Skip to main content

A registered result in its source context

Original ledger classification: Identity/assembly [C] (A2 net existence by established AQFT; R1 reduced to GATE.QGEO via A0* uniqueness) + [O] (the irreducible {pi,v_geo} geometric core, a theorem by v153)

Recorded statement: PREMISE (A) MAXIMAL HONEST CLOSURE (the two residual gates A2 + R1 pinned to their floor; (A) carries ZERO independent open content): (1) A2 (NET EXISTENCE) CLOSES BY ASSEMBLY [C] - every ingredient is a constructed object: 16 free…

Statement, assumptions and sources

Paper context: Research contracts

The exact identifier, original classification and full claim are available below.

The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.

Read the exact registered claim and its dependencies

GATE.METRIC.19

Original ledger classification: Identity/assembly [C] (A2 net existence by established AQFT; R1 reduced to GATE.QGEO via A0* uniqueness) + [O] (the irreducible {pi,v_geo} geometric core, a theorem by v153)

Original claim text

PREMISE (A) MAXIMAL HONEST CLOSURE (the two residual gates A2 + R1 pinned to their floor; (A) carries ZERO independent open content): (1) A2 (NET EXISTENCE) CLOSES BY ASSEMBLY [C] - every ingredient is a constructed object: 16 free Majoranas => free-fermion conformal net (Buchholz-Mack-Todorov / Boeckenhauer-Evans), holomorphic c=8 lattice net = (E8)1 (Frenkel-Kac-Segal VOA / Dong-Xu net / Kawahigashi-Longo machinery), mu4 simple-current extension = Longo Q-system index 4 (v125), KLM mu(B)=16/16=1 => holomorphic, modular data checked 248=120(NS)+128(R), character E4/eta^8=j^{1/3} (v156); the ONLY TFPT-specific identification (seam Calderon kernel = free-fermion 2-point function) is DONE since the DtN/Calderon symbol is universally |k| (Lee-Uhlmann, v156/v157) => A2 is citation/assembly of published theorems, not a finite computation we owe (re-typed [A]->[C]); (2) R1 (SEAM CLOCK) REDUCES TO GATE.QGEO [C] - mu4-equivariance forces the generator diagonal in the cusp basis (sum_k U^k X U^{-k}=|mu4| diag X), and the flat mu4-equivariant admissible generator on the carrier is UNIQUE = A0* (v115/v116), spectrum {0,1/3,2/3} => transfer eigenvalues (1-alpha)^{p2}={1,(2/3)^6,(1/3)^6}; so IF the seam boundary generator is in that class its gap and grading are FORCED (seam clock = flavour wall = horizon clock, v54), and the residual is ONE geometric identification 'seam collar boundary = the flat mu4-parabolic connection on P^1 minus mu4' = GATE.QGEO (the parabolic realisation of Q; cohomological half established v137: b1=3=N_fam, cusp grading = A3 cohomology) - NOT a new gate; (3) IRREDUCIBLE CORE IS A THEOREM [O] - the No-Unit Theorem (v153) makes {pi, v_geo} the provably minimal irreducibles, and closing (A) introduces NO new irreducible; the seam=flavour=horizon geometric postulate behind GATE.QGEO is in that same irreducible class. FINAL ACCOUNTING: premise (A) = (A2 assembly [C]) + (R1 = GATE.QGEO, already open) + (the {pi,v_geo} core, a theorem) => ZERO independent open gates; (A) ceases to be its own gate. Honest scope: a unification + re-typing, NOT an unconditional proof

Original classification detail

Closure [C]: A2 = net-construction assembly, R1 = GATE.QGEO; (A) has zero independent open gates, irreducible core {pi,v_geo} a theorem

Dependencies as recorded

GATE.METRIC.16; GATE.METRIC.17; GATE.METRIC.18; v115; v116; v125; v137; v153; v156

Open the original ledger source, row 247

Location 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.

Sections that explicitly cite this claim

A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.

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.

All 16 linked sections

Registered verification modules

  • v165_premise_a_closure.pyRegistered verification module · registry
    Read the description recorded in the module registry

    premise (A), the honest maximal closure — the two residual gates are pinned to their floor, so (A) carries ZERO independent open content: (1) A2 (net existence) closes by ASSEMBLY of established mathematics [C] — 16 free Majoranas => free-fermion net (BMT/Böckenhauer-Evans), holomorphic c=8 lattice net = (E8)1 (Frenkel-Kac-Segal/Dong-Xu/Kawahigashi-Longo), μ4 extension = Longo Q-system index 4 (v125), μ(B)=16/16=1, 248=120+128, character E4/η⁸=j^{1/3} (v156); the only TFPT input (seam Calderón kernel = free-fermion 2-point fn) is done via DtN=|k| (v156/v157); (2) R1 (seam clock) reduces to GATE.QGEO [C] — μ4-equivariance forces diagonal-in-cusp, the flat μ4-equivariant generator is UNIQUE = A0* (v115/v116) so the gap (2/3)^6 is forced, residual = 'seam boundary = the μ4-punctured sphere P¹∖μ4' = GATE.QGEO (cohomology established, v137); (3) the irreducible core stays {π,v_geo}, a THEOREM by the No-Unit Theorem (v153). FINAL ACCOUNTING: (A) = A2 assembly [C] + R1=GATE.QGEO + the {π,v_geo} core => ZERO independent open gates; a unification + re-typing, NOT an unconditional proof.

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries