The complete active claim ledger and the eligible source reviewed research findings, including conditional achievements and precise negative results. The original statement, premises and status remain attached.
Research snapshot 2026-11-02 · 783 active ledger claims · 696 scientific findings · 707 registered scripts. These are different inventories, not counts of independent physical confirmations.
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 All 788 ledger rows, including superseded rows, remain in the download.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 697 findings; 1 administrative record is excluded from public scientific content, with the omission recorded in the coverage file.
The scientific findings include 505 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 3ddcc9643e499ce39900d9c5 · snapshot SHA256 7622b36de7ed79901ae75361b009fa423a6505076f388f4fbaf2d42e1ba7dcf5
3 matching records · page 1 of 1
Original ledger status
FORM.P2.02
P2 carrier algebra (hypercharge/family) machine-verified
Recorded status: Formal
Canonical status: Formal
Dependencies: AX.P2.01
Scripts: lean4-carrier-rigidity
Location: tfpt_1;tfpt_2
Original CSV, line 4Original ledger status
FORM.CAR.01
Theorem A (carrier rank uniqueness g_car=5) machine-formalised in Lean 4: the Pascal carrier condition 2^(g-1)=C(g,0)+C(g,1)+C(g,2), division-free 2^g=g^2+g+2, has the UNIQUE solution g=5 (theorem carrier_rank_pascal_unique: forall g, 2^g=g^2+g+2 <-> g=5; growth lemma pascal_growth for g>=6; g_car_unique ExistsUnique; carrier_closure_integers N_fam=(2^4-1)/5=3, g+N_fam=8=rank E8). AUDIT: PASS (no sorry/admit, no domain axioms, only propext/Classical.choice/Quot.sound). Complements FORM.P2.02 (P2 carrier algebra)
Recorded status: Formal
Canonical status: Formal [F]
Dependencies: AX.P2.01; CAR.UNIQ.01; v6; v14
Scripts: lean4-carrier-rigidity
Location: tfpt_1;tfpt_3
Original CSV, line 145Original ledger status
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)
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 330Each 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.
What is determined by complete future behavior, and what additional positive word-kernel source is needed to reconstruct a cyclic operator realization?
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?
Does the joint discrete theorem determine a concrete connection and a family coupling compatible with the determinant seam action?
Do the original reflection/projector structures determine the full physical time generator and required field transfer?
Which flavor quantity is fixed on the derived discrete stratum, and which requires the continuous holonomy anchor?
Which closure equation follows for a fixed seam projector, and which inputs still need justification?
Do common matter-only observations derive geometric horizon flow and the area response from the original gravity source?
Which complete quadratic response can the actual clock images reconstruct?
How does the actual Gaussian J act on the complete marked source?
Which data separate sources with identical complete neutral vacuum response?
Can existing native charge fields produce the quarter-twist time response of the seam?
What does the complete phase search decide, and which additional state information prevents a false source solution?
Which charge, state type and time action belong to the root partner and original sheet pairing?
Which tools generate operator maps, learn counterexamples, and can search for the full positive source?
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?
Which operational conditions are independently required, which inequivalent models satisfy them, and which observable distinctions remain for selection?
Which carrier and glue statements are already present in the papers and Lean sources, and which physical selection does not follow?
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.
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?