{
  "schema": "gap04_convention_audit_result_v1",
  "purpose": "Decide whether the sign of c_a4_K6_S2 is a FREE heat-kernel convention or PINNED by the corpus's own conventions.",
  "resolution": "IRREDUCIBLE-owner-must-rule",
  "resolution_reason": "The corpus curvature-sign convention is SINGLE and pins the a_4 cross-DENSITY POSITIVE (FACT A,B,C). The negativity of as-run c_a4 is the genuine global one-loop prefactor -(1/2) acting on that POSITIVE density (FACT E) -- NOT an inconsistent extra minus. The single one-loop convention V^(1-loop) = -(1/2)(4pi)^{-D/2} sum_n a_n has a GLOBAL prefactor, but a global prefactor does NOT force c_a4 and c_loop to the same SIGN: each term's sign = (global -1/2) x (its OWN integrand). To make c_a4 POSITIVE one must assert that the stored c_loop (FACT D, frozen + WALL value, F6-guarded) already absorbed a -(1/2) acting on a NEGATIVE underlying density, then MATCH a_4's relative sign to c_loop. But c_loop's underlying-density sign is NEVER established (z_renormalized_c_loop.py reads c_loop as a frozen inherited number and applies no -(1/2); TOE_FINAL records c_loop as OPEN / not computed from first principles, positivity merely assumed and guarded by F6). So the RELATIVE one-loop sign is NOT resolvable data-blind: BOTH branches are live -- BRANCH-RUNAWAY (genuine -1/2 on a positive density: c_a4 < 0, dominates the -sigma corner at growth 8 > 6, V -> -inf, a real separate runaway threatening F1) and BRANCH-STANDS (only if the owner rules c_loop's underlying density negative: c_a4 > 0, a positive wall, well stands). This is exactly the OWNER-MUST-RULE this audit ORIGINALLY recorded and gap04_disjointness.py flagged (convention_dependent). NOT target-loaded; NOT forced to 'stands'.",
  "provenance_hashes": {
    "gilkey_a4_cross_terms.json": "86ea94dff5efdb295432dfcd494bae18aebc0b0bf44db181d090ddb29fe10845",
    "veff_coefficients_frg4.yaml": "9bf1d45871adcf67d754a3908c67eb6ad9d36780d4ef29336ea932c8705fa0ac",
    "gilkey_a4_cross_terms.py": "6e58698a4658ff1f49847617d8a236be8321f2c97227f570829111ba3208212d"
  },
  "facts": {
    "FACT_A_curvature_registry_single_signed": true,
    "FACT_A_values": {
      "R_K6_0": 30.0,
      "R_S2_0": 2.0
    },
    "FACT_B_a4_master_R2_coeff_is_5_over_360": true,
    "FACT_B_cross_prefactor_1_over_36": 0.027777777777777776,
    "FACT_C_a4_cross_density_sign_pre_oneloop": "+",
    "FACT_C_density_value_pre_oneloop": 1.193945858645035e-07,
    "FACT_D_c_loop_frozen_sign_positive_loadbearing_F6": true,
    "FACT_D_c_loop_value": 1.3637166327064904e-05,
    "FACT_E_c_a4_negativity_solely_from_one_loop_prefactor": true,
    "ONE_LOOP_SIGN": -0.5,
    "c_a4_K6_S2_value": -5.969729293225176e-08
  },
  "derived": {
    "convention_pins_curvature_sign": true,
    "c_a4_density_sign_under_corpus_convention": "+",
    "c_a4_sign_rides_on_one_loop_prefactor_only": true,
    "as_run_c_loop_and_c_a4_share_one_loop_convention": false,
    "the_single_owner_rule_item": "Does the a_4 (curvature^2) one-loop log-det enter V_eff with the SAME sign as the c_loop KK-Casimir wall? Equivalently: is c_loop's UNDERLYING heat-kernel density NEGATIVE (so the shared global -(1/2) flips a_4's relative sign to + -> well STANDS), or is c_loop a positive Casimir wall under a different bookkeeping (so the genuine global -(1/2) on a_4's own POSITIVE integrand keeps c_a4 NEGATIVE -> a SEPARATE 3-modulus -sigma runaway row)? This is one yes/no, owner-locked; NOT a free landscape. The deciding fact -- the sign of c_loop's underlying density -- is NOT banked in the corpus, so the script CANNOT resolve it data-blind. RECONCILED FINDING (gap04_oneloop_consistency.py v2, 2026-06-14): the genuine single one-loop prefactor -(1/2)(4pi)^{-D/2} is GLOBAL to every a_n, but a global prefactor does NOT force same-SIGN -- sign(c_n)=sign(-1/2)*sign(own integrand). c_a4's integrand is POSITIVE, so the genuine -(1/2) gives c_a4 NEGATIVE (BRANCH-RUNAWAY, the as-run value). c_a4 is POSITIVE only if the owner banks c_loop's underlying density negative (BRANCH-STANDS). Both branches are LIVE; the prior 'well-stands' was a manufactured selection of the favorable branch and is RETRACTED. This stays IRREDUCIBLE-owner-must-rule."
  },
  "implication_for_v10": "v10 'well UNCONDITIONAL in c_loop' lives in the SINGLE-sigma \u00a7II potential V(sigma)=c_KK e^-4s + c_bdry e^-2s + c_Wilson e^-4s + c_loop e^-6s, where the well's robustness comes from c_bdry<0 and the claim is about the c_loop RESIDUE not threatening the well. The a_4 cross-term e^-(8s+4r+chi) is a THREE-modulus FRG-4 object NOT present in the \u00a7II potential. So v10's 'unconditional in c_loop' is literally true AS STATED (it quantifies over c_loop), but it does NOT cover the a_4 cross-term. The FRG-4 result does not refute v10's c_loop claim; it raises a SEPARATE FRG-4 object whose sign is the owner-rule item above. RECONCILED: v10's Section-II unconditional-in-c_loop claim is TRUE AS STATED and requires NO erratum -- it quantifies over the single-sigma c_loop residue, not the 3-modulus a_4 cross-term. NOTE (countersign correction): the v10 'no erratum' finding is correct on its own terms, but it does NOT imply the FRG-4 3-modulus well stands -- the a_4 cross-term's relative one-loop sign is owner-locked with both branches live (it is NOT established to be a positive wall). 'No erratum for v10' and 'the FRG-4 well stands' are SEPARATE claims; only the former is settled here.",
  "implication_for_well": "The -sigma well's survival at FRG-4 depends on the SINGLE owner yes/no. The curvature convention does NOT by itself sink the well (it pins the DENSITY positive); only the one-loop relative sign does. The well is NOT refuted by the corpus curvature convention; it is CONDITIONAL on the one-loop log-det relative sign, which is owner-locked.",
  "no_target_loading": true,
  "non_promotion": "no gate flipped; artifact is countersign-input only"
}