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A registered result in its source context

Original ledger classification: Reduction [E] (modular data + condensation tower + Gauss-Milgram) + [O] (one bit)

Recorded statement: MODULAR-DATA / ANYON-CONDENSATION LAYER OF THE Tier-B HOLOMORPHY BIT (2026-06-18): complements v277 (det+character) with the anyon/modular-data view. [E] #anyons = |det Gram|: E8 -> 1 (holomorphic, single sector), D8=SO(16)_1 -> 4 (anyons…

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Paper context: Frontier and open physical interfaces

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QGAMB.MODULAR.01

Original ledger classification: Reduction [E] (modular data + condensation tower + Gauss-Milgram) + [O] (one bit)

Original claim text

MODULAR-DATA / ANYON-CONDENSATION LAYER OF THE Tier-B HOLOMORPHY BIT (2026-06-18): complements v277 (det+character) with the anyon/modular-data view. [E] #anyons = |det Gram|: E8 -> 1 (holomorphic, single sector), D8=SO(16)_1 -> 4 (anyons 1,v,s,c), carrier D5(+)A3 -> det(D5)*det(A3)=4*4=16. [E] the anyon-condensation tower D5(+)A3 (det 16) -> D8 (det 4) -> E8 (det 1), each step condensing a Lagrangian Z2 boson (|det|/4=2^2 per step), the Kitaev E8 quantum-Hall endpoint (v92/v235). [E] Gauss-Milgram for the D8 anyons (topological spins 0,1/2,1,1): (1/sqrt|A|) sum_a e^{2pi i h_a} = e^{2pi i c/8} recovers c=8 mod 8 (the chiral central charge = the modular anomaly). [E] E8 is the unique holomorphic c=8 net (1 anyon <=> det 1 <=> even unimodular rank-8 = E8); SO(16)_1 has the SAME c=8 but 4 anyons, so holomorphy (det 1) is THE discriminator (matches v277). [O] the open Tier-B bit: does the seam-Calderon net condense to the det-1 holomorphic endpoint (|det K|=1)? Reduced to one bit, not closed.

Original classification detail

[E] #anyons=|det Gram| + the condensation tower 16->4->1 + Gauss-Milgram c=8 + E8 the unique holomorphic point; [O] the single holomorphy bit. The modular-data view of QG.AMB.01 Tier-B; complements v277. Exact core mirrored in Wolfram.

Dependencies as recorded

QGAMB.TIERB.01; GATE.HOLO.02; QGAMB.ROADMAP.01; E8.GLU.01

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Registered verification modules

  • v281_holomorphy_modular_data.pyRegistered verification module · frontier
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    QGAMB.MODULAR.01 — the modular-data / anyon-condensation layer of the QG.AMB.01 Tier-B holomorphy bit. [E] #anyons=|det Gram|: E8→1 (holomorphic), D8=SO(16)→4, carrier D5⊕A3→16; [E] the anyon-condensation tower D5⊕A3 (16) → D8 (4) → E8 (1), each step condensing a Lagrangian Z2 boson (|det|/4=2²), the Kitaev E8 endpoint (v92/v235); [E] Gauss-Milgram (D8 spins 0,1/2,1,1) recovers c=8; [E] E8 is the unique holomorphic c=8 (det 1) — SO(16) has the same c=8 but 4 anyons, so holomorphy is THE discriminator (v277); [O] the open bit: does the seam-Calderón net condense to det K=1? Reduced to one bit, not closed.

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