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A registered result in its source context

Original ledger classification: Lattice [E] (modular-commutator ground-state measurement + controls + exact additivity) + [O] (continuum limit; SEAM.EQUIV.01 unchanged)

Recorded statement: THE CHIRAL CENTRAL CHARGE c_- = 8 MEASURED FROM THE BULK GROUND STATE (2026-07-20; ground-state witness round): the Kim-Shehab-Kim modular commutator J(A,B,C) = i Tr(rho_ABC [K_AB, K_BC]) = (pi/3) c_- (PRL 128 (2022);…

Statement, assumptions and sources

Paper context: tfpt research contracts

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SEAM.CCC.01

Original ledger classification: Lattice [E] (modular-commutator ground-state measurement + controls + exact additivity) + [O] (continuum limit; SEAM.EQUIV.01 unchanged)

Original claim text

THE CHIRAL CENTRAL CHARGE c_- = 8 MEASURED FROM THE BULK GROUND STATE (2026-07-20; ground-state witness round): the Kim-Shehab-Kim modular commutator J(A,B,C) = i Tr(rho_ABC [K_AB, K_BC]) = (pi/3) c_- (PRL 128 (2022); arXiv:2110.06932/2110.10400), evaluated on the EXACT BdG ground state of the v367 p+ip seam lattice model via the Peschel Majorana covariance (W_X = -2 artanh Gamma_X, J = (1/4) Tr([W_AB, W_BC] Gamma_ABC)), a disk about the torus centre tripartitioned into three 120-degree wedges. This is the FIRST ground-state witness for premise (i) of SEAM.EQUIV.01 (c_- = 8) that is INDEPENDENT of both the Chern-number route (v367: FHS curvature of the Bloch bundle) and the counting route (v378: KLM/det-Cartan arithmetic) -- J is read off entanglement data alone; no band topology or representation theory enters the measurement. [E] GROUND-STATE PURITY: eig(i Gamma) = +-1 to 6e-15 (exact pure state, not an approximation). [E] PER-LAYER c_- = 1/2: c_- = 3J/pi = 0.499998 at L=32, R=12 (convergence 0.499793 at L=16 -> 0.500000 at L=48, R=18, dev -1.8e-7; suite runs L=32 with tol 1e-4). [E] CONTROLS: trivial M=3 (Chern 0) gives c_- = 0.000000; orientation flip M=-1 gives -0.499986 (sign flip) -- J tracks the phase, not the algorithm. [E] LAYER ADDITIVITY EXACT: J(2 decoupled layers) - 2 J(1 layer) = 1.4e-14 (block-diagonal Gamma), so the carrier value is 16x the per-layer value. [E] THE 16-LAYER CARRIER: c_- = 8 = g_car + N_fam -- direct 16-layer computation 7.9967 (L=16, tol 1e-2; the L=24 direct run gives 7.999781) and additivity route 8.0000 (tol 1e-3). [E] CLIP INVARIANCE: the artanh regularisation eps = 1e-8 vs 1e-12 moves c_- by 5e-8. [O] HONEST FENCE: this pins c_- = 8 on the LATTICE ground state (third independent witness after v367/v378); it does NOT close SEAM.EQUIV.01 -- the continuum scaling limit (MMST, v336) stays [O] and the mu4 condensation SO(16)_1 -> (E8)_1 stays the cited KLM step (v378/v154/v351). No gate closes, no marker moves.

Original classification detail

Ground-state witness [E]/[O]: c_- = 0.499998 per layer (0.500000 at L=48), 16-layer carrier c_- = 8 = g_car + N_fam (direct 7.9967 / additivity 8.0000), trivial 0 and orientation-flip controls, exact layer additivity -- premise (i) of SEAM.EQUIV.01 pinned from entanglement alone; SEAM.EQUIV.01 stays [O]

Dependencies as recorded

SEAM.EQUIV.01; SEAM.S3.LATTICE.01; SEAM.S3.MODULAR.01; SEAM.MMST.INCLASS.01; v336; v351; v367; v368; v376; v377; v378

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Registered verification modules

  • v489_seam_modular_commutator.pyRegistered verification module · core
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    SEAM.CCC.01: the chiral central charge c_- = 8 measured DIRECTLY from the bulk ground state of the v367 seam lattice model, via the Kim-Shehab-Kim modular commutator J(A,B,C) = i Tr(rho_ABC [K_AB, K_BC]) = (pi/3) c_- on a 120-degree pie tripartition -- the first ground-state witness for premise (i) of SEAM.EQUIV.01 (c_- = 8) INDEPENDENT of both the Chern route (v367) and the KLM counting route (v378); everything reduces to the Peschel Majorana covariance (W = -2 artanh Gamma). [E] purity: eig(i Gamma) = +-1 to 6e-15 (exact BdG ground state). [E] per-layer c_- = 0.499998 (L=32, R=12; 0.499793 at L=16 -> 0.500000 at L=48, dev -1.8e-7). [E] controls: trivial M=3 -> 0.000000, orientation flip M=-1 -> -0.499986. [E] layer additivity exact (1.4e-14). [E] 16-layer carrier: direct c_- = 7.9967 (L=16; L=24 gives 7.999781), additivity route 8.0000 = g_car + N_fam. [E] clip invariance 5e-8. [O] honest fence: pins c_- = 8 on the lattice ground state; does NOT close SEAM.EQUIV.01 (continuum limit MMST v336 stays [O], mu4 condensation stays the cited KLM step v378). Numerical (numpy), Python-only by nature.

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