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Original ledger classification: DECIDED at probe level for the declared reading ([E] exact Weil/Q(zeta_8) algebra, exact invariant subspace, characters + 1/960 grid, ledgers, levelwise 4-design, Z2 anchor arithmetic, change-of-variables corollary, controls; numeric documented: transports 28+ digits, SVD memberships 1e-8/1e-3, certificates fresh tau, HM kernels 30+ digits; [C] the typed premises TP-1..TP-4; [O] the constructive BCOV derivation of w_m -- since DERIVED at probe level by v523, narrowing the [O] to the global BCOV integral beyond the fibre zero-mode factor; NO marker moves)

Recorded statement: THE WP5E BCOV MEASURE QUESTION DECIDED AT PROBE LEVEL (2026-07-22; delta-1e + delta-1f consolidated in the v518 style, one module, 39 checks, ~20 s; ERFOLG-A on the preregistered decision layer): which of the two exact, mutually…

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Paper context: TFPT — Introduction and reading guide

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CELEST.WP5E.MEASURE.01

Original ledger classification: DECIDED at probe level for the declared reading ([E] exact Weil/Q(zeta_8) algebra, exact invariant subspace, characters + 1/960 grid, ledgers, levelwise 4-design, Z2 anchor arithmetic, change-of-variables corollary, controls; numeric documented: transports 28+ digits, SVD memberships 1e-8/1e-3, certificates fresh tau, HM kernels 30+ digits; [C] the typed premises TP-1..TP-4; [O] the constructive BCOV derivation of w_m -- since DERIVED at probe level by v523, narrowing the [O] to the global BCOV integral beyond the fibre zero-mode factor; NO marker moves)

Original claim text

THE WP5E BCOV MEASURE QUESTION DECIDED AT PROBE LEVEL (2026-07-22; delta-1e + delta-1f consolidated in the v518 style, one module, 39 checks, ~20 s; ERFOLG-A on the preregistered decision layer): which of the two exact, mutually contradictory measures on PT/Z4 is the true BCOV measure -- (A) the DECLARED completion reading (v516: unphased sector trace, w_m = 4 h_m, supplies psi = 64) or (B) the DERIVED chiral measure (v518: multiplier character chi_4 on Gamma_1(4); all three testers fail)? ANSWER: single-valuedness of the physical one-loop lattice factor is DERIVED from two independent constructive sources, not postulated, and the completion reading (A) wins. (1) THE INVARIANT SUBSPACE (delta-1e D2): dim_Q {v : rho(T) v = v, rho(S) v = v} = 8 = 4 x 2 in the dressed 16-component Weil system (exact rational nullspace); EVERY kernel vector lies in the Q(zeta_8)-span of {e_H, e_H'} -- the two Lagrangian gluings, both theta = E4, level-1 quartic = Q^(0) = the unphased trace; strict trivial-character solutions at physical weight (m, k) = (0, 0): ZERO for every dressing (11 combinations, both orientations). (2) SOURCE 1 -- THE F-LEMMA (delta-1f A1): the only strict chiral families are chi_4 (dims (3,3)) and chi_10 (dims (1,1)), both with nontrivial T-character EXACTLY; the canonical column-matched chi_4 member's total block sum obeys G(gamma tau) = chi_4(gamma) G(tau) pointwise (certificate 3.9e-16 over two fresh tau, nonvacuous |G| >= 59.6); EXACT change of variables: fundamental-domain independence forces int = 0 for EVERY chiral integrand -- under TP-1 + TP-2 the chiral route can never source psi = 64: the v518 route was never a well-defined nonvanishing moduli integral (the kill is SHARPENED, its unfolded values are convention bookkeeping). (3) SOURCE 2 -- THE QUILLEN PAIRING (delta-1f A2): |t conj(t) - 1| < 8.3e-40 on all 15 pairs and both generators (measured unitarity); |chi_4|^2 = 1 exactly vs one-sided chi_4^2 = e(2/3) != 1 (T-fixed: 640 != 0 mod 960, 15/15 defective); the doubled 256-dim hol x antihol Weil system closes STRICTLY at trivial character and physical weight (nullspaces (28, 17) >= 11), contains the unphased diagonal (~2e-15) AND the physical columns w_b (x) conj(w_b) (sigma 4.9e-16/8.3e-16); negative control hol (x) hol: EMPTY nullspace (0, 0). (4) CONSISTENCY CLOSURE (delta-1f A3): the forced unphased numerator inside the v518 scaffold reproduces sum_m V prop (1, 2, 1, 0, 0) = <x,x>^2 EXACTLY on every level n <= 8 (levelwise Okubo/4-design); J-weighted spreads ~5e-41, T5/T3 fractions ~7e-42, zero negative-exponent cells; psi(skeleton) = +0.2302 = -psi(contact) -- the J-weighted mirror image of psi(A_fix) = +64 / psi(contact) = -64; linearity 4.6e-41: the circle to v516 is CLOSED. (5) D3 -- THE Z2/EH ANCHOR (delta-1e): only the declared reading hits the anchor (9<x,x>^2 = (1/4) x 36<x,x>^2, psi(A_2) = -8, scale tooth c = 1/2 = |Z2| h^(A1) unique); ALL THREE derived Z2 instantiations fail the anchor testers (spreads 1.12/0.895/0.516, psi sign wrong). (6) D1 -- COLUMN CANONICALISATION (delta-1e): the physical AB column sum_m i^(bm) e_(m,m) is contained EXACTLY in the chi_4 family (sigma 1.8e-16/1.7e-16, one scalar per orbit -- canonicalising the (N1, N2) freedom); the canonical member STILL fails every tester (sharpened kill). NEGATIVE CONTROLS: SO(16)/D8 (T5 = 20/T3 = -40 exact, mu_2-only supply), wrong form (|Gauss|^2 = 64 != 16, S^2 = C breaks), wrong weight (transport dev 0.78 at exponent 2), shuffled weights (T5 = -14/T3 = 36), planted family detected (1.5e-16), hol (x) hol empty. [C] TYPED PREMISES (the mandatory fence): TP-1 (the twisted one-loop contribution is an F-independent moduli-space integral), TP-2 (it is nonzero -- it must source psi = 64), TP-3 (the v518 kernel-family weight convention), TP-4 (BCOV F1 is Quillen/Ray-Singer: the one-loop factor pairs hol x conj(hol)). [O] the constructive BCOV derivation of the w_m normalisation itself (the residual open item) -- since executed and DERIVED at probe level by v523 (CELEST.WP5E.WM.01: Atiyah-Bott mode ledger + zeta/Quillen determinant + consistency chain, typed premises TP-REG/TP-Q/TP-NUM/TP-CH); the residual [O] narrows to the GLOBAL BCOV integral on PT/Z4 beyond the fibre zero-mode factor; SEAM.EQUIV.TWISTOR.01 stays Open. Discovery provenance: delta-1e (28/28) and delta-1f (23/23) probes in experiments/tfpt-discovery/ (2026-07-22). NO marker moves anywhere.

Original classification detail

DECIDED (ERFOLG-A at probe level): single-valuedness is derived from two independent constructive sources (F-independence + Quillen pairing) under the typed premises TP-1..TP-4; the v516 completion reading wins, the v518 kill is sharpened; residual [O]: the w_m normalisation is since DERIVED at probe level by v523 (1/det_j = the Atiyah-Bott/zeta-determinant fixed-point factor, three independent sources); what remains open is the global BCOV integral beyond the fibre zero-mode factor

Dependencies as recorded

CELEST.SEAM.01; CELEST.WP5E.M2.01; CELEST.WP5E.DELTA1.01; SEAM.EQUIV.TWISTOR.01; v502; v505; v508; v511; v514; v515; v516; v517; v518

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Registered verification modules

  • v520_celestial_wp5e_measure_decision.pyRegistered verification module · frontier
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    CELEST.WP5E.MEASURE.01: the WP5e BCOV measure question DECIDED at probe level (delta-1e + delta-1f consolidated, v518 style) -- 'single-valuedness is derived, the completion reading wins': which of the two exact, contradictory measures on PT/Z4 is the true BCOV measure, (A) the DECLARED completion reading (v516) or (B) the DERIVED chiral measure (v518)? ERFOLG-A on the decision layer (39 checks, ~20 s). [E] INVARIANT SUBSPACE: dim_Q {v: rho(T) v = v, rho(S) v = v} = 8 = 4 x 2 in the dressed 16-component Weil system, EVERY kernel vector in the Q(zeta_8)-span of {e_H, e_H'} (the two Lagrangian gluings, both theta = E4, level-1 quartic = Q^(0) = the unphased trace); strict trivial-character solutions at (m, k) = (0, 0): ZERO for every dressing (11 combinations). [E] SOURCE 1 (F-LEMMA): the only strict chiral families chi_4 (dims (3,3)) and chi_10 (dims (1,1)) carry nontrivial T-characters exactly; pointwise covariance of the canonical column member certified (3.9e-16, |G| >= 59.6); exact change of variables => fundamental-domain independence forces int = 0 for EVERY chiral integrand -- the v518 route was never a well-defined nonvanishing moduli integral (kill sharpened). [E] SOURCE 2 (QUILLEN PAIRING): |t conj(t) - 1| < 8.3e-40 on all 15 pairs/both generators; |chi_4|^2 = 1 exact vs one-sided chi_4^2 = e(2/3) != 1 (T-fixed: 640 != 0 mod 960, 15/15 defective); the doubled 256-dim hol x antihol system closes strictly at trivial character and physical weight (nullspaces (28, 17) >= 11), contains the unphased diagonal (~2e-15) AND the physical columns w_b (x) conj(w_b) (sigma 4.9e-16/8.3e-16); negative control hol (x) hol: empty nullspace (0, 0). [E] CONSISTENCY CLOSURE: the forced unphased numerator in the v518 scaffold reproduces sum_m V prop (1, 2, 1, 0, 0) = <x,x>^2 exactly on every level n <= 8; J-weighted spreads ~5e-41, T5/T3 ~7e-42, zero negative cells; psi(skeleton) = +0.2302 = -psi(contact), the J-weighted mirror image of psi(A_fix) = +64 / psi(contact) = -64; linearity 4.6e-41 -- the circle to v516 is closed. [E] D3 Z2/EH ANCHOR: only the declared reading hits (9<x,x>^2 = (1/4) x 36, psi = -8, scale tooth c = 1/2 = |Z2| h^(A1)); all three derived instantiations fail (spreads 1.12/0.895/0.516, psi sign wrong). [E] D1 COLUMN CANONICALISATION: the physical AB column sum_m i^(bm) e_(m,m) is EXACTLY contained in the chi_4 family (sigma 1.8e-16/1.7e-16, one scalar per orbit -- canonicalises the (N1, N2) freedom); the canonical member still fails all testers. [E] NEGATIVE CONTROLS: SO(16)/D8 (T5 = 20/T3 = -40 exact, mu_2-only), wrong form (|Gauss|^2 = 64), wrong weight (dev 0.78), shuffle (T5 = -14/T3 = 36), planted family detected (1.5e-16), hol (x) hol empty. [C] TYPED PREMISES (the mandatory fence): TP-1 (F-independent moduli integral), TP-2 (nonvanishing -- must source psi = 64), TP-3 (v518 kernel convention), TP-4 (Quillen structure of BCOV F1). [O] the constructive BCOV derivation of the w_m normalisation itself. VERDICT: ERFOLG-A per the preregistered criteria (both sources independent, the consistency closure carries); the [O] question 'which is the true BCOV measure' is DECIDED at probe level in favour of (A) under TP-1..TP-4. SEAM.EQUIV.TWISTOR.01 stays Open; NO marker moves.

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