Publication history: 2026-08-20

Key points

1. 1
   The SEAM.EQUIV.01 contract states the minimal theorem (the scaling limit of the gapped \mu_4-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 (E_8)_1 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 \mu_4-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 c=8 reconstruction; \det K=1 vs the same-c rival SO(16)_1), 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: c=8 alone must NOT suffice — the red-team point; MF-S2: index-2 glue must yield SO(16)_1; MF-S3: the trivial M=3 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. 2
   The ALPHA.QUILLEN.EXACT.01 contract states the two-step theorem T1 (gap-stable continuum limit c_1(\det D_{\mathrm{finite}})\to c_1(\det_\zeta D_{\mathrm{seam}}) 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 (\delta_\tau(\log\det_\zeta\Delta_{U(1)}+8b_1c_3^6\log\varphi_{\mathrm{seam}})=0 = Bismut–Freed curvature = inflow response with the exact corpus coefficients k_0=|C|=1, k_Y=5/3, b_1=41/10, c_3=1/(8\pi), exponent -5/4=-q(D_5)), the two named open faces (the analytic diagonal-\zeta/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 \alpha anywhere in the construction; MF-A2: deck/carrier/Chern-level ablations must destroy the CODATA match; MF-A3: M=3\Rightarrow C=0, M=-1\Rightarrow C=-1; MF-A4: the \{0,3,6\} \pi-power/metric-independence partition) and the review's three acceptance tests verbatim (no experimental \alpha input; unique physical fixed point 137.0359992168; ablations destroy the hit) plus one structural test;
3. 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 \to AUDIT OK; manifests regenerated LAST. Both targets stay [O]; NO RH claim anywhere