A registered result in its source context
Original ledger classification: Honest attempt / reduction [E]/[O] (a solvable-model zeta-det mechanism + the reduction of ALPHA.QUILLEN.EXACT.01 to the named sub-target 'seam a_2 = 8 b1 c3^6'; the headline target stays OPEN, not closed)
Recorded statement: An HONEST attempt at the external target ALPHA.QUILLEN.EXACT.01 (door #5, 2026-06-24): it REDUCES the open step to a sharper named sub-target via a solvable model, but does NOT close it -- the status of ALPHA.QUILLEN.EXACT.01 stays [O]…
Statement, assumptions and sources
Paper context: Architecture, E8 and the electromagnetic fixed point
The exact identifier, original classification and full claim are available below.
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ALPHA.QUILLEN.PROGRESS.01
Original ledger classification: Honest attempt / reduction [E]/[O] (a solvable-model zeta-det mechanism + the reduction of ALPHA.QUILLEN.EXACT.01 to the named sub-target 'seam a_2 = 8 b1 c3^6'; the headline target stays OPEN, not closed)
Original claim text
An HONEST attempt at the external target ALPHA.QUILLEN.EXACT.01 (door #5, 2026-06-24): it REDUCES the open step to a sharper named sub-target via a solvable model, but does NOT close it -- the status of ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384). [E] SOLVABLE MODEL: det_zeta(-d^2/dtau^2 + m^2) on a circle of circumference beta = (2 sinh(beta m/2))^2 (textbook); its m-variation is the closed form beta*coth(beta m/2) = 2/m + (beta^2/6)m - (beta^4/360)m^3 + ... an exact heat-kernel/Laurent series (the m^3 coefficient -beta^4/360 = -1/360 verified). [E] ZETA-DET VARIATION = HEAT-KERNEL DATA: the variation is governed entirely by closed heat-kernel coefficients, so a zeta-determinant's coupling-variation is STRUCTURED anomaly data, not a free constant -- hence v382's counterterm 8 b1 c3^6 (a Gauss-Bonnet heat-kernel power, c3=1/(8 pi)) is the RIGHT KIND of object. [E] THE v382 SPLIT re-verified at alpha^-1=137.0359992 (8 b1=(4/5)*41 a U(1) index, c3^3/c3^6 heat-kernel powers). [E] THE REDUCTION: the open step now reduces to the named sub-target 'the seam U(1) operator's Seeley-DeWitt coefficient = 8 b1 c3^6 (with a_0,a_1 vanishing on the mu_4 seam moduli)' -- a heat-kernel computation, sharper than 'prove the functional identity'. [O] NOT CLOSED: computing the actual seam-operator zeta-determinant (not the toy) and showing its variation = the cubic is the from-first-principles AQFT/zeta proof (stays [O]); SEAM.EQUIV.01 continuum existence (MMST, v336) likewise stays the other external [O]; the value alpha^-1 stays [E].
Original classification detail
[E] the solvable model (det_zeta(-d^2+m^2) on a circle and its closed-form heat-kernel variation), the heat-kernel-data mechanism (so 8 b1 c3^6 is the right kind of object), the re-verified v382 split, and the reduction to a named sub-target; [O] the headline ALPHA.QUILLEN.EXACT.01 stays open (NOT closed here) and SEAM.EQUIV.01 continuum existence stays the other external [O]. An honest attempt that reduces, does not close; no new number, alpha^-1 stays [E].
Dependencies as recorded
ALPHA.QUILLEN.EXACT.01; SEAM.EQUIV.01; EM.WARD.01; v336; v341; v382
Open the original ledger source, row 455Location recorded in the ledger
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- Architecture, E8 and the electromagnetic fixed point
Sections that explicitly cite this claim
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- 2026-06-24 (Honest attempt at an external target: v391 reduces it, not a closure)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 whole integer skeleton from one pair [formula in source]input 4 origin theory
- 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
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)tfpt 1 architecture e8
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)tfpt 1 architecture e8
- The whole integer skeleton from one pair [formula in source]Origin Theory
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)Architecture, E8 and the electromagnetic fixed point
- 2026-06-24 (Website: an animated ``Universal Gap Lab'' visualising v383– v391)Research changelog; TFPT — Introduction and reading guide
All 13 linked sections
- =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)
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)
- Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)
- The whole integer skeleton from one pair [formula in source]
Registered verification modules
- v391_alpha_quillen_progress.pyRegistered verification module · em
Read the description recorded in the module registry
ALPHA.QUILLEN.PROGRESS.01: an HONEST attempt at the external target ALPHA.QUILLEN.EXACT.01 (v382) -- it REDUCES the open step to a sharper named sub-target via a solvable model but does NOT close it; ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384). [E] solvable model: det_zeta(-d^2/dtau^2+m^2) on a circle = (2 sinh(beta m/2))^2, m-variation beta*coth(beta m/2) = 2/m + (beta^2/6)m - (beta^4/360)m^3+... a closed heat-kernel/Laurent series (m^3 coeff -1/360 verified). [E] a zeta-det variation is structured heat-kernel data, so v382's 8 b1 c3^6 counterterm (Gauss-Bonnet heat-kernel power) is the right KIND of object. [E] the v382 split re-verified at alpha^-1=137.0359992. [E] reduction: the open step reduces to the named sub-target 'seam Seeley-DeWitt coefficient = 8 b1 c3^6'. [O] NOT CLOSED: the actual seam zeta-det proof stays open, SEAM.EQUIV.01 continuum existence (v336) the other external [O]; alpha^-1 stays [E]. An attempt that reduces, does not close.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.