Original ledger status
GATE.METRIC.19
GATE.METRIC.19
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
Recorded status: 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)
Dependencies, status detail and source
Canonical status: Closure [C]: A2 = net-construction assembly, R1 = GATE.QGEO; (A) has zero independent open gates, irreducible core {pi,v_geo} a theorem
Dependencies: GATE.METRIC.16; GATE.METRIC.17; GATE.METRIC.18; v115; v116; v125; v137; v153; v156
Scripts: v165_premise_a_closure.py
Location: tfpt_research_contracts
Original CSV, line 247