Celestial wp5e beta equivariant ledger
v505_celestial_wp5e_beta_equivariant_ledger.py · frontier
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CELEST.WP5E.BETA.01: WP5e-beta of the celestial-holographic research contract CELEST.SEAM.01 -- 'the equivariant anomaly ledger on twistor space', the twistor-side milestone of WP5e (the BCOV/Costello-Li twistor uplift; preregistered kill: the anomaly inflow demands a level != 1); WP5e-alpha (v502) anchored the CFT side. The Atiyah-Bott/Lefschetz fixed-point skeleton of the one-loop box anomaly (Costello arXiv:2111.08879; Bittleston-Sharma-Skinner CMP 403) evaluated EXACTLY on C^2/Z4 with the E8 mu4-glue monodromy. Exact sympy/Fraction, no floats. [E] AB LEDGER: denominators det(1 - g_j^{-1}) = (2, 4, 2); sum of reciprocals 5/4 = (|Z4|^2-1)/12 (Dedekind); equivariant characters tr_{g_j}(Ad E8) = (248, 0, -8, 0) by TWO routes (graded dims / root sum); invariant average 60 = the D5+A3 carrier; Frobenius 61568; tr_{g_2} = -8 = 120 - 128 (so16 supertrace). [E] OKUBO PER SECTOR (honest sharpening): the invariant sector is exactly Okubo-quadratic (Q^(0) = 36<x,x>^2, 36 = lambda~^2_e8 -- v495 re-derived through the glue grading); the TWISTED sectors do NOT reduce (independent-quartic content T5: (-8, 32, -8), T3: (48, -64, 48)); the AB-weighted sum cancels the D5 quartic EXACTLY and leaves the RIGID residual 32 T3; no reweighting of the twisted sectors alone is quartic-free, the only quartic-free weighting is the uniform Z4 projector; the graded GS-exchange ansatz is exactly rank-obstructed in sectors 1, 2, 3; heterotic identities exact (Tr_120 = 8tr^4 + 3(tr^2)^2, Tr_128 = -8tr^4 + 6(tr^2)^2, Tr_E8 = 9(tr^2)^2). [E] INDEX BRIDGE (centrepiece): f(m) = (1/4) sum_j (i^{jm}-1)/det_j = (0, -3/8, -1/2, -3/8) = ch2(T_m) = -(C^{-1})_mm/2 EXACTLY -- fixed-point ledger = McKay/Kronheimer intersection ledger; glue-bundle ch2 defect -78 by BOTH routes (per class (-24, -30, -24); -30 = -h_vee, a [C] coincidence); bridge identity sum_m h_A3(m) = 5/4 = sum_j 1/det_j; sphere pairing <alpha,h> integer on all 240 roots, Killing sums (320, 320, 240, 320), total 1200 = 2 h_vee (h,h). [E] k = 1 GEOMETRIC: lattice current count (norm-2/k in the glue cosets) = 240 at k = 1, EXACTLY 0 at k = 2, 3, 4 (no adjoint closure); embedding residual 47k^2+219k-266 = (0, 360, 814, 1362); h(J;k) = k integer for ALL k -- integrality alone fixes nothing (honest, as v502); one scale => one level (v493 lockstep periods, det(A-1) = -4: no invariant flux vector). [E] E3 REFUTED (prominent): a0 in O(8) fills the GRAVITON slot O(2), NOT the BSS axion slot O(-2) (Hamiltonian weights X = -2 != +2 = Y; mismatch 4 = |mu4|, a [C] coincidence) -- 'the theory brings its GS axion as a0' is REFUTED; instead the three H2(ALE) classes carry exactly the Coxeter eigencharacters {i, -1, -i} = the three twisted ledger slots (bijection, no invariant class); slot count 1 + 3 = 4 = |mu4| soft. [E] NEGATIVE CONTROLS: diag(i,i) breaks the ledger four ways (sum 1/det = 1/4, omega-weight -1 not CY, 5 invariant-ring generators); SO(16) glue: characters (120, 0, +120, 0), defect -30 != -78, bulk Okubo FAILS (T5 = 16, T3 = -32: independent quartic Casimir, no single-axion GS); k = 2: current count 0, c-prefactor -31/48 != -1/3 (integrality dials stay integer -- the kill is the closure dial). [C] dictionaries (CS(rho) mod 1 = discriminant weight; 32 = (h,h)+(h',h'); -30 = -h_vee; the Omega-contraction identification). [O] the global BCOV/Kodaira-Spencer quantisation on PT/Z4, non-fixed-point contributions, the O(-2) bulk-axion construction, CPS level-from-flux, and the pairing of the 32 T3 residual with the three sphere axions. VERDICT B; the preregistered kill ('inflow demands a level != 1') does NOT fire on the equivariant skeleton; SEAM.EQUIV.01 untouched, no marker moves. Exact (sympy/Fraction).
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