Celestial wp5e m2 twisted ks measure
v516_celestial_wp5e_m2_twisted_ks_measure.py · frontier
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CELEST.WP5E.M2.01: milestone M2 of the celestial-holographic research contract CELEST.SEAM.01 (WP5e back-reaction programme) -- 'the twisted Kodaira-Spencer measure', executed (SUCCESS on the preregistered v514 S8.2 criterion, on the DECLARED completion measure -- verdict B): the one-loop box coefficient per sector on PT/Z4 under the completion contact term contact_j = (Q^(0) - Q^(j))/det_j. Exact sympy/Fraction, no floats (23 checks, ~1 s). [E] THE COMPLETION-WEIGHT IDENTITY (the centrepiece): per glue class the contact weights are w_m = sum_j (1 - i^{jm})/det_j = (0, 3/2, 2, 3/2) = 4 h_m = |mu4| h_m = -4 ch2(T_m) EXACTLY (h_m = m(4-m)/8 the v502 sector Casimir energies, ch2(T_m) the McKay/Kronheimer charges of the tautological bundles, v505 S4.3 index bridge): THE THREE SPHERE AXIONS PAIR THROUGH THEIR OWN ch2 CHARGES -- an exact identity, NO free scale, no fit. [E] PARAMETER-FREE LOCKS: T5 = 0 for ANY scale c (the ch2 pattern alone kills T5); ratio h_2 : h_1 = 4 : 3 = the delta-1-forced leading ratio (REPRODUCED, not fitted); the T3 budget fixes the scale c = 4 = |mu4| uniquely; the unique delta-1 leading weights (3/2, 2) reproduced as (4h_1, 4h_2). [E] THE CONTACT TERM: channel form sum_j (Q^(0) - Q^(j))/det_j = class form sum_m 4 h_m Q_m = (36, 120, 60, 0, -32) EXACTLY (one object, two bases); the contacts carry nonzero T5/T3 per channel (genuine contact, not exchange -- the v508 product theorem replicated as control). [E] SUCCESS TABLE: skeleton_j + contact_j = Q^(0)/det_j = 36<x,x>^2/det_j -- a PERFECT Okubo square (T5 = T3 = 0, lambda~^2 = 36) in EVERY twisted channel ((18, 9, 18) x <x,x>^2); total A_fix + contact = 45<x,x>^2 = (5/4) x 36<x,x>^2 = (Dedekind sum) x (Okubo) = the UNIQUE quartic-free weighting of v505 S3.8 (the rigidity theorem is exactly what the measure lands on); both v508 certificates killed (Phi_T3: 32 -> 0, Phi_P: 72 -> 0); the v511 slice psi = 64 SUPPLIED EXACTLY (psi(contact) = -64) -- no cubic d-channel needed, c_d is free to be 0; remainder inside the exchange span (45<x,x>^2 = (45/16) E22 = (1/80) E00, Phi_P = 0): the BULK axion cancels every channel with the SAME lambda~^2 = 36, the twisted propagator carrying the AB zero-mode factor 1/det_j; the v514 S3.4 measure chain stays mu-blind. [E] NEGATIVE CONTROLS: wrong scale c in {1, 2, 3, 5} leaves T3 = (24, 16, 8, -8) -- only c = 4 = |mu4| clears the budget; shuffled weights (h_1 <-> h_2) break T5 = -14 AND T3 = 36; SO(16) glue keeps T5 = 20 / T3 = -40 in the summed trace -- the KILL branch FIRES there (Okubo failure inherited, E8 doubly special); diag(i, i) degenerates to the Z2 target and breaks the conjugation pairing + the index bridge; the Z2/Eguchi-Hanson anchor PASSES with the same mechanism (A_2 + contact = 9<x,x>^2 = (1/4) x 36<x,x>^2, coupling scale 2 = |Z2| = centre count). [E] MULTIPLIER NOTE (cross-reference only, the substance belongs to the parallel delta-1d strand): the contact weights 4h are REAL RATIONALS carrying no multiplier system of their own; the delta-1c residual phases are the SQUARES of the A3 discriminant T-phases e(3a^2/8) -- orders (1, 8, 2, 8) squaring to (1, 4, 1, 4), a finite mu4 system; Gauss sums 2e(3/8) (A3), 2e(5/8) (D5), full Weil sum 4 (signature 0 mod 8). [C] THE COMPLETION READING (the mandatory fence): the loop of twisted states carries the UNPHASED sector trace with the same zero-mode normalisation -- declared, supported by the delta-1 modular-completion finding, NOT derived from the BCOV integral. [O] the BCOV-integral derivation of the completion reading (delta-1b/1c/1d territory); M3 executed separately (v517); SEAM.EQUIV.TWISTOR.01 untouched (preparation, not construction). VERDICT: SUCCESS wording met on the declared completion measure -- lambda~^2 = 36 reproduced in EVERY sector, the 32 T3 cancelled exactly by the ch2-weighted sphere-axion contacts; the KILL branch does NOT fire; NO marker moves anywhere.
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