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A registered result in its source context

Original ledger classification: Lattice [L] (residual 1 closed) + [P]/[A] (residuals 2-3 open)

Recorded statement: Red-team Target A residual 1 CLOSED [L] (holomorphy is necessary AND sufficient to pin (E8)_1): at level 1 the number of primaries = det(Cartan) = |fundamental group|, giving A3=4, D5=4, D8=4, E8=1. So holomorphy (single vacuum sector =…

Statement, assumptions and sources

Paper context: Red-team audit

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GATE.METRIC.04

Original ledger classification: Lattice [L] (residual 1 closed) + [P]/[A] (residuals 2-3 open)

Original claim text

Red-team Target A residual 1 CLOSED [L] (holomorphy is necessary AND sufficient to pin (E8)_1): at level 1 the number of primaries = det(Cartan) = |fundamental group|, giving A3=4, D5=4, D8=4, E8=1. So holomorphy (single vacuum sector = mu-index 1 = det 1) excludes the SAME-c rival (D8)_1=SO(16)_1 (c=120/15=8 but 4 primaries 1,v,s,c) - equal central charge is necessary not sufficient - AND is sufficient: a holomorphic c=8 chiral CFT is the lattice theory of an even unimodular rank-8 lattice, of which there is exactly ONE, E8, by the Minkowski-Siegel mass formula (mass=1/|W(E8)|=1/696729600=1/(2^14*3^5*5^2*7), and |Aut(E8)|=|W(E8)| saturates it; E8 Gram even, det 1). The (D5)_1x(A3)_1 conformal embedding c=5+3=8=c(E8) is compatibility (16 primaries vs 1), NOT the subnet identification. CONSEQUENCE: with this, the constructive map need only show the seam-Calderon boundary net is holomorphic & c=8 (then E8 is automatic), so Target A drops from 3 residuals to 2: (i) boundary-net holomorphy+c=8 (Delta_eff>0 supports, not proves), (ii) bulk-reconstruction uniqueness - both still [P]/[A]

Original classification detail

Lattice [L]: holomorphy => (E8)_1 unique (residual 1 closed); residuals 2 (constructive map) + 3 (bulk uniqueness) remain [P]/[A]

Dependencies as recorded

REDTEAM.A.01; GATE.METRIC.03; v77; v66; v1

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Registered verification modules

  • v83_e8net_holomorphic_uniqueness.pyRegistered verification module · frontier
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    closes red-team Target A residual 1: #primaries=det(Cartan) ⇒ holomorphy (E8 det 1) is necessary AND sufficient — (D8)₁=SO(16)₁ shares c=8 but has 4 primaries; E8 the unique even-unimodular rank-8 lattice (mass=1/|W(E8)|). A drops 3→2 residuals; + Target B reduced to the half-spinor midpoint K=(g−1)/2

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