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Original ledger classification: Lattice [L] (classification + machine contrast) + [P]/[A] (the one remaining hypothesis)

Recorded statement: Red-team Target A residual (ii) CONDITIONALLY CLOSED [L] -> Target A = ONE residual: bulk-reconstruction uniqueness is NOT independent of residual (i). By the AQFT classification of full 2D CFTs over a chiral net (Longo-Rehren 1995;…

Statement, assumptions and sources

Paper context: Red-team audit

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GATE.METRIC.05

Original ledger classification: Lattice [L] (classification + machine contrast) + [P]/[A] (the one remaining hypothesis)

Original claim text

Red-team Target A residual (ii) CONDITIONALLY CLOSED [L] -> Target A = ONE residual: bulk-reconstruction uniqueness is NOT independent of residual (i). By the AQFT classification of full 2D CFTs over a chiral net (Longo-Rehren 1995; Kawahigashi-Longo-Mueger 2001; Bischoff-Kawahigashi-Longo-Rehren arXiv:1405.7863) the possible bulks = haploid commutative Q-systems = physical modular invariants of Rep(A); for a HOLOMORPHIC net Rep(A)=Vect so the bulk pairing is UNIQUE. MACHINE-CHECKED CONTRAST: the same-c rival SO(16)_1 (discriminant category Z2xZ2 of D8, q=(0,1/2,1,1), mu-index=4, S/T built explicitly, S^2=I, (ST)^3=I) admits exactly SIX modular invariants (Z>=0 integer, Z_00=1, [Z,S]=[Z,T]=0, entries<=2): diagonal, s<->c swap, BOTH E8-extension invariants |chi_0+chi_{s,c}|^2 (= the lattice glue E8=D8 u (D8+s): h_s=1 bosonic/condensable, index 2, det=4/4=1 even unimodular, cf v1/v83) and two twisted pairings => without holomorphy the c=8 bulk is MULTIPLY ambiguous; with one primary trivially Z=(1) unique. CONSEQUENCE: the whole of Target A reduces to the SINGLE theorem 'seam-Calderon boundary net is holomorphic with c=8' - then (E8)_1 (v83/GATE.METRIC.04) AND the unique bulk (this row) follow; the hypothesis stays [P]/[A]. Honest scope: nothing here proves the seam net IS holomorphic

Original classification detail

Lattice [L]: bulk uniqueness rides on holomorphy; Target A = ONE residual

Dependencies as recorded

GATE.METRIC.04; REDTEAM.A.01; v83; v77

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Registered verification modules

  • v87_bulk_uniqueness_reduction.pyRegistered verification module · registry
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    red-team Target A = ONE residual: holomorphy ⇒ unique 2D bulk (LR/KLM/BKLR); machine contrast: SO(16)₁ admits SIX modular invariants (incl. both E₈-extension pairings) ⇒ non-holomorphic c=8 bulk is multiply ambiguous

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