Follow a result back to its evidence.

CELEST.WP5E.WM.01: the constructive derivation of the w_m normalisation -- '1/det_j is the Atiyah-Bott / zeta-determinant fixed-point factor, COMPUTED from three independent sources', closing the residual [O] of v516/v520 at the fibre-zero-mode level (verdict ERFOLG per the frozen preregistration; 26 checks, ~1 s). [E] ATIYAH-BOTT (route i): the equivariant mode ledger of the fibre C^2 equals the closed form 1/((1-q i^j)(1-q i^{-j})) exactly in Q(i) for all n <= 120; REGULAR at q = 1 with Abel value (1/2, 1/4, 1/2) = 1/det_j, det_j = det(1-g^j) = (2, 4, 2); (C,2) Cesaro convergence in exact arithmetic; the fixed-point factor splits off EXACTLY at every truncation level d in {7, 12, 25}, for the phased (skeleton) AND the v520-forced unphased (completion) trace alike -- the Abel-limit contact_j = (Q^(0) - Q^(j))/det_j is the v516 contact vector COMPUTED, not declared. [E] ZETA/QUILLEN (routes ii/iii): det_zeta of the g^j-twisted circle Laplacian = 4 sin^2(pi j/4) = det_j EXACTLY (Lerch + reflection formula symbolically; Hurwitz certificates ~1e-41); Quillen split det Delta = det_j^2, |det dbar| = det_j, with the real positive holomorphic section UNIQUE via the SU(2) conjugation pairing; the delta-1f f1f3 block at the (0, b) nodes carries the exact constant term 1/det_b (deviations <= 5.2e-28). [E] CONSISTENCY CHAIN: the derived weight reproduces the v516 chain number by number -- w_m = (0, 3/2, 2, 3/2) = 4h_m = |mu4| h_m = -4 ch2(T_m); T5 = 0 at every scale; h_2 : h_1 = 4 : 3; the T3 budget 32 - 8c forces c = 4 = |mu4| uniquely (leftovers 24/16/8/0/-8); per-sector Okubo squares (18, 9, 18)<x,x>^2; total 45<x,x>^2; Phi_T3: 32 -> 0, Phi_P: 72 -> 0; psi(A_fix) = +64, psi(contact) = -64. [E] NEGATIVE CONTROLS: 1/det^2 gives w' = (0, 5/8, 1, 5/8) with leftovers (2, 12) and a Quillen contradiction (det Delta = det^4 vs measured det^2); 1/|1-i^j| gives w''_1 = 1+sqrt2 notin Q; the Z2/Eguchi-Hanson anchor PASSES with the same derivation (det = 4, w = 1/2 = |Z2| h^{A1}, 9<x,x>^2 = (1/4) x 36, c = 2 = |Z2|); the SO(16)/D8 KILL fires; diag(i,i) breaks the zeta = AB identity itself (real (2,4,2) vs complex (2i,4,-2i), no real Quillen section); k = 3, 5 orbifolds: w_m = m(k-m)/2 = k h_m exactly in Q[x]/Phi_k -- the weights wander correctly with the centre count, only k = 4 = |mu4| carries the E8-glue chain. [C] TYPED PREMISES (the mandatory fence): TP-REG (Abel/Cesaro/zeta regularisation IS the definition of the equivariant character), TP-Q (Quillen structure of BCOV F1 = v520 TP-4), TP-NUM (unphased numerator = the v520 ERFOLG-A decision layer), TP-CH (the insertion channel (0, j) computes the box-channel weight). [O] the GLOBAL BCOV integral on PT/Z4 beyond the fibre zero-mode factor; the resolved-ALE route (v514/v517) not built; SEAM.EQUIV.TWISTOR.01 untouched. Discovery provenance: experiments/tfpt-discovery/celestial_seam_wp5e_wm_bcov_derivation_probe.py (26/26, 2026-07-23). NO marker moves.

Linked claims

CELEST.WP5E.WM.01

Paper sections

Source section 1Source section 2Source section 3Source section 4Source section 5Source section 6Source section 7Source section 8Source section 9Source section 10Source section 11Source section 12Source section 13Source section 14Source section 15Source section 16Source section 17Source section 18Source section 19