{
  "claim_check": {
    "heat_max_relative_error": 8.043499689134494e-08,
    "envelope_constant_from_exact_quadrature": 1.0127611146915414,
    "tail_target": 0.08
  },
  "benchmark": [
    {
      "q": 0.040000000000000036,
      "adaptive_degree": 1,
      "adaptive_coefficients": 5,
      "adaptive_actual_relative_tail": 0.036741479563667905,
      "fixed_degree": 4,
      "fixed_coefficients": 70,
      "fixed_actual_relative_tail": 4.856707549007043e-05,
      "coefficient_ratio_adaptive_over_fixed": 0.07142857142857142
    },
    {
      "q": 0.19999999999999996,
      "adaptive_degree": 3,
      "adaptive_coefficients": 35,
      "adaptive_actual_relative_tail": 0.0389580803115464,
      "fixed_degree": 4,
      "fixed_coefficients": 70,
      "fixed_actual_relative_tail": 0.007459493367324075,
      "coefficient_ratio_adaptive_over_fixed": 0.5
    },
    {
      "q": 0.55,
      "adaptive_degree": 8,
      "adaptive_coefficients": 495,
      "adaptive_actual_relative_tail": 0.032433547891005235,
      "fixed_degree": 4,
      "fixed_coefficients": 70,
      "fixed_actual_relative_tail": 0.12228936657535362,
      "coefficient_ratio_adaptive_over_fixed": 7.071428571428571
    }
  ],
  "interpretation": "Exact diagonal-Gaussian density-ratio approximation using Hermite coefficients; fixed degree 4 is the control. Coefficients are distribution-level, not per-sample latent codes."
}