A registered result in its source context

CELEST.WP5E.M2.01

Original ledger classification: Formal/Identity [E] (exact weight/contact/table/control arithmetic: completion-weight identity w = 4h = -4 ch2 with no free scale, parameter-free locks (T5 = 0 any scale, 4:3 ratio, T3 budget => c = |mu4|), contact term two bases, per-sector Okubo squares 36<x,x>^2/det_j, total (5/4) x 36, certificate kills 32 -> 0 / 72 -> 0 / psi 64 -> 0, exchange-span remainder, mu-blind chain, all five controls -- sympy/Fraction exact, Wolfram-mirrored) + [C] (the DECLARED completion reading: loop = unphased sector trace with the same zero-mode measure -- supported by the delta-1 modular-completion finding, not derived) + [O] (the BCOV-integral derivation of the completion reading, delta-1b/1c/1d; SEAM.EQUIV.TWISTOR.01 unchanged)

Original claim text

MILESTONE M2 OF THE CELESTIAL-HOLOGRAPHIC CONTRACT EXECUTED (2026-07-22; CELEST.SEAM.01 WP5e back-reaction programme, milestone M2 -- 'the twisted Kodaira-Spencer measure', SUCCESS on the preregistered v514 S8.2 criterion ON THE DECLARED COMPLETION MEASURE, verdict B; exact sympy/Fraction arithmetic, no floats, 23 checks, ~1 s): quantise the O(-2) tower on PT/Z4 using the eps1 mode ledger and compute the one-loop box coefficient PER SECTOR (preregistered SUCCESS = the bulk sector reproduces lambda~^2 = 36 with the eps1 measure bookkeeping AND the twisted sectors pair with the three sphere axions cancelling the rigid 32 T3 residual; KILL = a leftover independent quartic (T3-type) in ANY sector). DECLARED MEASURE ANSATZ (stated before computing): v508 killed every exchange realisation; the delta-1 exploration identified the twisted contact term as the MODULAR COMPLETION of the Atiyah-Bott data with forced leading (T5, T3) ratio 4:3; M2 declares contact_j = (Q^(0) - Q^(j))/det_j -- in the channel with the g^j zero-mode normalisation 1/det_j the twisted-sector LOOP contributes the UNPHASED sector trace, of which the AB skeleton kept only the phase-weighted insertion part. [E] THE COMPLETION-WEIGHT IDENTITY (the centrepiece): per glue class 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, 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 = class form = (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, 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), 2e(5/8), full Weil sum 4. [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; since executed and DECIDED by v518 -- kill under the derived measure, tension stated -- and the measure question since DECIDED at probe level by v520: the completion reading is now DERIVED at probe level from two independent constructive sources (F-independence + Quillen pairing) under the typed premises TP-1..TP-4 (v520); the residual [O] is the constructive BCOV derivation of the w_m normalisation itself -- since DERIVED at probe level by v523 (CELEST.WP5E.WM.01): 1/det_j is the Atiyah-Bott/zeta-determinant fixed-point factor, computed from three independent sources under the typed premises TP-REG/TP-Q/TP-NUM/TP-CH, and the residual [O] narrows to the GLOBAL BCOV integral beyond the fibre zero-mode factor); SEAM.EQUIV.TWISTOR.01 untouched (preparation, not construction). VERDICT: SUCCESS wording met on the declared completion measure; the KILL does NOT fire; NO marker moves anywhere.

Original classification detail

M2 [E]/[C]/[O] (SUCCESS on the preregistered criterion, on the DECLARED completion measure): M2 executed via v516 -- the completion contact contact_j = (Q^(0) - Q^(j))/det_j carries the exact weight identity w_m = sum_j (1 - i^{jm})/det_j = 4 h_m = |mu4| h_m = -4 ch2(T_m) (the sphere axions pair through their own McKay ch2 charges, no free scale); parameter-free locks (T5 = 0 for any scale, ratio 4:3 reproduced, T3 budget forces c = 4 = |mu4|); every twisted channel becomes the perfect Okubo square 36<x,x>^2/det_j, total 45<x,x>^2 = (5/4) x 36 = Dedekind x Okubo (the v505 S3.8 unique quartic-free weighting); both v508 certificates killed and the v511 psi = 64 slice supplied exactly -- the cubic d-channel is NOT needed (c_d free = 0); controls: wrong scale/shuffle/so16 (KILL fires there)/diag(i,i)/Z2-EH anchor (scale 2 = |Z2|). FENCE [C]: the completion reading (loop = unphased sector trace with the same zero-mode normalisation) is DECLARED within this module, supported by the delta-1 modular-completion finding, NOT derived from the BCOV integral here -- the completion reading is since DERIVED at probe level from two independent constructive sources (F-independence + Quillen pairing) under the typed premises TP-1..TP-4 (v520); the w_m normalisation is now DERIVED at probe level -- 1/det_j is the Atiyah-Bott/zeta-determinant fixed-point factor, computed from three independent sources (v523); the residual [O] narrows to the global BCOV integral beyond the fibre zero-mode factor; no marker moves

Dependencies as recorded

CELEST.SEAM.01; CELEST.WP5E.BETA.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.DELTA2.01; CELEST.WP5E.EPS1.01; CELEST.WP5E.M1.01; SEAM.EQUIV.TWISTOR.01; v495; v502; v505; v508; v511; v513; v514; v515