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A registered result in its source context

Original ledger classification: Identity/Lie [I]/[L]

Recorded statement: Boundary-CFT bridge (WZW central charges = compiler atoms) + SU(3)<->SU(4) reconciliation [I]/[L]; NOT a closure. (A) level-1 WZW central charges c=dim(g)/(1+h^v) are the atoms: c(E8)_1=248/31=8=rank E8, c(D5=SO10)_1=45/9=5=g_car,…

Statement, assumptions and sources

Paper context: Origin Theory

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ARCH.CFT.01

Original ledger classification: Identity/Lie [I]/[L]

Original claim text

Boundary-CFT bridge (WZW central charges = compiler atoms) + SU(3)<->SU(4) reconciliation [I]/[L]; NOT a closure. (A) level-1 WZW central charges c=dim(g)/(1+h^v) are the atoms: c(E8)_1=248/31=8=rank E8, c(D5=SO10)_1=45/9=5=g_car, c(A3=SU4)_1=15/5=3=N_fam; coset c=8-5-3=0 = conformal-embedding criterion => (D5)_1x(A3)_1 ⊂ (E8)_1 is a conformal embedding (CFT mirror of the lattice glue (D5(+)A3)+mu4->E8); (5,3) split = central-charge additivity = rank split; the 8 in c3=1/(8pi) = c(E8)_1 (NOT oversold - the content is c_coset=0, per Alessandro's earlier caveat). (B) SU(3)<->SU(4) reconciliation: P^1\\mu4 has n=4 punctures => H_1=Z^(n-1) => N_fam=|mu4|-1=3; carrier side = puncture/center Z4=mu4 (A3=SU4); flavor side = monodromy rho on H_1=Z^3, SU(3)-valued, center Z3=triality, phases {0,1/3,2/3}=parabolic weights (NOT SU(4)_1 weights {0,3/8,1/2}); SU(3) ⊂ SU(4) via 4->3+1. => NOT one WZW for all gates (C falsified), but ONE geometry P^1\\mu4 with two dual sides. CHECKED: Cardy route c=8->S=A/4 is NOT a shortcut (c=8 is matter central charge; area law needs geometric Brown-Henneaux c~ell/G) - restates the open Seam-Horizon coefficient, does not close it

Original classification detail

Identity/Lie [I]/[L]

Dependencies as recorded

BND.GLUE.01; v6; v15; v19; SEAM.THEOREM.01

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Registered verification modules

  • v61_cft_bridge.pyRegistered verification module · horizon
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    boundary-CFT mirror: c(E₈)=8, c(D₅)=5, c(A₃)=3

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