A registered result in its source context
Original ledger classification: Identity [I] (exact Pfaffian/Wick + polarization theorems + bookkeeping) + Physical [P] (premise merge)
Recorded statement: ONE KERNEL IS THE WHOLE NET (the QBL input merges with the R2/holomorphy premise; anchors the carrier choice to the Gate-A objects): (1) MAJORANA BOOKKEEPING [I] - level-1 central charges c(D5)_1 = 45/9 = 5 = g_car, c(A3)_1 = 15/5 = 3 =…
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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Read the exact registered claim and its dependencies
CAR.QFREE.01
Original ledger classification: Identity [I] (exact Pfaffian/Wick + polarization theorems + bookkeeping) + Physical [P] (premise merge)
Original claim text
ONE KERNEL IS THE WHOLE NET (the QBL input merges with the R2/holomorphy premise; anchors the carrier choice to the Gate-A objects): (1) MAJORANA BOOKKEEPING [I] - level-1 central charges c(D5)_1 = 45/9 = 5 = g_car, c(A3)_1 = 15/5 = 3 = N_fam, c(SO16)_1 = 120/15 = 8, c(E8)_1 = 248/31 = 8; the carrier net (D5)_1 x (A3)_1 = SO(10)_1 x SO(6)_1 = 10 + 6 = 16 FREE MAJORANA FERMIONS with c = 16/2 = 8; the whole extension tower carrier(mu=16) -> SO(16)_1(mu=4) -> E8_1(mu=1) carries the SAME 16 fermions, only the certified glue grows (index steps 2 x 2 = 4 = |mu_4|, GATE.METRIC.06/07). (2) WICK/PFAFFIAN [I] (exact, 10-Majorana Jordan-Wigner model): ALL 210 vacuum 4-point functions AND all 210 6-point functions equal the Pfaffian of the single 2-point kernel - one kernel determines all correlations; quasi-freeness realised exactly. (3) THE KERNEL IS A CALDERON INVOLUTION OF RANK g [I]: M = I + iA with A integer antisymmetric, A^2 = -I; P = M/2 is a projection with rank P = 5 = g_car = c(D5)_1; eps = iA is an involution; at seam level (16 Majoranas) the rank is 8 = rank E8 - THE CENTRAL CHARGE IS THE RANK OF THE ONE KERNEL (5 carrier block, 8 seam hull). (4) ONE KERNEL <=> ONE STATE [I]: the joint kernel of the five annihilators is exactly 1-dimensional - the polarization fixes the vacuum uniquely; kernel => state => (Wick) all correlations. (5) PREMISE MERGE [P] (recorded, not claimed): QBL's remaining input 'single scalar 2-point kernel' = 'the seam state is quasi-free' = the defining property of the free-fermion net the R2 gate already posits (Gate-A (H') index-4 extension, GATE.METRIC.06); QBL adds NO assumption beyond R2; upgrade contract: R2 closes => the carrier choice closes [L] along free net => one kernel => sheet-odd (CAR.PAIR.02) => self-counting tower (CAR.PAIR.01/CAR.COUNT.01) => complete transport (CAR.QTRANS.01) => carrier; gate typing [P]/[A] unchanged
Original classification detail
Identity: one quasi-free kernel determines the whole net (rank = c); QBL input = R2 premise; upgrade contract R2 => carrier [L]
Dependencies as recorded
CAR.PAIR.02; CAR.COUNT.01; CAR.QTRANS.01; ARCH.QUAD.01 (QBL); GATE.METRIC.03-07 (Gate A); CAR.LADDER.01
Open the original ledger source, row 197Location 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
- Research contracts
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.
- 2026-06-30 ( v463/ v464 + Lean + Wolfram — the [formula in source] holomorphic-uniqueness pin and the one-particle realisation rigidity: the SEAM.EQUIV.01 residual reduced to entirely certification on both halves)Research changelog; TFPT — Introduction and reading guide
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)tfpt research contracts
- How to read this documenttfpt 1 architecture e8
- Honest statusinput 4 origin theory
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportArchitecture, E8 and the electromagnetic fixed point
- Honest statusorigin theory
- =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
All 32 linked sections
- -1.2cm TFPT — Research Contracts for the Remaining Interfaces:\\v_ geo [formula in source] G_ net [formula in source] F_ transfer [formula in source] (U_ wall) [formula in source] (G_ metric) [formula in source] [formula in source] / _1/ _2/ _3 [formula in source] next)
- The hard reduction: the live residual as typed interfaces
- How to read this document
- Honest status
- Front matter / support
- 2026-06-13 (the cone reduces to one particle: premise A's scope premise discharged to a 16-dim statement, v161)
- 2026-06-12 (origin_theory style alignment + box reduction)
- Research Contract 2 — [formula in source]
- 2026-06-11
- Front matter / support
- 2026-06-12 (version system, predictions/K5, readability pass B3)
- Front matter / support
- Front matter / support
- Honest status
- Front matter / support
- 2026-06-13 (premise A as a conditional fixed-point theorem; the load relocates to one scope premise, v160)
- -1.2cm TFPT — Research Contracts for the Remaining Interfaces:\\v_ geo [formula in source] G_ net [formula in source] F_ transfer [formula in source] (U_ wall) [formula in source] (G_ metric) [formula in source] [formula in source] / _1/ _2/ _3 [formula in source] next)
- 2026-06-13 (the final identification: premise A factors into the already-open A2 + R1, no new open content, v162)
- Research Contract 2 — [formula in source]
- Research Contract 1 — [formula in source]
- Research Contract 2 — [formula in source]
- Front matter / support
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
Registered verification modules
- v113_quasifree_kernel.pyRegistered verification module · registry
Read the description recorded in the module registry
ONE KERNEL IS THE WHOLE NET (the QBL input merges with the R2/holomorphy premise): MAJORANA BOOKKEEPING — c(D₅)₁ = 45/9 = 5 = g_car, c(A₃)₁ = 15/5 = 3 = N_fam; the carrier net (D₅)₁×(A₃)₁ = SO(10)₁×SO(6)₁ = 10+6 = 16 FREE MAJORANA FERMIONS, c = 16/2 = 8 — the whole extension tower carrier(μ=16) → SO(16)₁(μ=4) → E8₁(μ=1) carries the SAME 16 fermions, only the certified glue grows (index 2×2 = 4 = |μ₄|); WICK/PFAFFIAN exact: in the 10-Majorana Jordan–Wigner model ALL 210 vacuum 4-point AND all 210 6-point functions equal the Pfaffian of the single 2-point kernel — one kernel determines all correlations; THE KERNEL IS A CALDERÓN INVOLUTION OF RANK g: M = I+iA, A²=−I, P = M/2 projection with rank 5 = g_car, at seam level rank 8 = rank E8 ⇒ THE CENTRAL CHARGE IS THE RANK OF THE ONE KERNEL; vacuum unique (joint annihilator kernel 1-dim); PREMISE MERGE [P]: 'single 2-point kernel' = 'quasi-free seam state' = the defining property of the free-fermion net the holomorphy gate already posits — QBL adds NO assumption beyond R2; upgrade contract: R2 closes ⇒ carrier choice closes [L]
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