{
  "schema": "gap04_disjointness_result_v1",
  "disjoint": true,
  "basis": "DIRECTIONALLY DISJOINT operator structure: the -sigma corner is governed by the operator 'c_a4_K6_S2' (growth rate 8, coeff -); the +modulus corner has NO operator with positive growth rate (all decay => V->0+, no perturbative wall => the corner IS the named non-perturbative object B-UQFC-14-NP-1 (non-perturbative wall mechanism required)). The two corners are dominated by different operators in different asymptotic directions. HOWEVER the v10 well-wall term c_loop (exp(-6 sigma)) is NOT the governing -sigma term at FRG-4 (the a4 cross-term exp(-8 sigma) is, with negative coefficient): so the v10 'well unconditional in c_loop' claim is CONVENTION-DEPENDENT (heat-kernel sign convention), which is owner-locked and NOT resolved by this script.",
  "provenance_hash": "9bf1d45871adcf67d754a3908c67eb6ad9d36780d4ef29336ea932c8705fa0ac",
  "veff_source": "Final_physics_articles/scripts/gap_04/outputs/veff_coefficients_frg4.yaml",
  "acceptance_conditions": {
    "cond1_different_governing_operator": true,
    "cond2_no_positive_wall_in_+modulus": true,
    "cond3_-sigma_is_a_real_runaway": true
  },
  "neg_sigma_direction": {
    "direction": "-sigma (negative-modulus runaway)",
    "unit_ray_(sigma,rho,chi)": [
      -1.0,
      0.0,
      0.0
    ],
    "dominant_operator": "c_a4_K6_S2",
    "dominant_growth_rate": 8.0,
    "dominant_coefficient": -5.969729293225176e-08,
    "V_asymptotic_limit": "-inf",
    "any_operator_grows": true,
    "per_operator": [
      {
        "operator": "c_a4_K6_S2",
        "exponent_vec_(sigma,rho,chi)": [
          8.0,
          4.0,
          1.0
        ],
        "coefficient": -5.969729293225176e-08,
        "growth_rate_along_d": 8.0,
        "sign_of_coefficient": "-"
      },
      {
        "operator": "c_loop_Z",
        "exponent_vec_(sigma,rho,chi)": [
          6.0,
          -0.0,
          -0.0
        ],
        "coefficient": 1.3637166327064904e-05,
        "growth_rate_along_d": 6.0,
        "sign_of_coefficient": "+"
      },
      {
        "operator": "c_KK",
        "exponent_vec_(sigma,rho,chi)": [
          4.0,
          -0.0,
          -0.0
        ],
        "coefficient": 0.009498860966469166,
        "growth_rate_along_d": 4.0,
        "sign_of_coefficient": "+"
      },
      {
        "operator": "c_Wilson",
        "exponent_vec_(sigma,rho,chi)": [
          4.0,
          -0.0,
          -0.0
        ],
        "coefficient": -4.875756906074309e-05,
        "growth_rate_along_d": 4.0,
        "sign_of_coefficient": "-"
      },
      {
        "operator": "c_bdry",
        "exponent_vec_(sigma,rho,chi)": [
          2.0,
          -0.0,
          2.0
        ],
        "coefficient": -0.012665147955292222,
        "growth_rate_along_d": 2.0,
        "sign_of_coefficient": "-"
      },
      {
        "operator": "c_S2",
        "exponent_vec_(sigma,rho,chi)": [
          -0.0,
          4.0,
          -0.0
        ],
        "coefficient": 0.009498860966469166,
        "growth_rate_along_d": -0.0,
        "sign_of_coefficient": "+"
      },
      {
        "operator": "c_KK_S1Y",
        "exponent_vec_(sigma,rho,chi)": [
          -0.0,
          -0.0,
          4.0
        ],
        "coefficient": 0.009498860966469166,
        "growth_rate_along_d": -0.0,
        "sign_of_coefficient": "+"
      }
    ]
  },
  "plus_modulus_direction": {
    "direction": "+modulus (decompactification)",
    "unit_ray_(sigma,rho,chi)": [
      0.5773502691896258,
      0.5773502691896258,
      0.5773502691896258
    ],
    "dominant_operator": "c_bdry",
    "dominant_growth_rate": -2.3094010767585034,
    "dominant_coefficient": -0.012665147955292222,
    "V_asymptotic_limit": "0+",
    "any_operator_grows": false,
    "per_operator": [
      {
        "operator": "c_bdry",
        "exponent_vec_(sigma,rho,chi)": [
          2.0,
          -0.0,
          2.0
        ],
        "coefficient": -0.012665147955292222,
        "growth_rate_along_d": -2.3094010767585034,
        "sign_of_coefficient": "-"
      },
      {
        "operator": "c_KK",
        "exponent_vec_(sigma,rho,chi)": [
          4.0,
          -0.0,
          -0.0
        ],
        "coefficient": 0.009498860966469166,
        "growth_rate_along_d": -2.3094010767585034,
        "sign_of_coefficient": "+"
      },
      {
        "operator": "c_S2",
        "exponent_vec_(sigma,rho,chi)": [
          -0.0,
          4.0,
          -0.0
        ],
        "coefficient": 0.009498860966469166,
        "growth_rate_along_d": -2.3094010767585034,
        "sign_of_coefficient": "+"
      },
      {
        "operator": "c_KK_S1Y",
        "exponent_vec_(sigma,rho,chi)": [
          -0.0,
          -0.0,
          4.0
        ],
        "coefficient": 0.009498860966469166,
        "growth_rate_along_d": -2.3094010767585034,
        "sign_of_coefficient": "+"
      },
      {
        "operator": "c_Wilson",
        "exponent_vec_(sigma,rho,chi)": [
          4.0,
          -0.0,
          -0.0
        ],
        "coefficient": -4.875756906074309e-05,
        "growth_rate_along_d": -2.3094010767585034,
        "sign_of_coefficient": "-"
      },
      {
        "operator": "c_loop_Z",
        "exponent_vec_(sigma,rho,chi)": [
          6.0,
          -0.0,
          -0.0
        ],
        "coefficient": 1.3637166327064904e-05,
        "growth_rate_along_d": -3.4641016151377553,
        "sign_of_coefficient": "+"
      },
      {
        "operator": "c_a4_K6_S2",
        "exponent_vec_(sigma,rho,chi)": [
          8.0,
          4.0,
          1.0
        ],
        "coefficient": -5.969729293225176e-08,
        "growth_rate_along_d": -7.505553499465137,
        "sign_of_coefficient": "-"
      }
    ]
  },
  "c_loop_well_wall": {
    "operator": "c_loop_Z",
    "coefficient": 1.3637166327064904e-05,
    "governs_neg_sigma_at_FRG4": false,
    "v10_amendment_claim": "well UNCONDITIONAL in c_loop (sigma->-inf)"
  },
  "convention_dependent": true,
  "convention_note": "FRG-4 status_certificate: F1 PASS at FRG-2 is OVERTURNED at FRG-4 unless the opposite Vassilevich heat-kernel sign convention is adopted. The -sigma well thus stands at DECISION grade ONLY under the heat-kernel sign convention that flips the a4 cross-term sign; that choice is a genuine physics decision = owner-locked.",
  "named_blocker_plus_modulus": "B-UQFC-14-NP-1 (non-perturbative wall mechanism required)",
  "no_target_loading": true,
  "non_promotion": "no gate flipped; artifact is countersign-input only"
}