{
  "status": "PASS",
  "checks": 58999,
  "categories": {
    "Exact binary primal residual": 626,
    "Binary primal equals valid risk witness": 625,
    "Optimal decision risk attains binary deficiency": 625,
    "All tested bounded Bayes transfers": 50000,
    "Three-state unique forward kernel and rank witness": 1,
    "Same classification risk is insufficient": 1,
    "Restricted binary loss detects lost information": 1,
    "Full-support loss detects lost information": 1,
    "Asymmetric exact deficiency": 1,
    "Asymmetric explicit primal and dual": 1,
    "Fair prior misses minimax witness": 1,
    "BSC exact garbling including fair boundary": 66,
    "BSC reverse identity upper": 66,
    "BSC matching risk lower": 66,
    "Every submitted martingale has convex order": 53,
    "Martingale square cost identity": 53,
    "Posterior martingale square cost": 1,
    "Posterior coupling constructs actual garbling": 1,
    "Hinge decision strict advantage": 1,
    "Same binary TV need not mean experiment equivalence": 1,
    "Convex-order variance necessity": 221,
    "Knot certificate agrees with intervening thresholds": 5525,
    "Independent max-affine convex probes": 884,
    "Failed order supplies concrete hinge witness": 169,
    "Distinct martingale plans same squared cost": 1,
    "Ordinary plan cheaper but not martingale": 1,
    "Ordinary plan row moments rejected": 1,
    "Variance counterexample incomparable": 1,
    "Negative kernel rejected": 1,
    "Wrong row sum rejected": 1,
    "Duplicate supports rejected": 1,
    "Unbounded dual reward rejected": 1,
    "Invalid prior rejected": 1
  },
  "binary_experiment_pairs": 625,
  "binary_deficiency_histogram": {
    "0": 273,
    "1/10": 16,
    "1/12": 24,
    "1/14": 8,
    "1/16": 8,
    "1/2": 10,
    "1/20": 16,
    "1/28": 8,
    "1/3": 8,
    "1/4": 50,
    "1/5": 16,
    "1/6": 24,
    "1/7": 8,
    "1/8": 48,
    "2/5": 8,
    "2/7": 8,
    "3/10": 8,
    "3/14": 8,
    "3/16": 8,
    "3/20": 16,
    "3/28": 8,
    "3/7": 8,
    "3/8": 20,
    "5/28": 8,
    "9/28": 8
  },
  "five_site_laws": 70,
  "equal_mean_pairs": 390,
  "convex_ordered_pairs": 221,
  "three_site_martingale_plans": 50,
  "asymmetric_certificate": {
    "value": "1/3",
    "kernel": [
      [
        "5/6",
        "1/6"
      ],
      [
        "0",
        "1"
      ]
    ],
    "prior": [
      "1/3",
      "2/3"
    ],
    "reward": [
      [
        "1",
        "0"
      ],
      [
        "0",
        "1"
      ]
    ]
  },
  "posterior_certificate": {
    "fine_experiment": [
      [
        "1/3",
        "2/3",
        "0"
      ],
      [
        "0",
        "2/3",
        "1/3"
      ]
    ],
    "coarse_experiment": [
      [
        "2/3",
        "1/3"
      ],
      [
        "1/3",
        "2/3"
      ]
    ],
    "garbling": [
      [
        "1",
        "0"
      ],
      [
        "1/2",
        "1/2"
      ],
      [
        "0",
        "1"
      ]
    ],
    "coarse_fine_joint": [
      [
        "1/6",
        "1/3",
        "0"
      ],
      [
        "0",
        "1/3",
        "1/6"
      ]
    ]
  },
  "scope": "Finite rational certificates. General finite theorems are proved in prose; no claims for arbitrary infinite experiments, unrestricted losses, or generic martingale optimization."
}