A registered result in its source context
Original ledger classification: central charge c=8 from finite-size entanglement scaling of the lattice (chiral, c_-=8) [E]
Recorded statement: S3 closure stack (2026-06-23): the central charge c=8 extracted NUMERICALLY from the lattice via the Calabrese-Cardy finite-size entanglement-entropy scaling of the critical free-fermion content -- the standard, rigorous lattice->CFT…
Statement, assumptions and sources
Paper context: Research contracts
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SEAM.S3.CENTRALCHARGE.01
Original ledger classification: central charge c=8 from finite-size entanglement scaling of the lattice (chiral, c_-=8) [E]
Original claim text
S3 closure stack (2026-06-23): the central charge c=8 extracted NUMERICALLY from the lattice via the Calabrese-Cardy finite-size entanglement-entropy scaling of the critical free-fermion content -- the standard, rigorous lattice->CFT central-charge diagnostic (the quantitative core of the MMST scaling-limit claim), on OUR model, not a re-assertion. [E] the Peschel correlation-matrix EE of one critical tight-binding chain scales as (c/3)ln[(L/pi)sin(pi l/L)] with fitted c=1.0000 (L=258,386; the L=4m+2 sizes avoid the half-filling zero-mode). [E] the collar is N_Maj=dim S^+=2^(g_car-1)=16 Majoranas = 8 complex modes (v367), c additive over decoupled modes => c=8=g_car+N_fam. [E] chiral c_-=8 (bulk Chern |C|=1 per Majorana v367; non-gappable chiral edge v368), so the scaling limit is a CHIRAL c=8 CFT. [O] the specific net (E8)_1 is v377/v378; the abstract continuum EXISTENCE is the cited MMST theorem (v336).
Original classification detail
[E] the numerical c=1 per mode (EE scaling) + additive c=8 + the chirality cross-link; [O] the specific-net identification (v377/v378) + the continuum existence (v336). Numerical evidence that the scaling limit has c=8; does NOT close SEAM.EQUIV.01.
Dependencies as recorded
SEAM.EQUIV.01; v367; v368; v336
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- Research contracts
Sections that explicitly cite this claim
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- 2026-06-23 (S3 closure stack — the target of the seam scaling limit pinned at EVERY computable level: central charge [formula in source] from the lattice ( v376), the [formula in source] character ( v377), the genus-1 torus count [formula in source] ( v378), and reflection positivity ( v379); only the abstract continuum existence (cited MMST) stays external)Research changelog; TFPT — Introduction and reading guide
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.
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)tfpt research contracts
- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- Honest statusinput 4 origin theory
- Front matter / supportResearch contracts
- The unique attractor: a gapped transport selects ONE fixed pointorigin theory
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- 2026-06-23 (Status propagation: the v365– v380 [formula in source] FORM.SEAM.MMST.01 status carried into the remaining papers, the README and the Zenodo description)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
All 33 linked sections
- Honest status
- =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)
- What this means for the theory-of-everything question
- Outcome
- The hard reduction: the live residual as typed interfaces
- Honest status
- Front matter / support
- 2026-06-24 (Attacking the last open lemma: v392 the scaling-limit central charge converges)
- The unique attractor: a gapped transport selects ONE fixed point
- Front matter / support
- Front matter / support
- Honest status
- Front matter / support
- The [formula in source] compiler: [formula in source] as a closure, not an input
- The [formula in source] compiler: [formula in source] as a closure, not an input
- Research Contract 1 — [formula in source]
- The compact status formula: three honest layers
- 2026-06-23 (Lean: the S3 continuum leg formalised as ``closed modulo a cited theorem'' — FORM.SEAM.MMST.01)
- Front matter / support
- The [formula in source] compiler: [formula in source] as a closure, not an input
- Full quantum gravity — induced from the boundary kernel
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
- The unique attractor: a gapped transport selects ONE fixed point
- In plain words
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
Registered verification modules
- v376_seam_s3_centralcharge.pyRegistered verification module · core
Read the description recorded in the module registry
S3 closure stack: the central charge c=8 extracted NUMERICALLY from the lattice via Calabrese-Cardy finite-size entanglement scaling of the critical free-fermion content (the quantitative core of the MMST scaling-limit claim, on OUR model). [E] one critical complex mode gives c=1.0000 (Peschel correlation-matrix EE); [E] the collar is 16 Majoranas = 8 complex modes (v367), c additive => c=8=g_car+N_fam; [E] chiral c_-=8 (Chern |C|=1 per Majorana v367, non-gappable edge v368). [O] the specific net (E8)_1 is v377/v378; the continuum existence is the cited MMST theorem (v336). Numerical c=8 from the lattice; does NOT close SEAM.EQUIV.01.
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