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A registered result in its source context

Original ledger classification: Reduction [E] (full (E8)_1 match + discriminator) + [C] (seam-side) + [O] (one holomorphy bit)

Recorded statement: SEAM-CALDERON -> (E8)_1 MATCHING CERTIFICATE (2026-06-18): the concrete Tier-B step of QG.AMB.01 (v275) -- computes the full (E8)_1 matching target and pins the residual to ONE bit (does NOT close it; the rt_A 'reduced, not closed' verdict…

Statement, assumptions and sources

Paper context: Frontier and open physical interfaces

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QGAMB.TIERB.01

Original ledger classification: Reduction [E] (full (E8)_1 match + discriminator) + [C] (seam-side) + [O] (one holomorphy bit)

Original claim text

SEAM-CALDERON -> (E8)_1 MATCHING CERTIFICATE (2026-06-18): the concrete Tier-B step of QG.AMB.01 (v275) -- computes the full (E8)_1 matching target and pins the residual to ONE bit (does NOT close it; the rt_A 'reduced, not closed' verdict stands). [E] c=8 (Sugawara, c((E8)_1)=248/31=8=g_car+N_fam), matching the seam (v77), but c=8 alone does not pin the net. [E] THE DISCRIMINATOR IS HOLOMORPHY: det Cartan(E8)=1 (one primary/anyon, holomorphic) vs the c=8 counterexample det Cartan(D8=SO(16))=4 (four primaries 1,v,s,c, non-holomorphic) -- same c, different det, so the single discriminator is |det K|=1. [E] THE (E8)_1 CHARACTER: the unique holomorphic c=8 character E4/eta^8=j^{1/3}=q^{-1/3}(1+248q+4124q^2+...) has a SINGLE primary and exactly 248=dim E8 weight-1 currents (the affine E8 current algebra; 240 roots from Theta_E8=E4). [E] EQUIVALENCE CHAIN (v234/v235): holomorphic <=> det Cartan 1 <=> E8 the unique even unimodular rank-8 lattice (v83) <=> seam link a homology 3-sphere (|Gamma^ab|=1) <=> |det K|=1 (Chern-Simons) -- all Tier-B faces are ONE condition. [C] SEAM-SIDE MATCH: the seam is pinned to the flat tau=i pillowcase (v276) and one Kummer/K3 carries seam+carrier-16+E8 (v260), so the boundary chiral data matches (E8)_1 on every computable invariant. [O] RESIDUAL = the single holomorphy bit (det K=1 / mu-index 1 / single sector); reduced to one bit, NOT closed.

Original classification detail

[E] the full (E8)_1 matching target (c=8, det 1, 248 currents, single primary) + the explicit D8 counterexample isolating holomorphy as THE discriminator; [C] the seam-side match via v276/v260; [O] the single holomorphy bit stays open. Reduces QG.AMB.01 Tier-B to one checkable condition; does NOT close it.

Dependencies as recorded

QGAMB.ROADMAP.01; GATE.METRIC.03; REDTEAM.A.01; QGEO.SYM.03; ARCH.K3.01; GATE.HOLO.02

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Registered verification modules

  • v277_seam_calderon_e8_match.pyRegistered verification module · frontier
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    QGAMB.TIERB.01 — the seam-Calderón → (E8)₁ matching certificate, the concrete Tier-B step of QG.AMB.01 (v275): computes the full (E8)₁ matching target and pins the residual to ONE bit (does NOT close it). [E] c=8 (Sugawara, 248/31=g_car+N_fam), but c=8 alone does not pin the net; [E] the discriminator is holomorphy — det Cartan(E8)=1 (1 primary, holomorphic) vs the c=8 counterexample det Cartan(D8=SO(16))=4 (4 primaries, non-holomorphic), so the single discriminator is |det K|=1; [E] the (E8)₁ character E4/η⁸=j^{1/3}=q^{-1/3}(1+248q+4124q²+…) has a single primary + exactly 248=dim E8 weight-1 currents (240 roots); [E] equivalence chain holomorphic ⟺ det Cartan 1 ⟺ unique even unimodular rank-8 (v83) ⟺ homology-sphere link ⟺ |det K|=1 (v235); [C] seam-side match via v276 (flat τ=i) + v260 (Kummer/K3); [O] residual = the single holomorphy bit, reduced to one bit, NOT closed (rt_A verdict stands).

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