A registered result in its source context
Original ledger classification: Second honest step / grounding [E]/[O] (a solvable 4D model exhibiting the nonzero a_4 conformal-anomaly order + the v391<->v342 connection; the headline target stays OPEN, not closed)
Recorded statement: A SECOND HONEST step on the external target ALPHA.QUILLEN.EXACT.01 (2026-06-27, v433): it GROUNDS and CONNECTS, it does NOT close it -- ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384), alpha^-1 stays [E]. [E] SOLVABLE 4D…
Statement, assumptions and sources
Paper context: Architecture, E8 and the electromagnetic fixed point
The exact identifier, original classification and full claim are available below.
The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.
Read the exact registered claim and its dependencies
ALPHA.QUILLEN.PROGRESS.02
Original ledger classification: Second honest step / grounding [E]/[O] (a solvable 4D model exhibiting the nonzero a_4 conformal-anomaly order + the v391<->v342 connection; the headline target stays OPEN, not closed)
Original claim text
A SECOND HONEST step on the external target ALPHA.QUILLEN.EXACT.01 (2026-06-27, v433): it GROUNDS and CONNECTS, it does NOT close it -- ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384), alpha^-1 stays [E]. [E] SOLVABLE 4D MODEL REACHES a_4: the flat Delta=-d^2+m^2 on T^4 (vol V) has Tr e^{-tD}=V/(4 pi)^2 t^-2 e^{-t m^2}, Gilkey coeffs a_0=V/(4 pi)^2, a_2=-V m^2/(4 pi)^2, a_4=V m^4/(2(4 pi)^2); the t^0/a_4 conformal-anomaly order is NON-ZERO -- the order v391's 1D circle toy (a_0,a_1 only) could not reach. [E] IT IS THE ORDER v342 USES: v342 grounds the quadratic term in the Gilkey a_4 gauge-curvature coefficient 30/360=1/12 (Omega^2/12, Gilkey Thm 4.8.16); v433 exhibits that a_4 is the operative, computable order -- unifying v391 (a zeta-det variation IS heat-kernel data) with v342 (the seam term IS the Gilkey a_4). [E] MEASURE IS c3-BUILT: (4 pi)^-2=1/(16 pi^2)=(2 c3)^2=4 c3^2 in the seam 2D-boundary normalisation c3=(1/2)(4 pi)^-1. [E] the v382 split re-verified at alpha^-1=137.0359992. [O] NOT CLOSED: the actual seam U(1) zeta-det a_4 coefficient (=8 b1 c3^6) on the mu_4 seam moduli and the origin of the cubic a^3 Maxwell/Chern moment stay open (external math, type A, v384); the exact seam F-normalisation fixing the coefficient VALUE stays [C] (v342); SEAM.EQUIV.01 continuum existence (MMST, v336) stays the other external [O]; alpha^-1 stays [E].
Original classification detail
[E] the solvable 4D model reaching the nonzero a_4 (t^0) conformal-anomaly order (the order v391's 1D circle could not reach and the very order v342 grounds via Gilkey 30/360=1/12), the v391<->v342 unification (a zeta-det variation IS heat-kernel data AT the a_4 order), the measure identity (4 pi)^-2=4 c3^2, and the re-verified v382 split; [O] the headline ALPHA.QUILLEN.EXACT.01 stays open (the actual seam a_4=8 b1 c3^6 and the cubic a^3 Chern term, v384), and the exact seam F-normalisation fixing the coefficient value stays [C] (v342). A second honest step that grounds/connects, does not close; no new number, alpha^-1 stays [E].
Dependencies as recorded
ALPHA.QUILLEN.EXACT.01; ALPHA.QUILLEN.PROGRESS.01; SEAM.EQUIV.01; EM.WARD.01; v336; v341; v342; v382; v391
Open the original ledger source, row 456Location recorded in the ledger
These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.
- Architecture, E8 and the electromagnetic fixed point
Sections that explicitly cite this claim
A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.
- 2026-06-27 ( v433 — a second honest step on the [formula in source] Quillen target: a solvable 4D model reaches the [formula in source] order, connecting v391 and v342)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)tfpt 1 architecture e8
- 2026-06-28 ( v434 — a third honest step on the [formula in source] Quillen target: [formula in source] is the [formula in source] heat-kernel coefficient, and the three residuals collapse to one [formula in source] [formula in source] one [formula in source] )Research changelog; TFPT — Introduction and reading guide
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)tfpt 1 architecture e8
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)Architecture, E8 and the electromagnetic fixed point
- =150 2026-08-20 (CXI) (the externalization contracts — the two open non-RH kind-(A) external-math targets SEAM.EQUIV.01 and ALPHA.QUILLEN.EXACT.01 packaged as short, self-contained EXTERNALIZATION CONTRACTS for outside specialist mathematicians (conformal nets/VOA/AQFT for the seam; determinant lines/ [formula in source] -invariants/index theory for alpha), added as two new sections at the end of tfpt_research_contracts (before ``Certifiability and recommended order''), plus a one-sentence pointer in the head keybox; DOCUMENTATION ONLY — no module touched, no number changed, no status marker moved, no gate closed or narrowed, NO RH claim: (1) the SEAM.EQUIV.01 contract states the minimal theorem (the scaling limit of the gapped [formula in source] -equivariant CAR collar exists in local-net topology; the index-4 simple-current extension functor commutes with the limit; the OS reconstruction is the holomorphic [formula in source] lattice net) broken into the four review-named lemmata L1 (uniform energy/nuclearity bounds — honestly typed: NO uniform nuclearity estimate exists in the corpus), L2 (convergence of local algebras, the cited Osborne–Stottmeister scaling-limit theorem with the [formula in source] -equivariant structure retained), L3 (crossed product commutes with the limit; the finite index-4 Q-system is explicit, v125/ v154/ v469) and L4 (uniqueness of the holomorphic [formula in source] reconstruction; [formula in source] vs the same- [formula in source] rival [formula in source] ), with the complete typed hypothesis list (12 PROVEN-FINITE rows citing v302/ v113/ v155/ v160/ v356/ v366/ v367/ v368/ v461/ v376/ v377/ v378/ v379/ v125/ v154/ v216/ v286, 5 CITED-CLASSICAL rows, 1 OPEN target), the runnable finite models, the HONEST Lean axiom surface ( SeamScalingLimit.lean kernel-proves only the arithmetic hypotheses by decide; the analytic content is named cited axioms over opaque Props; no sorry; explicitly flagged: L1–L4 have ZERO Lean content beyond the composition audit), five must-fail controls (MF-S1: [formula in source] alone must NOT suffice — the red-team point; MF-S2: index-2 glue must yield [formula in source] ; MF-S3: the trivial [formula in source] collar must give no chiral limit; MF-S4: non-order-4 clock breaks the marks; MF-S5: the v286 import firewall) and four acceptance tests; (2) the ALPHA.QUILLEN.EXACT.01 contract states the two-step theorem T1 (gap-stable continuum limit [formula in source] under norm-resolvent convergence with the Fermi gap uniformly open over the twist torus — the Dai–Freed section has no zero; finite side computed, v472) and T2 ( [formula in source] [formula in source] Bismut–Freed curvature [formula in source] inflow response with the exact corpus coefficients [formula in source] , [formula in source] , [formula in source] , [formula in source] , exponent [formula in source] ), the two named open faces (the analytic diagonal- [formula in source] /multiplicity face v484/ v485 and the topological EM1 lemma v48/ v435), the typed hypothesis list (10 PROVEN-FINITE rows citing v3/ v48/ v341/ v382/ v434/ v470/ v435/ v342/ v367/ v472/ v484/ v485/ v391/ v433, 5 CITED-CLASSICAL rows, 1 OPEN target), the runnable finite models, the HONEST Lean statement (there is NO Lean formalisation of this target — stated plainly), four must-fail controls (MF-A1: no experimental [formula in source] anywhere in the construction; MF-A2: deck/carrier/Chern-level ablations must destroy the CODATA match; MF-A3: [formula in source] , [formula in source] ; MF-A4: the [formula in source] [formula in source] -power/metric-independence partition) and the review's three acceptance tests verbatim (no experimental [formula in source] input; unique physical fixed point [formula in source] ; ablations destroy the hit) plus one structural test; (3) the website paper mirror of tfpt_research_contracts ( papers.ts) gains one section entry covering both contracts; tfpt_research_contracts.pdf and changelog.pdf recompiled and mirrored via bash build.sh website; maps and changelog.ts regenerated via bash build.sh gen; bash build.sh audit [formula in source] AUDIT OK; manifests regenerated LAST. Both targets stay [O]; NO RH claim anywhere)Research changelog; TFPT — Introduction and reading guide
- 2026-06-29 ( v435 — a fourth honest step on the [formula in source] Quillen target: a [formula in source] -power test isolates the cubic [formula in source] as the unique metric-independent (topological) rung, and types its coefficient as a conditional integer level)Research changelog; TFPT — Introduction and reading guide
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)tfpt research contracts
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)Research contracts
All 10 linked sections
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)
- 2026-07-02 ( v469/ v470 — the closure-route round on the two named targets: the SEAM.EQUIV.01 extension leg re-founded on 1995–2001 peer-reviewed crossed-product theorems [formula in source] the realisation axiom reduced to invariant level; the [formula in source] level [formula in source] the computed bulk Chern invariant [formula in source] the seam [formula in source] -normalisation [formula in source] the embedding index [formula in source] ; both targets stay )
Registered verification modules
- v433_alpha_quillen_heatkernel.pyRegistered verification module · em
Read the description recorded in the module registry
ALPHA.QUILLEN.PROGRESS.02: a SECOND honest step on the external target ALPHA.QUILLEN.EXACT.01 (v382) -- it GROUNDS and CONNECTS, it does NOT close it; ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384), alpha^-1 stays [E]. [E] a solvable 4D model (flat Delta=-d^2+m^2 on T^4) reaches the a_4 (t^0) conformal-anomaly order: a_4=V m^4/(2(4pi)^2) NON-ZERO -- the order v391's 1D circle toy (a_0,a_1 only) could not reach. [E] it is the order v342 grounds (Gilkey a_4 gauge-curvature 30/360=1/12), unifying v391 (a zeta-det variation IS heat-kernel data) with v342 (the term IS the Gilkey a_4). [E] (4pi)^-2 = 4 c3^2 is c3-built. [E] the v382 split re-verified at alpha^-1=137.0359992. [O] NOT CLOSED: the actual seam a_4 (=8 b1 c3^6) and the cubic a^3 Chern moment stay open (v384); the exact seam F-normalisation stays [C] (v342). Grounds/connects, does not close.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.