A registered result in its source context
Original ledger classification: the chiral c=8 content is (E8)_1 (248 currents, 1 primary) via the exact character + mu4/GSO promotion [E]
Recorded statement: S3 closure stack (2026-06-23): the chiral c=8 content of the seam is the SPECIFIC net (E8)_1, not just 'some c=8' -- shown by the exact affine character q-series and the mu4/GSO promotion SO(16)_1 -> (E8)_1 (the genus-0 character…
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Paper context: Research contracts
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SEAM.S3.E8CHARACTER.01
Original ledger classification: the chiral c=8 content is (E8)_1 (248 currents, 1 primary) via the exact character + mu4/GSO promotion [E]
Original claim text
S3 closure stack (2026-06-23): the chiral c=8 content of the seam is the SPECIFIC net (E8)_1, not just 'some c=8' -- shown by the exact affine character q-series and the mu4/GSO promotion SO(16)_1 -> (E8)_1 (the genus-0 character discriminator that pins the target of the scaling limit). [E] chi = E4/eta^8 = q^{-1/3}(1+248q+4124q^2+...): eta^8=q^{1/3}prod(1-q^n)^8 gives the prefactor q^{-c/24}=q^{-1/3} => c=8; the level-1 coefficient 248=dim E8 (one primary = the vacuum module), computed exactly from E4*prod(1-q^n)^{-8}. [E] the promotion: 248=240+8=(E8 roots)+(Cartan rank), 240=dim S^+*g_car*N_fam=16*5*3 (carrier trace); equivalently 248=120+128=dim SO(16)+spinor(128) -- the order-4 mu4 clock condenses the SO(16)_1 vacuum+spinor into the single (E8)_1 module. [E] discriminator: (E8)_1 has 1 primary and 248 level-1 currents vs SO(16)_1 4 primaries and 120. [O] the continuum existence (v336); the mu4 projection = the seam one-sidedness (S3).
Original classification detail
[E] the exact character q-series (c=8, 248, 4124) + the integer promotion identities (248=240+8=120+128, 240=16*5*3) + the 1-vs-4 primary discriminator; [O] the continuum existence (v336) + the mu4 projection = S3. Pins the target net (E8)_1; does NOT close SEAM.EQUIV.01.
Dependencies as recorded
SEAM.EQUIV.01; v336; v351; v83; v1
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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
- 2026-07-20 (V) ( v492 [formula in source] the new research contract CELEST.SEAM.01 — the celestial-holographic route: the [formula in source] [formula in source] -glue is the flat [formula in source] monodromy of the equivariant celestial chiral algebra on the [formula in source] ALE space, with the exact correction clock [formula in source] deck (spin bridge [formula in source] , [formula in source] ); verdict B, no gate closes, no marker moves, SEAM.EQUIV.01 stays )Research changelog; TFPT — Introduction and reading guide
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)tfpt research contracts
- Research Contract 1 — [formula in source]tfpt research contracts
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)tfpt research contracts
- =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
- Research Contract — SEAM.BULK4D.RECON.01 (from seam data to a 4D local quantum theory)tfpt research contracts
- The celestial and twistor continuum routeinput 5 tfpt 3 e8 audit bootstrap
All 20 linked sections
- Front matter / support
- 2026-06-24 (Attacking the last open lemma: v392 the scaling-limit central charge converges)
- Front matter / support
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)
- The celestial and twistor continuum route
- The celestial and twistor continuum route
- Research Contract 1 — [formula in source]
- Research Contract — SEAM.BULK4D.RECON.01 (from seam data to a 4D local quantum theory)
- Front matter / support
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
- Research Contract — SEAM.BULK4D.RECON.01 (from seam data to a 4D local quantum theory)
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
Registered verification modules
- v377_seam_s3_e8character.pyRegistered verification module · core
Read the description recorded in the module registry
S3 closure stack: the chiral c=8 content is the SPECIFIC net (E8)_1, via the exact affine character q-series + the mu4/GSO promotion. [E] chi = E4/eta^8 = q^{-1/3}(1+248q+4124q^2+...): leading -c/24=-1/3 => c=8; level-1 = 248 = dim E8 (one primary). [E] mu4/GSO promotion SO(16)_1 -> (E8)_1: 248=240+8=(E8 roots)+(Cartan), 240=dim S^+*g_car*N_fam=16*5*3; 248=120+128=dim SO(16)+spinor. [E] discriminator: (E8)_1 has 1 primary/248 currents vs SO(16)_1 4 primaries/120. [O] continuum existence (v336); mu4 projection = seam one-sidedness (S3). Pins the target net; does NOT close SEAM.EQUIV.01.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.