{
  "schema": "gap04_cloop_casimir_firstprinciples_result_v1",
  "purpose": "Try the elegant path: read the sign of c_loop's underlying heat-kernel density off a genuine first-principles scalar KK-tower spectral-zeta Casimir computation; FIRST verify the flagged machinery (pub1_casimir.py / closure4_spectral_zeta.py) is that object.",
  "outcome": "MACHINERY-DIFFERENT-OBJECT-owner-locked",
  "machinery_applies": "NO. pub1_casimir.py and closure4_spectral_zeta.py do NOT compute the scalar KK-Casimir wall that produces the e^{-6 sigma} c_loop coefficient. They are a DIFFERENT object: a multi-factor boson+fermion species-counted flux-balance RADIUS-STABILIZATION (minimize c_K6/R^6 + c_S2/R^2 + c_S1/R + flux), with the K6 coefficient TYPED IN as a self-disclaimed rational (c_K6_scalar = 1/945 'estimated'; c_K6_spinor = -31/15120 'rough estimate'). Neither loops over the SU(3) rep tower (no C_2(p,q) computed in code -- it appears only in a comment), neither forms zeta_{Delta_K6}(s) nor continues it to s=-1/2, and neither isolates the single scalar e^{-6 sigma} wall term. The 1/R_K6^6 == e^{-6 sigma} breathing exponent coincides, but exponent-match is NOT object-identity (c_a4 e^{-(8s+4r+x)} and c_KK e^{-4s} also scale as breathing powers and are different objects).",
  "c_loop_underlying_density_sign": "GATED-ON-OPEN (UNBANKED -- not supplied by the flagged machinery)",
  "branch_selected": "still-owner-locked",
  "debit_reclassification": "STAYS BARE-COUNTED (the relative-one-loop-sign debit in gap04_reason_hunt.py is NOT promoted to DERIVED: the flagged machinery was checked and does NOT supply the scalar c_loop underlying-density sign)",
  "object_definition_the_real_producer_must_compute": {
    "c_loop_operator": "c_loop_Z * exp(-6 sigma) in V_eff (veff_coefficients_frg4.yaml)",
    "sigma_is": "K6 breathing mode: Vol(K6)=V_K6_0*exp(+2 sigma) -> R_K6 ~ exp(-2 sigma) -> Casimir ~ (1/R_K6)^6 = exp(-6 sigma)",
    "producer": "c_loop = -(1/2)*(4 pi)^{-D/2}*zeta_{Delta_K6}(-1/2) [scalar KK tower]",
    "zeta_K6": "sum_(p,q) deg(p,q) * [C_2(p,q)/R_K6^2]^{-s}, deg from T^2-zero-weight mult, eigenvalue = SU(3) Casimir",
    "underlying_density_sign_is": "sign[ zeta_{Delta_K6}(-1/2) ] BEFORE the -(1/2) prefactor"
  },
  "part_A_scalar_K6_tower_built_data_blind": {
    "n_max": 12,
    "n_triality0_modes_listed": 56,
    "smallest_modes_(p,q,C2,deg)": [
      [
        1,
        1,
        3.0,
        2
      ],
      [
        0,
        3,
        6.0,
        1
      ],
      [
        3,
        0,
        6.0,
        1
      ],
      [
        2,
        2,
        8.0,
        3
      ],
      [
        1,
        4,
        12.0,
        2
      ],
      [
        4,
        1,
        12.0,
        2
      ]
    ],
    "partial_zeta_K6_at_s=2_convergent_witness": 0.46475883374910654,
    "note": "The tower is real and the eigenvalues are the SU(3) Casimirs of triality-0 reps (the (1,1) adjoint at C_2=3 is the first nonzero scalar KK level). At s=-1/2 this sum DIVERGES and REQUIRES Epstein-Hurwitz / Mellin analytic continuation on the SU(3) Casimir lattice -- precisely the multi-week object the candidates explicitly DEFER ('Full spectral zeta function ... 2-4 week dedicated calculation'). We did NOT continue it here because no data-blind continuation produces the FROZEN inherited c_loop magnitude without the owner's FRG-2 NLO shell-projection scheme; asserting a sign from a half-built continuation would be the manufactured favorable-branch step the countersign exists to catch."
  },
  "part_B_object_check_of_flagged_candidates": {
    "pub1_casimir.py": {
      "C1_loops_su3_rep_tower_and_computes_C2_in_code": false,
      "C1_has_rep_loop": false,
      "C1_computes_casimir_in_code": false,
      "C2_forms_and_continues_zeta_K6_to_minus_half": false,
      "C2_forms_zeta_K6": false,
      "C2_uses_zeta_continuation": false,
      "C3_derives_K6_coeff_from_continuation_not_typed_rational": false,
      "C3_hardcoded_1over945_or_31over15120_present": true,
      "C4_isolates_scalar_e_minus_6sigma_wall_single_term": false,
      "C4_is_flux_balance_radius_minimization": true,
      "C4_is_boson_fermion_species_counted": true,
      "produces_scalar_c_loop_wall": false
    },
    "closure4_spectral_zeta.py": {
      "C1_loops_su3_rep_tower_and_computes_C2_in_code": false,
      "C1_has_rep_loop": false,
      "C1_computes_casimir_in_code": false,
      "C2_forms_and_continues_zeta_K6_to_minus_half": false,
      "C2_forms_zeta_K6": false,
      "C2_uses_zeta_continuation": false,
      "C3_derives_K6_coeff_from_continuation_not_typed_rational": false,
      "C3_hardcoded_1over945_or_31over15120_present": true,
      "C4_isolates_scalar_e_minus_6sigma_wall_single_term": false,
      "C4_is_flux_balance_radius_minimization": true,
      "C4_is_boson_fermion_species_counted": true,
      "produces_scalar_c_loop_wall": false
    },
    "decisive_findings": [
      "C1 FAILS both: no for-loop over the SU(3) (p,q) rep tower with a C_2(p,q) computed in code; 'C_2(p,q)' appears only in a docstring comment.",
      "C2 FAILS both: neither forms zeta_{Delta_K6}(s) nor continues to s=-1/2; no Riemann/Hurwitz/Epstein zeta continuation is invoked.",
      "C3 FAILS both: the K6 coefficient is the typed-in self-disclaimed rational (1/945 'estimated', 31/15120 'rough estimate'), NOT a continuation output.",
      "C4 FAILS both: each is a boson+fermion species-counted (N_b, N_f=45) multi-factor flux-balance RADIUS minimization (minimize c_K6/R^6 + c_S2/R^2 + c_S1/R + V_flux), not a single isolated scalar e^{-6 sigma} wall term."
    ]
  },
  "numerical_disjointness_after_object_check": {
    "candidate_c_K6_total_sign_required_for_their_flux_balance": "NEGATIVE (they require c_K6<0 to stabilize)",
    "candidate_c_K6_total_approx": "~ -0.08 (12*(1/945) - 45*(31/15120))",
    "c_loop_wall_value": 1.3637166327064904e-05,
    "c_loop_wall_sign": "POSITIVE (+1.3637e-5)",
    "disjoint": "Different SIGN, different MAGNITUDE (candidate ~ -8e-2 vs c_loop +1.4e-5, 3+ orders apart), different DEFINITION (combined boson+fermion species count vs FRG-2 NLO Litim-regulator scalar shell projection). The candidate K6 number is NOT c_loop."
  },
  "prior_survey_nearest_hit_reconfirmed_different": "k6_zeta_casimir_insertion.py remains a DIFFERENT object: it closes only the LOCAL Dirac/fermion-bundle Seeley-DeWitt a_4 coefficient at the Einstein point and explicitly 'does not claim to compute the full finite nonlocal determinant'. It is neither the scalar KK-Casimir wall nor the flux-balance stabilizer.",
  "object_check": "The flagged machinery computes a fermion-and-boson species-counted multi-factor flux-balance radius stabilization with a TYPED-IN, self-disclaimed K6 rational (1/945, 31/15120) -- NOT the scalar KK-Casimir wall (e^{-6 sigma}, the breathing-mode zero-point sum). k6_zeta_casimir_insertion.py is a third, also-different object (local Dirac-bundle Seeley-DeWitt coefficient). None executes the scalar zeta_{Delta_K6}(-1/2) sum whose sign decides the branch.",
  "well_verdict": "OWNER-LOCKED / CONDITIONAL, UNCHANGED -- but the elimination is now COMPLETE: the two flagged scalar-Casimir candidates (and the prior near-hit) have been checked and do NOT supply the scalar c_loop underlying-density sign. The -sigma FRG-4 3-modulus well's survival stays gated on the named OPEN first-principles object B-UQFC-14-FRG-2. The favorable branch was NOT forced (the genuine global -(1/2) on a_4's own positive density gives c_a4 NEGATIVE = -5.970e-08 -> runaway); the well is NOT forced to fail (the relative sign vs c_loop is unbanked). Both branches stay live with named falsifiers.",
  "what_requires_chris": "A REAL first-principles c_loop producer must: (1) enumerate the SCALAR K6=SU(3)/T^2 KK tower in CODE -- loop over SU(3) reps (p,q) of triality 0, eigenvalue = C_2(p,q)/R_K6^2, degeneracy = T^2-zero-weight multiplicity (built data-blind here in Part A); (2) form the spectral zeta zeta_{Delta_K6}(s) = sum deg*lambda^{-s} and ANALYTICALLY CONTINUE it (Epstein-Hurwitz / Mellin on the SU(3) Casimir lattice, MS-bar scheme matching the FRG-2 Litim regulator) to s = -1/2; (3) apply the universal -(1/2)(4 pi)^{-D/2} one-loop prefactor and READ OFF sign[zeta_{Delta_K6}(-1/2)] = the underlying-density sign; (4) confirm it reproduces the frozen c_loop magnitude (1.3637877e-5) under the FRG-2 NLO shell-projection scheme, closing B-UQFC-14-FRG-2. None of the flagged machinery does steps 1-3; the K6 zeta(-1/2) continuation is the deferred multi-week object.",
  "provenance_hashes": {
    "pub1_casimir.py": "07a459f795a581078eefe8fbcb0e0b1479e8a8f562aa9928b485dacc6f2ff463",
    "closure4_spectral_zeta.py": "ae53b7e9838461762a905020759589258971019951daacb0564323852606c973",
    "k6_zeta_casimir_insertion.py": "c68c4b021bd8df0b1f1684e110cdcdadea575479a0831ad99cee5299e940388f",
    "veff_coefficients_frg4.yaml": "9bf1d45871adcf67d754a3908c67eb6ad9d36780d4ef29336ea932c8705fa0ac",
    "gilkey_a4_cross_terms.json": "86ea94dff5efdb295432dfcd494bae18aebc0b0bf44db181d090ddb29fe10845"
  },
  "frozen_inputs_used": {
    "R_K6_0": 30.0,
    "R_S2_0": 2.0,
    "a4_cross_prefactor_1_over_36": 0.027777777777777776,
    "D_bulk": 13,
    "factor_4pi_to_minus_D_over_2": 7.163675151870211e-08,
    "global_one_loop_prefactor": -0.5,
    "c_loop_wall_value_read_after_object_check": 1.3637166327064904e-05
  },
  "no_target_loading": true,
  "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 scalar K6 tower in Part A is built from the frozen geometry (Einstein constant +5, dim 6) and SU(3) group theory ALONE. The c_loop WALL value was read ONLY after the object check, and only as a geometry-side coefficient for the disjointness witness -- never as an input to a derivation. The favorable (well-stands) branch was NOT forced: no sign was asserted for zeta_{Delta_K6}(-1/2); the well is left owner-locked because the deciding object is not supplied by the flagged machinery.",
  "non_promotion": "no gate flipped; no status word emitted for any gate; countersign-ready object-mismatch analysis only."
}