: No-Ambient-Dependency [E]/[C]: no frozen readout is computed from QG.AMB.01 -- it is a certification SINK (every dependent is a gravity-gate/QG row, no prediction), not a value source (script '-'; predictions computed by v3/v7/v9/v268, never an ambient-measure script), and its only predictive link is theta13's architectural 4D-QFT contract edge (coherence, not numerical); the gap margin Delta_eff~1.648>0 decouples its back-reaction (v337). v369 prose -> machine-checked DAG/script fact [E]; verdict [C], does NOT prove SEAM.EQUIV.01

Later scope correction: the DtN form estimate alone does not prove the transfer gap.

Dependencies, status detail and source

Canonical status: Numerical

Dependencies: QG.AMB.01; DECOUPLING.THEOREM.01; SEAM.EQUIV.01; v337; v369; v384

Scripts: v423_no_ambient_dependency.py

Location: tfpt_4

Original CSV, line 490

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?