1{
 2  "claim_check": {
 3    "heat_max_relative_error": 8.043499689134494e-08,
 4    "envelope_constant_from_exact_quadrature": 1.0127611146915414,
 5    "tail_target": 0.08
 6  },
 7  "benchmark": [
 8    {
 9      "q": 0.040000000000000036,
10      "adaptive_degree": 1,
11      "adaptive_coefficients": 5,
12      "adaptive_actual_relative_tail": 0.036741479563667905,
13      "fixed_degree": 4,
14      "fixed_coefficients": 70,
15      "fixed_actual_relative_tail": 4.856707549007043e-05,
16      "coefficient_ratio_adaptive_over_fixed": 0.07142857142857142
17    },
18    {
19      "q": 0.19999999999999996,
20      "adaptive_degree": 3,
21      "adaptive_coefficients": 35,
22      "adaptive_actual_relative_tail": 0.0389580803115464,
23      "fixed_degree": 4,
24      "fixed_coefficients": 70,
25      "fixed_actual_relative_tail": 0.007459493367324075,
26      "coefficient_ratio_adaptive_over_fixed": 0.5
27    },
28    {
29      "q": 0.55,
30      "adaptive_degree": 8,
31      "adaptive_coefficients": 495,
32      "adaptive_actual_relative_tail": 0.032433547891005235,
33      "fixed_degree": 4,
34      "fixed_coefficients": 70,
35      "fixed_actual_relative_tail": 0.12228936657535362,
36      "coefficient_ratio_adaptive_over_fixed": 7.071428571428571
37    }
38  ],
39  "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."
40}