{
  "status": "dominant_tower_numerics_checked_full_physics_validation_pending",
  "passed": true,
  "count": 50,
  "checks": [
    {
      "name": "SciPy Bessel combinations match 60-digit mpmath",
      "passed": true,
      "witness": 6.661338147750939e-16
    },
    {
      "name": "Analytic log derivatives through fourth order (-0.999, 1)",
      "passed": true,
      "witness": 6.393774398816277e-13
    },
    {
      "name": "Analytic log derivatives through fourth order (-0.95, 2)",
      "passed": true,
      "witness": 5.10702591327572e-15
    },
    {
      "name": "Analytic log derivatives through fourth order (0.8, 1)",
      "passed": true,
      "witness": 6.661338147750939e-16
    },
    {
      "name": "Point 1: quadrature refinement",
      "passed": true,
      "witness": 6.654400227918402e-15
    },
    {
      "name": "Point 1: cutoff 35 to 45",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 1: recalibration residuals",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 1: bottom-inclusive diagnostic recalibration",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 1: no lower sampled point in [0,pi]",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 2: quadrature refinement",
      "passed": true,
      "witness": 8.129997187816392e-15
    },
    {
      "name": "Point 2: cutoff 35 to 45",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 2: recalibration residuals",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 2: bottom-inclusive diagnostic recalibration",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 2: no lower sampled point in [0,pi]",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 3: quadrature refinement",
      "passed": true,
      "witness": 5.209908471074024e-14
    },
    {
      "name": "Point 3: cutoff 35 to 45",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 3: recalibration residuals",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 3: bottom-inclusive diagnostic recalibration",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 3: no lower sampled point in [0,pi]",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 4: quadrature refinement",
      "passed": true,
      "witness": 5.193678226667634e-14
    },
    {
      "name": "Point 4: cutoff 35 to 45",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 4: recalibration residuals",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 4: bottom-inclusive diagnostic recalibration",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 4: no lower sampled point in [0,pi]",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 5: quadrature refinement",
      "passed": true,
      "witness": 2.5968391133340106e-14
    },
    {
      "name": "Point 5: cutoff 35 to 45",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 5: recalibration residuals",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 5: bottom-inclusive diagnostic recalibration",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 5: no lower sampled point in [0,pi]",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 6: quadrature refinement",
      "passed": true,
      "witness": 1.947629335000508e-14
    },
    {
      "name": "Point 6: cutoff 35 to 45",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 6: recalibration residuals",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 6: bottom-inclusive diagnostic recalibration",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 6: no lower sampled point in [0,pi]",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 7: quadrature refinement",
      "passed": true,
      "witness": 5.193678226668021e-14
    },
    {
      "name": "Point 7: cutoff 35 to 45",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 7: recalibration residuals",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 7: bottom-inclusive diagnostic recalibration",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 7: no lower sampled point in [0,pi]",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 8: quadrature refinement",
      "passed": true,
      "witness": 8.455957362793871e-14
    },
    {
      "name": "Point 8: cutoff 35 to 45",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 8: recalibration residuals",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 8: bottom-inclusive diagnostic recalibration",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 8: no lower sampled point in [0,pi]",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 9: quadrature refinement",
      "passed": true,
      "witness": 1.2984195566667734e-14
    },
    {
      "name": "Point 9: cutoff 35 to 45",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 9: recalibration residuals",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 9: bottom-inclusive diagnostic recalibration",
      "passed": true,
      "witness": null
    },
    {
      "name": "Point 9: no lower sampled point in [0,pi]",
      "passed": true,
      "witness": null
    },
    {
      "name": "Adaptive versus fixed quadrature for derivatives 2,3,4",
      "passed": true,
      "witness": [
        9.270362255620057e-14,
        6.439293542825908e-15,
        5.551115123125783e-16
      ]
    }
  ],
  "max_quadrature_drift": 8.455957362793871e-14,
  "max_published_relative_discrepancy": [
    0.0020474101946554857,
    0.0034548987609182014
  ],
  "max_bottom_diagnostic_relative_shift": [
    0.14720101015840692,
    0.0005416164016465164,
    0.0007681951621409944
  ],
  "bottom_diagnostic_columns": [
    "mass_squared",
    "lambda3",
    "lambda4"
  ],
  "bottom_recalibrated": [
    {
      "point": 1,
      "parameters": [
        0.3185747345823393,
        0.08064105627680665
      ],
      "result": {
        "derivatives": [
          -0.0007995691162551748,
          94014536266.9502,
          2569105859280.32,
          18101924291978.62
        ],
        "stationarity_scaled": -8.504739245692299e-15,
        "mass_squared": 15650.009999998403,
        "lambda3": 29.08105555190397,
        "lambda4": 0.020900309861120615
      },
      "relative_to_paper": [
        0.001758716910229774,
        0.0033754133999335245
      ]
    },
    {
      "point": 2,
      "parameters": [
        0.3187073519997434,
        0.0777856954111814
      ],
      "result": {
        "derivatives": [
          0.007761015536944367,
          94014536267.03947,
          2569078946988.485,
          18100319144018.535
        ],
        "stationarity_scaled": 8.255122925785124e-14,
        "mass_squared": 15650.010000013264,
        "lambda3": 29.0807509175694,
        "lambda4": 0.02089845657253109
      },
      "relative_to_paper": [
        0.001748223133634097,
        0.0032864413121023173
      ]
    },
    {
      "point": 3,
      "parameters": [
        0.321473560318551,
        -0.037208672380700566
      ],
      "result": {
        "derivatives": [
          -0.004391957318937125,
          94014536266.9184,
          2568365316513.558,
          18057873163175.85
        ],
        "stationarity_scaled": -4.671572602842932e-14,
        "mass_squared": 15650.00999999311,
        "lambda3": 29.072672960248212,
        "lambda4": 0.02084944884618874
      },
      "relative_to_paper": [
        0.0018150572104829177,
        0.003342100394068348
      ]
    },
    {
      "point": 4,
      "parameters": [
        0.42505772126392155,
        0.07941939423360879
      ],
      "result": {
        "derivatives": [
          0.0027163852948803515,
          94014536266.99239,
          2568956606913.479,
          18092995063736.598
        ],
        "stationarity_scaled": 2.889324781826309e-14,
        "mass_squared": 15650.010000005426,
        "lambda3": 29.079366086148532,
        "lambda4": 0.020890000258999383
      },
      "relative_to_paper": [
        0.0020456955943670696,
        0.0033621642170691413
      ]
    },
    {
      "point": 5,
      "parameters": [
        0.4251168006956572,
        0.07655371226012324
      ],
      "result": {
        "derivatives": [
          0.0016463122132304086,
          94014536266.98016,
          2568926406392.543,
          18091193925909.336
        ],
        "stationarity_scaled": 1.7511251755320144e-14,
        "mass_squared": 15650.010000003393,
        "lambda3": 29.07902423062558,
        "lambda4": 0.02088792068237067
      },
      "relative_to_paper": [
        0.002033915597022151,
        0.003262280613384627
      ]
    },
    {
      "point": 6,
      "parameters": [
        0.4263932524229167,
        -0.03506593109285852
      ],
      "result": {
        "derivatives": [
          0.0002705039653947679,
          94014536266.9606,
          2568076663462.2065,
          18040678463340.21
        ],
        "stationarity_scaled": 2.8772568172506434e-15,
        "mass_squared": 15650.010000000135,
        "lambda3": 29.06940554509237,
        "lambda4": 0.020829596009068373
      },
      "relative_to_paper": [
        0.002047760947685884,
        0.0033524089146614866
      ]
    },
    {
      "point": 7,
      "parameters": [
        0.3176958109066826,
        0.09646575779613908
      ],
      "result": {
        "derivatives": [
          0.0013405770470447107,
          94014536266.97711,
          2569276008557.8354,
          18112076758699.684
        ],
        "stationarity_scaled": 1.425925288019359e-14,
        "mass_squared": 15650.010000002883,
        "lambda3": 29.082981560742287,
        "lambda4": 0.020912031802771812
      },
      "relative_to_paper": [
        0.001825062374863462,
        0.0034564204784937047
      ]
    },
    {
      "point": 8,
      "parameters": [
        0.31775753878263074,
        0.09375411180845945
      ],
      "result": {
        "derivatives": [
          0.001569878421683984,
          94014536266.97588,
          2569264210839.8037,
          18111372737960.215
        ],
        "stationarity_scaled": 1.6698252036538504e-14,
        "mass_squared": 15650.010000002678,
        "lambda3": 29.082848016189335,
        "lambda4": 0.02091121894711259
      },
      "relative_to_paper": [
        0.0018204621491331174,
        0.003417415888320008
      ]
    },
    {
      "point": 9,
      "parameters": [
        0.31873261903935296,
        0.06157987511820089
      ],
      "result": {
        "derivatives": [
          0.00730241278766582,
          94014536267.03642,
          2569064059319.9243,
          18099436679555.957
        ],
        "stationarity_scaled": 7.767323094516141e-14,
        "mass_squared": 15650.010000012757,
        "lambda3": 29.080582396247134,
        "lambda4": 0.02089743768744397
      },
      "relative_to_paper": [
        0.001742418058805928,
        0.0032375270016307134
      ]
    }
  ],
  "max_bottom_recalibrated_difference_to_paper": [
    0.002047760947685884,
    0.0034564204784937047
  ],
  "sampled_global_minimum_only": true,
  "not_formally_certified": true,
  "not_experimental_validation": true,
  "rounding_mass_range_GeV": [
    107.19852485672308,
    161.54780009539002
  ],
  "limitations": [
    "Bottom omitted in main reconstruction; alternative includes bottom with Table 2/Appendix A inputs and recalibrates. Neither is a complete electroweak/model validation.",
    "Rounded k/ct and approximate gW=0.653; electroweak input scheme not reproduced.",
    "Recalibration uses stationarity and mH, never lambda3/lambda4. Agreement at one theta does not establish validity throughout parameter space.",
    "Positive curvature and sampled potential check are not a proof of the global minimum.",
    "7.4% published quartic fitting-curve/table discrepancy persists; its cause is not established."
  ],
  "source": "https://arxiv.org/html/2002.09262v3",
  "environment": {
    "numpy": "2.4.4",
    "scipy": "1.16.3",
    "mpmath": "1.3.0"
  },
  "code_sha256": {
    "ghu_potential.py": "6220b0a48717e22bd451c2aa0dda039951056e7e99d25b7335617edc1a4ee04f",
    "validate_potential.py": "3999d1d723d9a008533d08179ec8f6b18a2878c5c4e0453865bc4a242de06cf9"
  }
}