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Original ledger classification: Identity [I] + physical origin [P] (sharpened to a Quillen form by v341; to a heat-kernel origin by v342)

Recorded statement: EM Boundary Ward decomposition (Theorem C): F_U(1)=0 read as reduced boundary U(1) Ward identity in three terms - Maxwell alpha^3 + Calderon -2c3^3 alpha^2 (2=|Z2|) + transport -8b1 c3^6 log(1/phi_seam). Coefficient identities EXACT [I]:…

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Paper context: Architecture, E8 and the electromagnetic fixed point

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EM.WARD.01

Original ledger classification: Identity [I] + physical origin [P] (sharpened to a Quillen form by v341; to a heat-kernel origin by v342)

Original claim text

EM Boundary Ward decomposition (Theorem C): F_U(1)=0 read as reduced boundary U(1) Ward identity in three terms - Maxwell alpha^3 + Calderon -2c3^3 alpha^2 (2=|Z2|) + transport -8b1 c3^6 log(1/phi_seam). Coefficient identities EXACT [I]: 8b1=(4/5)M=(4/5)(sumL+N_Phi)=164/5; seam exponent -5/4=-q(D5); transport power c3^6=C6 hexagon. Root reproduces alpha^-1=137.0359992 (v3). Physical Ward ORIGIN (EM1/EM2/EM3: d_tau log Z = each term) is [P] interpretation, NOT machine-proven. SHARPENED 2026-06-22 (v341/ALPHA.QUILLEN.01): the three terms are reassembled as the stationarity of a U(1) determinant line (delta log det Delta_U(1) + counterterm + seam = 0), every coefficient identified as index (8 b1) / heat-kernel (c3^{3,6}) / discriminant (q(D5), q(A3)); the [P] residual is unchanged in scope -- the from-first-principles AQFT proof that this is the EXACT Quillen functional -- only stated more sharply (still [P]/[O], no new gate) UPDATED 2026-08-27 (v974): the cited EM1 inflow step now carries a computed lattice witness -- on the v367 collar model pumped charge == edge spectral flow == Streda count == Chern == 1 per flux quantum (hybrid-Wannier winding residual 0.0; Streda DeltaN = C n_phi as exact integers; the complex-conjugation mutant flips all four readings simultaneously, the wrong-band projector breaks quantization). Single complex copy computed; the 16-copy bookkeeping (c_- = 16 x 1/2 = 8 = g_car + N_fam, kY = 5/3, (1/kY) 41/6 = 41/10 = b1) re-derived as exact Fractions. The physical Ward ORIGIN keeps its [P]/[O] scope -- nothing upgrades here.

Original classification detail

Identity [I] + physical origin [P]

Dependencies as recorded

EM.FP.01; v3; v341; v342

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  • v48_em_ward.pyRegistered verification module · em
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    EM boundary Ward (Thm C): F_U(1) decomposition; 8b₁ = 164/5

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