Follow a result back to its evidence.

CELEST.WP5E.GAMMA.01: WP5e-gamma of the celestial-holographic research contract CELEST.SEAM.01 -- 'the sphere-axion pairing check', an honest rigid NEGATIVE result (v505 style): can the three twisted sphere axions eta_m (Coxeter eigencharacters {i, -1, -i} on H^2(ALE), v505 S5.8) cancel the rigid 32 T3 residual of the Atiyah-Bott ledger (A_fix = 9P1 - 30P2 - 15P3 + 32 T3, v505 S3.7) by Green-Schwarz-type EXCHANGE with sector-compatible quadratic vertices? NO, with certificate. Exact sympy/Fraction, no floats (27 checks). [E] VERTEX-SPACE THEOREM: the W(D5) x W(A3)-invariant quadratics on the 8-dim glue Cartan = EXACTLY span{s5, s3} (dim 2, bidegree dims (1,0,1)); quartics = EXACTLY span{P1, P2, P3, T5, T3} (dim 5, bidegree dims (2,0,1,0,2)) -- vertex basis complete (Weyl nullspace arithmetic over all bidegrees); PRODUCT THEOREM (the master kill): (a s5 + b s3)(c s5 + d s3) = ac P1 + (ad+bc) P2 + bd P3 identically -- ZERO T5/T3 content, so EVERY exchange image (any axion count, any rule, any couplings) is annihilated by Phi_T3, while Phi_T3(A_fix) = 32 != 0. [E] SELECTION ENUMERATION: strict two-index reading COLLAPSES (C_{j,j'} != 0 only for j' = -j => the rule forces m = 0 -- the sphere axions have NO invariant bilinear Cartan vertex at all); twist-insertion: eta_1 <-> K^(3), eta_2 <-> K^(2), eta_3 <-> K^(1), eta_0 <-> K^(0); channels E13 = (16, -96, 144, 0, 0), E22 = (16, 32, 16, 0, 0), E00 = 225 E22; SIDE DISCOVERY: K^(0) = -15 K^(2) (the even-sector quadratics are PARALLEL). [E] UNSOLVABILITY WITH CERTIFICATE (core): exchange matrix 5 x 2, rank 2, kernel 0; rank([M | A_fix]) = 3; annihilator certificate (Phi_T5, Phi_T3, Phi_P)(A_fix) = (0, 32, 72) with A_fix = (9, -30, -15, 0, 32) -- two independent obstructions: 32 T3 (structural, rule-independent) and Phi_P = 72 (rule-driven via the K^(0) || K^(2) collapse); ker M = 0 forces the unique non-disturbing coupling c = 0 (the sphere axions are RIGIDLY SILENT); Phi_P(Q^(0)) = 0 (the v505 sector-0 mechanism undisturbed); relaxed control: dropping charge conservation reaches the P-block (rank 3, det -64) but T5 = T3 = 0 persists. [E] NATURALNESS RESOLUTION: ch2-natural (9/64, 1/4) and AB-weight (1/2, 1/4) couplings both have certificate (0, 0) vs required (32, 72) -- the failure is scale- and coupling-INDEPENDENT (no 'unnatural factor': the ansatz space misses the target identically). [E] NEGATIVE CONTROLS: (a) invariant axion only = v505 S3.9 replicated + sharpened; (b) flipped rule m + j - j': the Phi_T3 kill is flip-invariant, Phi_P is rule-dependent; (c) SO(16): odd classes EMPTY, AB sum (15, -18, -15, -4, 40) does not even cancel T5 (E8 doubly special); (d) D8: 16 T8 + 12 s8^2, no T3 structure -- the question cannot even be posed. [C] number fences: 32 = (h,h) + (h',h') = 20 + 12; 72 = 2 lambda~^2_e8. [O] SHARPENED FENCE: the exchange sub-branch is DEAD; the 32 T3 residual MUST be carried by twisted BCOV contact terms -- binary criterion WP5e-delta-1: the one-loop coefficient on C^2/Z4 must come out exactly (9, -30, -15, 0, 32), COMPUTED, not fitted; named escape WP5e-delta-2: the full-tensor ledger (the collapse is Cartan-restricted); slot bijection (v505 S5.8) untouched; the preregistered level-kill still does NOT fire; SEAM.EQUIV.01 stays [O]; no marker moves. Exact (sympy/Fraction).

Linked claims

CELEST.WP5E.GAMMA.01

Paper sections

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