{
  "schema": "gap04_uv1_optionB_resummed_determinant_v1",
  "object": "OPTION B stability pass for B-UQFC-14-UV-1: is W_sigma = (1/2)Str log D_sigma^2 (full BV/BRST tower of the corpus spin-c Dirac D_sigma) bounded below as sigma -> -inf (Vol(K6)->0) under the frozen prescription?",
  "outcome": "NEEDS-AXIOM",
  "partA_full_tower_inputs": {
    "note": "Guard (1): the FULL nine-row gauge-fixed BV/BRST tower (metric+gauge+moduli+Higgs+chiral-fermion+ghost+projected+Weyl-rigid) inside the SINGLE operator D_sigma. n_B, n_F, Str[1] are banked, forced by the spin-c index -3.",
    "n_B": 35,
    "n_F": 90,
    "Str_identity_nB_minus_nF": -55,
    "per_dof_pole_residue_r0": -0.08120496685733616,
    "d_eff_collapse_slice": 3,
    "scalar_zeta_pole_at_minus_half_c_half": 0.28786411243788057,
    "residue_R_scheme_invariant": -0.08120496685733616,
    "finite_part_F_scheme_dependent": true
  },
  "partB_optionB_criterion": {
    "criterion_name": "Option-B boundedness criterion: (1/2)Str log D_sigma^2 is regulator-invariantly bounded below as sigma->-inf IFF the graded multiplicative anomaly cancels (Str_pole == 0) AND the surviving finite part is scheme-independent.",
    "sigma_linear_coefficient_object": "coeff of (-sigma) in W_sigma = Str[zeta_{D_0}(0)]-type graded heat-kernel number on the d_eff=3 slice -- the multiplicative anomaly of Str log D_sigma^2",
    "pole_present_d_eff_odd": true,
    "graded_pole_residue_Str_pole": 4.466273177153489,
    "graded_pole_cancels_Str1_eq_0": false,
    "Str1_integer": -55,
    "finite_part_scheme_independent": false,
    "optionB_closes": false
  },
  "partC_determinant_line_orientation": {
    "determinant_line": "canonical spin-c / Quillen determinant line of the index-(-3) bundle; BRST P_BRST restricts the one-loop determinant to the three physical channels (SELECTOR_DETERMINANT_CHANNEL_AUDIT, status D).",
    "fixes_fermion_global_phase": true,
    "phase_is_sigma_invariant_topological": true,
    "fixes_bosonic_logdet_lower_bound": false,
    "rescues_optionB": false,
    "reason": "The forced orientation is a sigma-INVARIANT (index -3) global PHASE of the FERMION determinant. A sigma-invariant phase cannot produce a sigma-LINEAR lower bound on the collapse ray, and it acts on the wrong (fermion, not bosonic K6-Casimir) sector. With Str[1]=-55 != 0 the bosonic multiplicative anomaly does not cancel, so no residual determinant-line phase converts it into a regulator-invariant bound. The determinant line does NOT rescue Option B."
  },
  "partD_finite_order_consistency_guard4": {
    "role": "CONSISTENCY ONLY (guard 4); NOT load-bearing for the verdict.",
    "a4_relative_sign": "DISPUTED/owner-locked (prior wall + convention runs)",
    "a6_sign": "OPEN (only tr[E^3]=+1/6 derived; c1..c8 + K6 K5..K8 missing)",
    "consistency": "The resummed-determinant obstruction (non-cancelling s=-1/2 pole, scheme-dependent finite part) is CONSISTENT with the banked finite-order picture (Lemma 1: along sigma->-inf no finite heat-kernel truncation is licensed to decide global stability). Neither the finite-order coefficients NOR a target value were used to reach the Option-B verdict; they only corroborate it."
  },
  "proven_inequality_or_obstruction": "Str_pole = r0 * Str[1] = (-0.081205)(-55) = 4.466273 != 0 -- the graded multiplicative anomaly of (1/2)Str log D_sigma^2 does NOT cancel (Str[1] = n_B - n_F = 35 - 90 = -55, an INTEGER forced by the spin-c index -3). On the d_eff=3 (ODD) collapse slice the scalar zeta has a simple POLE at s=-1/2 (c_half=0.28786 != 0), so the zeta-regularized log-det carries a multiplicative anomaly whose finite part is scheme-DEPENDENT (flips with mu). Therefore NO regulator/basis-independent lower bound on (1/2)Str log D_sigma^2 exists as sigma -> -inf: the sign of the would-be bound rides on the same unfilled CONVENTION_FREEZE the prior runs isolated.",
  "buried_premise_CFCA_stage4": "Option B's buried premise (CFCA Stage 4) is that (1/2)Str log D_sigma^2 admits a basis/regulator-INDEPENDENT lower bound. The premise is FALSE on this geometry: the resummed determinant is a zeta-regularized log-det on a d_eff=3 (ODD) slice, where zeta has a simple pole at s=-1/2; the associated multiplicative anomaly is exactly the graded supertrace residue Str_pole = r0*Str[1], which the banked run PROVED non-zero because the spin-c index -3 forces Str[1] = n_B - n_F = -55 != 0 (no bosonic partners for the 90 chiral fermionic dof). The determinant route therefore inherits the int_loop convention fight in its sharpest form. This is NOT 'the calculation fails' (guard 5): it is a PROVEN non-cancellation (an integer Str[1] != 0) that demonstrates no regulator-invariant bound can exist for the bare determinant -- a structural death condition for Option B, published rather than papered over.",
  "acceptance_tests": {
    "A_spectral_positivity_Str_F_>=_Ae^-psigma_-_B": "NOT the Option-B object (that is the SPECTRAL ACTION route). Under the named axiom B-UQFC-14-UV-1 the spectral action Str f >= 0 holds by construction; but that is Option A, and it is AXIOM-CONDITIONAL, not a proof of Option B.",
    "B_resummed_determinant_bounded_below": "FAILS to close unconditionally: the graded s=-1/2 pole does NOT cancel (Str_pole = +4.466 != 0), so (1/2)Str log D_sigma^2 has a scheme-dependent multiplicative anomaly and NO regulator-invariant lower bound. This is the precise obstruction.",
    "C_phase_exit_before_runaway": "NOT decided here (sibling Option-C object). The frozen companion (FREEZE-4: sigma_* = (1/2)ln R_K6_0 ~ 1.70 EFT-validity boundary) is available but its PROOF is the Option-C pass, not Option B."
  },
  "named_axiom_if_needed": "B-UQFC-14-UV-1 (SPECTRAL-ACTION UV-COMPLETION AXIOM): the fundamental UV object is the SPECTRAL ACTION Str f(D_sigma^2/Lambda^2) with a POSITIVE cutoff profile f >= 0 (positive UV spectral measure), NOT the bare resummed determinant (1/2)Str log D_sigma^2. UNDER this axiom the UV object is manifestly positive (a sum of f(eigenvalue^2/Lambda^2) >= 0 over the real non-negative spectrum of D_sigma^2) and carries NO subtraction, so the multiplicative-anomaly / int_loop convention fight that blocks Option B cannot arise -- the load-bearing sign becomes a positive MOMENT f_k > 0 of a positive profile, not a choosable scheme constant. The axiom replaces the resummed determinant with the spectral action as the primitive UV functional; it is DECLARED irreducible (CFCA 0.4), not derived. Honesty guard: if the true UV completion lacks a positive spectral measure, this single named axiom is where the downstream bounded-below/phase-exit theorem rests -- same hardness class as Lambda (guard 6), NOT the same solved problem.",
  "well_verdict": "OPTION B (RESUMMED DETERMINANT) DOES NOT CLOSE UNCONDITIONALLY; IT NEEDS THE NAMED AXIOM. The honest endpoint: the bare functional determinant (1/2)Str log D_sigma^2 is NOT regulator-invariantly bounded below as sigma -> -inf, because its graded multiplicative anomaly -- the s=-1/2 supertrace pole residue Str_pole = (-0.08120)(-55) = +4.466 -- does NOT cancel. The non-cancellation is FORCED by a banked theorem (the spin-c index -3 makes Str[1] = n_B - n_F = -55 an integer != 0), NOT a fresh convention, and it is precisely the determinant-route ambiguity the freeze flagged. The determinant line / Quillen orientation fixes only the sigma-invariant FERMION phase (index -3), not the bosonic K6-Casimir log-det bound, so it does not rescue B. WHAT SUFFICES is the single named UV-completion axiom B-UQFC-14-UV-1: take the SPECTRAL ACTION Str f(D_sigma^2/Lambda^2) with a POSITIVE profile f>=0 as the primitive UV object instead of the bare determinant; under it the UV functional is manifestly non-negative and the load-bearing sign becomes a positive moment f_k>0 (unchoosable), removing the multiplicative-anomaly fight. The axiom is DECLARED irreducible, not derived; its relationship to Lambda is same-hardness-class, not same-solved-problem. Both STANDS and RUNAWAY remain live for the BARE determinant; the axiom is the route by which a positive UV functional (Option A) supersedes the determinant route -- which is why Option A, not Option B, is where the frozen functional was already placed.",
  "integrity_guards_attest": {
    "1_full_gauge_fixed_tower": "Full nine-row BV/BRST tower used (n_B=35, n_F=90 inside the single D_sigma). NOT scalar-only / bosonic-only.",
    "2_no_target_loading": "No sign/branch chosen from STANDS. The committed c_loop=1.3637877e-5 was NEVER opened and entered NO sign decision; the verdict rides on the INTEGER Str[1]=-55 (index -3), which is target-blind and outcome-blind. The unfavorable NEEDS-AXIOM endpoint is reported, not STANDS.",
    "3_no_anthropic": "Runaway stays live; boundedness NOT asserted by 'we exist'.",
    "4_finite_order_consistency_only": "a4/a6/a8 appear only as a consistency corroboration (Part D); the verdict rides on the multiplicative-anomaly pole structure + the integer Str[1], never on a finite-order coefficient sign. Lemma 1 (finite-order undecidability) respected.",
    "5_boundedness_or_phase_exit_proven_not_calc_fails": "The endpoint is NOT 'the calculation fails'. It is a PROVEN non-cancellation: Str[1] = -55 is an integer != 0 forced by the index, so the multiplicative anomaly provably survives and no regulator-invariant bound for the BARE determinant exists. No physical -inf is asserted; the collapse safety is deferred to the positive-functional (Option A) route under the named axiom.",
    "6_lambda_scope_preserved": "No claim to solve Lambda. The axiom's relationship to Lambda is explicitly 'same hardness class, not same solved problem'.",
    "7_axiom_named_not_disguised": "The result is NAMED as the UV-completion axiom B-UQFC-14-UV-1 (spectral-action positive measure), NOT disguised as a derived boundedness theorem for the determinant.",
    "8_no_leans_language": "No 'leans/leaning runaway' language. Both branches stated as live for the bare determinant; the spectral-action route is the named axiom."
  },
  "what_requires_chris": "(1) Whether to ADOPT B-UQFC-14-UV-1 (positive UV spectral measure / spectral action as the primitive UV object) -- an owner-level UV-completion choice, the irreducible declared input. (2) If the bare resummed determinant is to be retained instead, the named FRG-2 NLO Litim shell-projection SCHEME that fixes the multiplicative-anomaly finite part (the unfilled CONVENTION_FREEZE slot, B-UQFC-14-FRG-2) -- but Option B has now PROVEN that without such a scheme choice the determinant has no regulator-invariant lower bound, so the bare-determinant route cannot close data-blind.",
  "no_target_loading_attest": "No observed value entered on any input side (no A_s, Lambda_obs, r, eta_B, n_s, N_eff, PDG, Omega_DM, H_0, S_8). The committed c_loop magnitude was NEVER read. The verdict rests on the banked integer Str[1]=-55 (spin-c index -3), the banked s=-1/2 pole (d_eff=3 zero-weight tower), and the banked scheme-dependence of the finite part -- all target-blind. The favorable CLOSES-wall was NOT forced: Option B is reported as NEEDS-AXIOM.",
  "provenance": {
    "Fable_Quantum.md_sha256": "cff0bf0cecdaa6eda26798c2ceafa4b53f72e90fbd767d31a1bce7ed319ff318",
    "Fable_GUT_3.md_sha256": "6c1a1561167053c84e5cf2b366294af47e03c2d063db4f7f246c107f02779652",
    "SELECTOR_DETERMINANT_CHANNEL_AUDIT.md_sha256": "931125f939d3cc864427850b4bfa6f146c048bd8c90da98cfd537e07748961d4",
    "uv1_frozen_functional_result.json_sha256": "fbdfed7b85e2481ff6788c02529565c5449e8da622b07e5d11233b705cd8d2de",
    "prior_supertrace_sha256": "70613b34b4360367180018dadf1b555d339108668c012eec428474f70fd6945c",
    "prior_zeta_sha256": "5fe5535f6d4d34fb3952c9c4ec3eaf992fe1f4a374a7514400ca28a21ec8a0ad",
    "mpmath_used": true
  },
  "non_promotion": "no gate flipped; no status word emitted for any gate. Option-B resummed-determinant stability pass only; terminal state NEEDS-AXIOM (B-UQFC-14-UV-1), both branches live for the bare determinant."
}