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Original ledger classification: DECIDED: kill under the derived measure, tension with v516 stated ([E] exact Weil/Q(zeta_8) algebra, loop words + koboundary defects + 1/960 phase arithmetic, ledgers, G = f1 f3, the decision table; [C] the f1f3/KS-weight identification + kernel-family convention + chi_k choice; [O] the BCOV-integral derivation that decides between the declared (v516) and derived (v518) measures -- since decided at probe level by v520 for the declared reading, residual [O] = the constructive w_m derivation; NO marker moves)

Recorded statement: THE DELTA-1 CHAIN OF THE CELESTIAL-HOLOGRAPHIC CONTRACT DECIDED (2026-07-22; CELEST.SEAM.01 WP5e, delta-1b + delta-1c + delta-1d consolidated -- 'the derived chiral measure kills the delta-1 route', an honest, decided NEGATIVE result in…

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Paper context: TFPT — Introduction and reading guide

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CELEST.WP5E.DELTA1.01

Original ledger classification: DECIDED: kill under the derived measure, tension with v516 stated ([E] exact Weil/Q(zeta_8) algebra, loop words + koboundary defects + 1/960 phase arithmetic, ledgers, G = f1 f3, the decision table; [C] the f1f3/KS-weight identification + kernel-family convention + chi_k choice; [O] the BCOV-integral derivation that decides between the declared (v516) and derived (v518) measures -- since decided at probe level by v520 for the declared reading, residual [O] = the constructive w_m derivation; NO marker moves)

Original claim text

THE DELTA-1 CHAIN OF THE CELESTIAL-HOLOGRAPHIC CONTRACT DECIDED (2026-07-22; CELEST.SEAM.01 WP5e, delta-1b + delta-1c + delta-1d consolidated -- 'the derived chiral measure kills the delta-1 route', an honest, decided NEGATIVE result in the v508 style; 30 checks, ~20 s): does the Harvey-Moore/BCOV fundamental-domain integral on PT/Z4, evaluated under a measure DERIVED from blockwise SL(2,Z) covariance of the dressed 16-component Weil system (solved for -- not declared, not scanned), deliver the twisted contact vector -A_fix = -(9,-30,-15,0,32) or the psi = 64 slice? NO. (1) THE 16-COMPONENT WEIL COMPLETION (delta-1c): discriminant module Z4 x Z4 with q = (5x^2+3y^2)/8 mod 1, Gauss sums 2 zeta_8^5 x 2 zeta_8^3 = 4 = sqrt(16) (signature 0 mod 8 = rank E8), exact Q(zeta_8) relations (S^2 = C, (ST)^3 = S^2, S^4 = 1, T^8 = 1), tensor split S = S_D5 (x) S_A3, the diagonal H and anti-diagonal H' the two invariant Lagrangians (both counts = E4: two E8 gluings), P_H S P_H = (1/4) J with 3/4 of every S-image weight on the 12 shifted classes; the 16-vector theta S-covariance CLOSES: the delta-1b E1.5 residual 2.91 = O(1) (naive 4-character rule) drops to ~1e-39, certified at two tau. (2) THE OBSTRUCTION IS A FINITE mu4 CHARACTER, IDENTIFIED (delta-1d): gauge blocks M = G[a,b] eta^{-8} with constant transport (28+ digits) recognised as exact 1/960-grid phases (1e-25); T-fixed pairs carry t = e(-1/2) = -1 EXACTLY (the naked level-matching defect); loops in Gamma_1(4) resp. Gamma_0(2)+-, joint holonomy eigenspaces dim 8/16 resp. 6/16, every eigen-phase of order <= 4; KOBOUNDARY TEST: the SL(2,Z) relation defects c_{S^4}, c_{(ST)^3 S^-2}, c_{[S^2,T]} are (1,1,1) EXACTLY on all 15 pairs -- the multiplier system is a CHARACTER of the orbit stabilisers, not a genuine 2-cocycle; on Gamma_1(4) it is lambda(gamma) = i^{2B + C/4}. (3) THE CANCELLATION EXISTS AND IS THE TWISTED FIBRE BLOCK f1 f3, NOT THE THREE SPHERE AXIONS: exact identity G[a,b] = f_1 f_3 (30+ digits; the axion T-phases are v502 vacuum-energy data); the T-fix mechanism is one line of exact phase arithmetic, (-1) x e(-1/6) = e(1/3) = chi_4(T) at every T-fixed node; CANCELLATION TABLE (exact, minimal residual order over eta^m x chi_k): none -> 4, f1f2f3 (the three sphere axions) -> 4, f2 -> 6, f1f3 -> 1 (hol AND anti), wrong weights (1,1,2)/(2,2,2) -> 4; the strict solutions are exactly chi_4 (dims (3,3)) and chi_10 (dims (1,1)) at eta^0, certified on the dressed functions at a fresh tau (1e-15, NO residual multiplier). (4) THE DECISION -- ALL THREE TESTERS FAIL: under both derived solutions the integral (30-digit kernels, negative-exponent cell audit, cut-6 vs cut-8 scan) fails T5(V) = 0 (fractions 0.5 / 0.83), fails W_2 : W_13 = 4 : 3 (W_13 = 0), fails V = -A_fix N (spreads 1.05 / 1.47) and the psi = -64 N slice; the honest (N1, N2) orbit rebalance: chi_4 reaches T5 = 0 only at psi > 0 (wrong sign), chi_10 only at N2/N1 = -4 < 0 (outside the orbifold projector) -- no branch fires anywhere in the positive cone: a GENUINE KILL on the derived surface. (5) NEGATIVE CONTROLS: Z2/Eguchi-Hanson (gauge-only residual order 2 -- the mu4 defect is Z4-specific -- and the SAME fibre dressing cancels it to 1: the mechanism replicates at the anchor); SO(16)/D8 (only even sectors survive, all axion b-characters in mu_2: the order-4 supply structurally absent); wrong discriminant form (x^2+y^2)/4 (|Gauss|^2 = 64 != 16, its S-rule fails at O(1) on the true thetas); wrong signature factor (S^2 = C breaks exactly). [C] FENCES: the f1f3 = KS-weight identification (deck weights (1,3) = the twistor fibre weights (+1,-1 mod 4) forced by the v514 incidence ledger -- exact match, NOT a complete BCOV derivation); the kernel-family convention (J(Delta,0/1/2) from weight bookkeeping); the discrete chi_k choice (both members evaluated, both fail -- the kill does not depend on it). TENSION, STATED HONESTLY (the mandatory fence): the DECLARED completion reading (v516/M2) delivers the psi = 64 slice and cancels 32 T3; the DERIVED chiral measure (v518) fails all three testers -- both are exact; the sharp open question is which of the two is the true BCOV measure (the declared reading is supported by the delta-1 modular-completion finding but not derived; the derived measure rests on the f1f3 identification). Neither result is hidden behind the other. [O] the BCOV-integral derivation on PT/Z4 that decides between the two measures -- the single open item of the delta-1 strand; the twisted-contact route of v508 S6.2 is DECIDED NEGATIVE under the derived measure. SINCE DECIDED at probe level by v520 in favour of the declared reading: single-valuedness is derived from two independent constructive sources (F-independence + Quillen pairing), the chi_4 route was never a well-defined nonvanishing moduli integral -- the kill of this module is SHARPENED (the column-canonicalised chi_4 member is boundary-consistent yet tester-dead); the residual [O] is the constructive w_m derivation. Discovery provenance: delta-1b (30/30), delta-1c (31/31), delta-1d (36/36) probes in experiments/tfpt-discovery/ (2026-07-22). NO marker moves anywhere.

Original classification detail

DECIDED (negative under the derived measure): the delta-1 chain is closed -- the derived chiral measure kills the route, the v516 declared-measure tension is the named [O]; since decided at probe level by v520 in favour of the declared reading (kill sharpened; residual [O]: the constructive w_m derivation)

Dependencies as recorded

CELEST.SEAM.01; CELEST.WP5E.M2.01; CELEST.WP5E.M3.01; CELEST.WP5E.EPS1.01; CELEST.WP5E.GAMMA.01; CELEST.WP5E.DELTA2.01; CELEST.DTERM.NONDERIV.01; SEAM.EQUIV.TWISTOR.01; v502; v505; v508; v511; v513; v514; v515; v516; v517

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  • v518_celestial_wp5e_delta1_derived_kill.pyRegistered verification module · frontier
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    CELEST.WP5E.DELTA1.01: the delta-1 chain (delta-1b + delta-1c + delta-1d) of the celestial-holographic research contract CELEST.SEAM.01 DECIDED -- 'the derived chiral measure kills the delta-1 route', an honest, decided NEGATIVE result (v508 style): does the Harvey-Moore/BCOV fundamental-domain integral on PT/Z4, evaluated under a measure DERIVED from blockwise SL(2,Z) covariance (solved for, not declared, not scanned), deliver -A_fix = -(9,-30,-15,0,32) or the psi = 64 slice? NO -- every member of the derived family fails all three preregistered testers (30 checks, ~20 s). [E] THE 16-COMPONENT WEIL COMPLETION (delta-1c): discriminant module Z4 x Z4 with q = (5x^2+3y^2)/8; Gauss sums 2 zeta_8^5 x 2 zeta_8^3 = 4 = sqrt(16) (signature 0 mod 8 = rank E8); S symmetric + unitary, S^2 = C, (ST)^3 = S^2, S^4 = 1, T^8 = 1 EXACTLY in Q(zeta_8); S = S_D5 (x) S_A3; the diagonal H and anti-diagonal H' are the two invariant Lagrangians (both counts = E4: two E8 gluings); P_H S P_H = (1/4) J with 3/4 of every S-image weight on the 12 shifted classes -- why the naive 4-character rule failed; the 16-vector theta S-covariance CLOSES: the delta-1b E1.5 residual 2.91 = O(1) drops to ~1e-39, certified at two tau. [E] THE OBSTRUCTION IS A FINITE mu4 CHARACTER, IDENTIFIED (delta-1d): gauge blocks M = G[a,b] eta^{-8} have constant transport (t_p, s_p) (28+ digits) recognised as exact 1/960-grid phases (1e-25); T-fixed pairs (0,b) carry t = e(-1/2) = -1 EXACTLY (the naked level-matching defect); loops land in Gamma_1(4) resp. Gamma_0(2)+-, joint holonomy eigenspaces dim 8/16 resp. 6/16, every eigen-phase of order <= 4 (the group is mu_4); KOBOUNDARY TEST: the SL(2,Z) relation defects c_{S^4}, c_{(ST)^3 S^-2}, c_{[S^2,T]} are (1,1,1) EXACTLY on all 15 pairs -- a CHARACTER of the stabilisers, NOT a genuine 2-cocycle; on Gamma_1(4): lambda(gamma) = i^{2B + C/4}. [E] THE CANCELLATION IS THE TWISTED FIBRE BLOCK f1 f3, NOT THE THREE SPHERE AXIONS: exact identity G[a,b] = f_1 f_3 (30+ digits); axion T-phases = v502 vacuum-energy data; T-fix mechanism one line of exact phase arithmetic: (-1) x e(-1/6) = e(1/3) = chi_4(T) at every T-fixed node; CANCELLATION TABLE (exact, minimal residual order over eta^m x chi_k): none -> 4, f1f2f3 (three sphere axions) -> 4, f2 -> 6, f1f3 -> 1 (hol AND anti), wrong weights (1,1,2)/(2,2,2) -> 4; strict solutions exactly chi_4 (dims (3,3)) and chi_10 (dims (1,1)) at eta^0, certified on the dressed functions at a fresh tau (1e-15, NO residual multiplier). [E] THE DECISION -- ALL THREE TESTERS FAIL: under both derived solutions the integral (30-digit kernels, negative-exponent audit, cut-6 vs cut-8 scan) fails T5(V) = 0 (fractions 0.5 / 0.83), fails W_2 : W_13 = 4 : 3 (W_13 = 0), fails V = -A_fix N (spreads 1.05 / 1.47) and the psi = -64 N slice; the honest (N1, N2) rebalance: chi_4 reaches T5 = 0 only at psi > 0, chi_10 only at N2/N1 = -4 < 0 (outside the orbifold projector) -- no branch fires in the positive cone. [E] NEGATIVE CONTROLS: Z2/Eguchi-Hanson (gauge-only residual order 2 -- the mu4 defect is Z4-specific -- and the SAME fibre dressing cancels it to 1); SO(16)/D8 (only even sectors, all axion b-characters in mu_2: the order-4 supply structurally absent); wrong form (x^2+y^2)/4 (|Gauss|^2 = 64 != 16, S-rule fails at O(1)); wrong signature (S^2 = C breaks exactly). [C] the f1f3 = KS-weight identification (deck weights (1,3) = the twistor fibre weights (+1,-1 mod 4) forced by the v514 incidence ledger -- exact match, NOT a complete BCOV derivation) + the kernel-family convention (J(Delta,0/1/2) from weight bookkeeping) + the discrete chi_k choice (both evaluated, both fail). TENSION, stated honestly (the mandatory fence): the DECLARED completion reading (v516/M2) delivers the psi = 64 slice and cancels 32 T3; the DERIVED chiral measure (this module) fails all three testers -- both are exact; the sharp open question is which of the two is the true BCOV measure (the declared reading is supported by the delta-1 modular-completion finding but not derived; the derived measure rests on the f1f3 identification). Neither result is hidden behind the other. [O] the BCOV-integral derivation on PT/Z4 that decides between the two measures -- the single open item of the delta-1 strand; the twisted-contact route of v508 S6.2 is DECIDED NEGATIVE under the derived measure. Discovery provenance: delta-1b (30/30), delta-1c (31/31), delta-1d (36/36) probes in experiments/tfpt-discovery/ (2026-07-22). NO marker moves anywhere.

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