{
  "schema": "c_loop_NLO_match_result_v1",
  "object": "c_loop = (1/2)(4 pi)^{-d/2} sum_i g_i l_0^d(w_i; eta) -- the FRG-2 NLO Litim shell-projection over the five retained shell masses; the e^{-6 sigma} KK-Casimir wall coefficient.",
  "outcome": "CONSTRUCTION-DEPENDENT-sign-owner-must-rule",
  "step1_principled_choices_committed_target_blind": {
    "O1_spectral_cutoff_scale": "k = mu_match = M_13 (corpus-pinned: z_renorm evaluates Z at mu_match); w_i = m_i^2 in M_13^2 units; projection over the FIVE FRG-2 retained shell masses (finite), NOT the unbounded bare K6 Casimir tower.",
    "O2_NLO_threshold_prescription": "Litim optimised bosonic threshold l_0^d(w;eta)=(2/d)(1-eta/(d+2))/(1+w) assembled with canonical EP-flow prefactor c_d=2 v_d/d =(1/2)(4pi)^{-d/2}/Gamma(d/2+1); d = total_compact_dimension = 9. d=9 is a SELECTION (corpus gilkey/zeta use bulk 13); band reported.",
    "O3_NLO_running": "eta = 1/(24 pi^2) per real scalar (Litim 2001 Eq. 38), via the NLO factor (1 - eta/(d+2)). Sub-percent.",
    "corpus_pins": {
      "O1_mu_match_pinned_in_zrenorm": true,
      "O1_retained_seeds_match_zrenorm": true,
      "O2_EPflow_identity_2vd_over_d_eq_half_4pi_minus_d2_over_Gamma": true,
      "O3_eta_1_over_24pi2_in_zrenorm": true,
      "shell_mass_sigma_numerator_is_3_over_2": true,
      "shell_mass_borb_numerator_is_2": true
    },
    "shell_masses_M13_2_units": {
      "sigma_K6": 0.009498860966469166,
      "rho_S2": 0.009498860966469166,
      "chi_Y": 0.009498860966469166,
      "theta_W": 4.875756906074309e-05,
      "b_orb_sc": 0.012665147955292222
    },
    "eta_litim": 0.004221715985097407
  },
  "step2_principled_c_loop_target_blind": {
    "c_loop_committed_EPflow_d9": 6.231023951110009e-06,
    "c_loop_committed_sign": "POSITIVE",
    "threshold_core_sum_d9": 1.1016250539107022,
    "c_loop_EPflow_d13": 2.7320164639463538e-08,
    "threshold_core_sum_d13": 0.7627415833430442,
    "assembly_band_d9": {
      "A_EPflow_c_d_times_core_bare": 5.356920088461488e-07,
      "B_half_times_core_full": 6.231023951110009e-06,
      "C_half_times_core_bare": 2.8039607779995037e-05,
      "D_plain_times_core_bare": 5.6079215559990074e-05
    },
    "assembly_band_d13": {
      "A_EPflow_c_d_times_core_bare": 9.489948512412547e-11,
      "B_half_times_core_full": 2.7320164639463538e-08,
      "C_half_times_core_bare": 1.7758107015651297e-07,
      "D_plain_times_core_bare": 3.5516214031302594e-07
    },
    "sign_robustly_positive_across_band": true
  },
  "step3_relative_sign_and_branch": {
    "a4_and_relative_sign": {
      "int_a4_sign": "POSITIVE",
      "int_a4_value": 1.6666666666666665,
      "c_a4_under_genuine_minus_half": -5.969729293225175e-08,
      "abs_c_a4": 5.969729293225175e-08,
      "relative_sign_rule": "relative sign(c_a4)/sign(c_loop) = sign(int_a4)/sign(int_loop). int_a4 = +(1/36)R_K6 R_S2 is POSITIVE & convention-invariant. int_loop (sign of c_loop's UNDERLYING density) is NOT banked; the branch rides entirely on it.",
      "int_loop_status_NOT_pinned": {
        "i_integration_direction": "Wetterich partial_t u > 0 is INSTANTANEOUS; accumulated UV->IR (dt<0) carries OPPOSITE sign -> does NOT fix accumulated-density sign.",
        "ii_scheme_dependence": "bare zeta has POLE at s=-1/2; residue NEGATIVE (invariant) but finite part FLIPS with mu (mu*~0.061) -> wall sign scheme-dep.",
        "iii_prior_disagreement": "gap04_litim_scheme_branch read SAME scheme family leading order as BRANCH-RUNAWAY (opposite branch).",
        "iv_circularity": "choosing the no-flip convention by reference to stored c_loop=+ uses the target's sign -> circular, forbidden."
      },
      "branch_if_int_loop_POSITIVE": "c_a4 SAME relative sign as c_loop. With genuine -(1/2) on positive int_a4, c_a4 = -5.97e-8 < 0; growth-8 operator dominates growth-6 c_loop wall at the -sigma corner -> V -> -inf -> BRANCH-RUNAWAY.",
      "branch_if_int_loop_NEGATIVE": "c_a4 OPPOSITE relative sign to c_loop -> c_a4 = +5.97e-8 > 0, a positive wall -> the -sigma well stands -> BRANCH-STANDS."
    },
    "leading_order_reading": "BRANCH-RUNAWAY",
    "leading_order_note": "assembled c_loop coefficient POSITIVE -> if int_loop inherited positive, c_a4 keeps sign -> c_a4 < 0 -> RUNAWAY. Reported honestly; NOT forced to STANDS.",
    "relative_sign_derived": false,
    "branch_selected": "still-owner-locked",
    "why_not_derived": "the relative sign rides on the sign of c_loop's UNDERLYING density (int_loop), which the corpus records as NOT banked (owner-must-rule) and which is scheme-dependent (zeta pole at s=-1/2; finite part flips with mu; instantaneous Wetterich flow sign != accumulated-density sign; prior reconstruction read RUNAWAY). Choosing the no-flip convention by reference to the stored + target is circular/forbidden."
  },
  "step4_magnitude_validation_post_hoc": {
    "performed_after_sign_and_structure": true,
    "frozen_c_loop_FRG2_target": 1.3637877214788921e-05,
    "committed_ratio_to_target": 0.45689104345015535,
    "committed_reproduces_within_factor_2": false,
    "ratio_band_all_principled_assemblies": {
      "d9_A_EPflow_c_d_times_core_bare": 0.03927972076660465,
      "d9_B_half_times_core_full": 0.45689104345015535,
      "d9_C_half_times_core_bare": 2.056009695525699,
      "d9_D_plain_times_core_bare": 4.112019391051398,
      "d13_A_EPflow_c_d_times_core_bare": 6.958523209258433e-06,
      "d13_B_half_times_core_full": 0.0020032563872797986,
      "d13_C_half_times_core_bare": 0.01302116651731869,
      "d13_D_plain_times_core_bare": 0.02604233303463738
    },
    "any_assembly_in_fold": false,
    "nearest_ratio": 2.056009695525699,
    "magnitude_reproduces_without_reverse_fit": false,
    "verdict": "Committed principled c_loop (O1+O2+O3, EP-flow d=9) = 6.231024e-06, ratio to target = 0.4569 -> OUTSIDE the factor-2 fold (does NOT reproduce). The + SIGN of the assembled coefficient is reproduced (robustly: sum of positive terms x positive prefactor), but the magnitude is NOT reproduced under the committed canonical normalization. Across the four internally-canonical assemblies x {d=9,d=13} the ratio spans 6.96e-06..4.11 (>~10^4); the target sits inside this wide band but NO single principled prescription lands cleanly in [0.5,2.0] (nearest = 2.056, just outside). Hitting 1.36e-5 exactly would require hand-picking the assembly = reverse-fit, which is FORBIDDEN and DECLINED."
  },
  "cloop_magnitude": "committed principled (EP-flow d=9) = 6.231024e-06 (POSITIVE); magnitude owner-locked / unpinned across equally-principled assemblies (~10^4 span); does NOT reproduce 1.36e-5 without reverse-fit.",
  "cloop_sign": "POSITIVE for the assembled coefficient (robust). The underlying-density sign that the BRANCH needs is NOT pinned (scheme-dependent / not banked).",
  "relative_sign": "CONSTRUCTION-DEPENDENT. sign(c_a4)/sign(c_loop)=sign(int_a4)/sign(int_loop); int_a4=+ (manifest) but int_loop (c_loop underlying density sign) is NOT banked and scheme-dependent. int_loop>0 -> RUNAWAY; int_loop<0 -> STANDS. NOT derived.",
  "branch_selected": "still-owner-locked",
  "well_verdict": "OWNER-LOCKED / CONDITIONAL. The FRG-2 NLO Litim shell-projection is now constructed from first principles target-blind: O1 (k=mu_match, w_i=m_i^2 over the five FRG-2 retained shell masses), O2 (Litim l_0^d threshold + canonical EP-flow prefactor c_d=2 v_d/d, d=9), O3 (eta=1/(24 pi^2)). The assembled c_loop is POSITIVE (robustly) but its MAGNITUDE does NOT reproduce 1.3637877e-5 under the committed canonical normalization (ratio 0.039); across equally-principled assemblies the magnitude is unpinned (>~10^4 span), so the magnitude is genuinely owner-locked and we DECLINE to reverse-fit it. The load-bearing DELIVERABLE -- the relative one-loop SIGN of c_a4 vs c_loop that decides STANDS vs RUNAWAY -- is NOT derived: it rides on the sign of c_loop's UNDERLYING density, which the corpus records as NOT banked (gilkey_a4_cross_terms.py: owner-must-rule) and which is NOT pinned by the construction for four independent reasons -- (i) the Wetterich partial_t u > 0 is instantaneous, the accumulated UV->IR contribution carries the opposite sign; (ii) the bare zeta has a POLE at s=-1/2 and the finite part flips with mu; (iii) the prior gap04_litim_scheme_branch read the SAME scheme family as BRANCH-RUNAWAY; (iv) selecting the no-flip convention by reference to the stored + target is circular. Equally principled readings give opposite branches (int_loop>0 -> RUNAWAY; int_loop<0 -> STANDS). The leading-order reading is the UNFAVORABLE RUNAWAY. We DEFAULT HOLD and do NOT force BRANCH-STANDS. The relative sign is CONSTRUCTION-DEPENDENT = owner-must-rule (Chris).",
  "magnitude_validation": "Committed principled c_loop (O1+O2+O3, EP-flow d=9) = 6.231024e-06, ratio to target = 0.4569 -> OUTSIDE the factor-2 fold (does NOT reproduce). The + SIGN of the assembled coefficient is reproduced (robustly: sum of positive terms x positive prefactor), but the magnitude is NOT reproduced under the committed canonical normalization. Across the four internally-canonical assemblies x {d=9,d=13} the ratio spans 6.96e-06..4.11 (>~10^4); the target sits inside this wide band but NO single principled prescription lands cleanly in [0.5,2.0] (nearest = 2.056, just outside). Hitting 1.36e-5 exactly would require hand-picking the assembly = reverse-fit, which is FORBIDDEN and DECLINED.",
  "reverse_fit_attestation": "O1/O2/O3 were committed in STEPS 1-3 (this docstring + code) BEFORE the target 1.3637877e-5 was read at STEP 4. The shell masses are the corpus FRG-2 LO rationals (3/2/(4pi)^2, 2/(4pi)^2, Wilson/(4pi)^2), geometry/group-forced; none equals the target or a simple multiple. The committed canonical normalization (EP-flow d=9) MISMATCHES the target (ratio 0.039); the closer assembly (d9 C ~ 2.06) is DECLINED (it is not THE canonical placement and choosing it to land nearer the target would be reverse-fit). The hard-coded target does NOT enter STEPS 1-3. MAGNITUDE side is genuinely target-blind. The SIGN side is explicitly NOT claimed derived precisely BECAUSE deriving it would require selecting the no-flip convention by reference to the target's known + sign -- the circular reverse-fit we refuse. (An earlier draft made exactly that circular selection and claimed STANDS as derived; this version corrects it to owner-must-rule.)",
  "what_requires_chris": "(SIGN -- the load-bearing deliverable) The sign of c_loop's UNDERLYING heat-kernel density (int_loop) -- the unfilled CONVENTION_FREEZE slot for the a_4 sector -- which fixes the relative one-loop sign of c_a4 vs c_loop and hence the branch (STANDS vs RUNAWAY). This is owner-must-rule per gilkey_a4_cross_terms.py and is NOT broken here. (MAGNITUDE / O1 / O2) The exact NLO threshold-assembly placement and the shell-projection dimension (d=9 compact vs d=13 bulk) that pin the magnitude to 1.3637877e-5 -- unpinned across equally-principled choices. (O3 is sub-percent and agreed.)",
  "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 construction is built from frozen geometry + SU(3)/T^2 group theory + the corpus FRG-2 LO coefficients (exact rationals over (4 pi)^2) + Litim 2001 threshold functions ALONE. The frozen magnitude 1.3637877e-5 was read ONLY at STEP 4 (post-hoc validator), strictly AFTER O1/O2/O3, the c_loop magnitude+sign, the relative-sign analysis, and the branch logic were fixed -- and ONLY as a comparison, never as an input. The favorable BRANCH-STANDS was NOT forced: the leading-order reading is the UNFAVORABLE RUNAWAY, the magnitude is reported as an honest mismatch, and the relative sign is reported CONSTRUCTION-DEPENDENT = owner-must-rule. The SIGN was NOT derived via the target's known + sign (which would be no-target-loading on the sign side).",
  "provenance": {
    "frozen_inputs.yaml": "8397469ebf982c0c31e7aadef0181337e2fe1b9c7160ca25c000a0cbb0cbac86",
    "z_renormalized_c_loop.py": "2d00436d4367d6f4581be5fd36ca574d70c823bd224cba93e2ab3d90e7cce2c0",
    "gilkey_a4_cross_terms.py": "6e58698a4658ff1f49847617d8a236be8321f2c97227f570829111ba3208212d",
    "veff_coefficients_frg4.yaml": "9bf1d45871adcf67d754a3908c67eb6ad9d36780d4ef29336ea932c8705fa0ac"
  },
  "non_promotion": "no gate flipped; no status word emitted for any gate. STAGED producer; promotable to gap_04/src ONLY if validated + owner-signed. Validation FAILS (magnitude mismatch + sign owner-locked), so NOT promotable as a sign-derivation."
}