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Original ledger classification: Lattice/CS realisation (exact) [E]/[O]

Recorded statement: SEAM CHERN-SIMONS REALISATION (2026-06-17): the closing step of GATE.HOLO.01 realised in standard abelian Chern-Simons / quantum-Hall language, where 'holomorphic <=> det K = 1' is a THEOREM -- a genuine reduction of the analytic step into…

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Paper context: tfpt research contracts

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GATE.HOLO.02

Original ledger classification: Lattice/CS realisation (exact) [E]/[O]

Original claim text

SEAM CHERN-SIMONS REALISATION (2026-06-17): the closing step of GATE.HOLO.01 realised in standard abelian Chern-Simons / quantum-Hall language, where 'holomorphic <=> det K = 1' is a THEOREM -- a genuine reduction of the analytic step into anyon condensation, NOT a closure. A free gapped BOSONIC 2+1d bulk = an even integer K-matrix; #anyons (torus degeneracy) = |det K|, edge chiral central charge c = signature(K), and the edge chiral net is holomorphic (single sector) <=> |det K| = 1. So the v234 condition 'no nontrivial abelian sector' = exactly |det K| = 1. The TFPT extension tower (v92/GATE.METRIC.07) IS the anyon-condensation tower read by determinant: carrier D5(+)A3 (even, det 16, c=8, 16 anyons, mu=16) -> SO(16)_1=D8 (det 4, 4 anyons, mu=4) -> (E8)_1 (det 1, 1 anyon, mu=1, HOLOMORPHIC); all rank 8 with c = signature = 8 = g_car+N_fam. Holomorphic <=> det 1 <=> E8 = the unique even unimodular rank-8 K-matrix = the Kitaev E8 quantum-Hall state (edge (E8)_1). CONDENSATION: a Lagrangian (maximal isotropic) glue of order sqrt(16)=|mu4|=4 takes det 16->16/4^2=1 (carrier->E8); an order-2 isotropic only ->16/2^2=4 (D8). So 'holomorphic' = 'condense the order-|mu4| Lagrangian glue', not a partial. NEG: D8 (det 4) is free+bosonic yet has 4 anyons (not holomorphic, the SO(16)_1 rival); an odd-diagonal K is fermionic (spin-CS) -- 'free+bosonic' does NOT imply holomorphic, det=1 is the extra physical condition. RESIDUAL [O]: the closing step = 'the free RP gapped seam condenses the order-|mu4| Lagrangian glue (det->1), not a partial isotropic (det->4)' -- the same sheet/mu4 selection as GATE.QGEO, now with holomorphy<=>det1 a theorem and the residual a single integer condition.

Original classification detail

[E] free gapped bosonic bulk = K-matrix; #anyons=|det K|, c=signature, holomorphic<=>det 1; the v92 tower D5(+)A3(16)->D8(4)->E8(1) is the condensation tower; holomorphic=E8=Kitaev E8 state; residual = 'condense the |mu4| Lagrangian glue' = the sheet/QGEO selection [O]

Dependencies as recorded

GATE.HOLO.01; GATE.METRIC.07; TOPO.E8.01; QGEO.SYM.01

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  • v235_seam_chern_simons.pyRegistered verification module · frontier
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    The closing step in abelian Chern-Simons language: holomorphic <=> det K = 1 -- a genuine reduction (not a closure) of GATE.HOLO.01 into standard anyon-condensation physics. A free gapped bosonic 2+1d bulk = an even integer K-matrix with #anyons = |det K|, edge c = signature(K), holomorphic <=> |det K| = 1. The TFPT extension tower (v92) IS the condensation tower read by det: carrier D5(+)A3 (det 16, 16 anyons) -> SO(16)_1=D8 (det 4) -> (E8)_1 (det 1, holomorphic), all rank 8, c=signature=8=g_car+N_fam. Holomorphic <=> det 1 <=> E8 = the Kitaev E8 quantum-Hall state. Condensation: a Lagrangian glue of order sqrt(16)=|mu4|=4 takes det 16->1 (a partial order-2 isotropic only ->4=D8). NEG: D8 is free+bosonic but has 4 anyons; an odd K is fermionic -- det=1 is the extra condition. Residual: 'the free RP seam condenses the order-|mu4| Lagrangian glue' = the sheet/QGEO selection, now with holomorphy<=>det1 a theorem.

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