{
  "schema": "ghu-hypothesis-certificates-v1",
  "date": "2026-10-14",
  "scope": "First batch: rational algebra, symbolic differentiation, exact published covariance and pointwise derivative enclosures. Not a full GHU certificate.",
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      "passed": true
    },
    {
      "name": "Unique valid covariance cell (4, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (5, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (6, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (7, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (8, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (9, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (10, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (11, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (12, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (13, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (14, 7)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (0, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (1, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (2, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (3, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (4, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (5, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (6, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (7, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (8, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (9, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (10, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (11, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (12, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (13, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (14, 8)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (0, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (1, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (2, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (3, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (4, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (5, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (6, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (7, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (8, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (9, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (10, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (11, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (12, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (13, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (14, 9)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (0, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (1, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (2, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (3, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (4, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (5, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (6, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (7, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (8, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (9, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (10, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (11, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (12, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (13, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (14, 10)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (0, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (1, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (2, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (3, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (4, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (5, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (6, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (7, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (8, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (9, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (10, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (11, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (12, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (13, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (14, 11)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (0, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (1, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (2, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (3, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (4, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (5, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (6, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (7, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (8, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (9, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (10, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (11, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (12, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (13, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (14, 12)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (0, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (1, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (2, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (3, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (4, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (5, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (6, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (7, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (8, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (9, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (10, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (11, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (12, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (13, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (14, 13)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (0, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (1, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (2, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (3, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (4, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (5, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (6, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (7, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (8, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (9, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (10, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (11, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (12, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (13, 14)",
      "passed": true
    },
    {
      "name": "Unique valid covariance cell (14, 14)",
      "passed": true
    },
    {
      "name": "Complete symmetric 15 by 15 covariance",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 1",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 2",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 3",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 4",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 5",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 6",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 7",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 8",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 9",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 10",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 11",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 12",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 13",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 14",
      "passed": true
    },
    {
      "name": "Exact LDL positive pivot 15",
      "passed": true
    },
    {
      "name": "Exact LDL reconstructs every entry",
      "passed": true
    },
    {
      "name": "All pairwise correlation squared bounds",
      "passed": true
    },
    {
      "name": "Lab uses the certified decimal covariance",
      "passed": true
    },
    {
      "name": "Exact density area is one",
      "passed": true
    },
    {
      "name": "Exact Jacobian null direction",
      "passed": true
    },
    {
      "name": "Exact transformed covariance null direction",
      "passed": true
    },
    {
      "name": "Exact normalization Jacobian rank is fourteen",
      "passed": true
    },
    {
      "name": "Observed likelihood remains disabled",
      "passed": true
    },
    {
      "name": "Rational determinant strictly positive: -999/1000",
      "passed": true
    },
    {
      "name": "Pointwise derivative absolute errors below 1e-7: -999/1000",
      "passed": true
    },
    {
      "name": "Rational determinant strictly positive: -19/20",
      "passed": true
    },
    {
      "name": "Pointwise derivative absolute errors below 1e-7: -19/20",
      "passed": true
    },
    {
      "name": "Rational determinant strictly positive: 4/5",
      "passed": true
    },
    {
      "name": "Pointwise derivative absolute errors below 1e-7: 4/5",
      "passed": true
    },
    {
      "name": "Reject interval crossing zero",
      "passed": true
    },
    {
      "name": "Engine rejects nonpositive determinant",
      "passed": true
    },
    {
      "name": "Archived physical coefficients replay, case 1",
      "passed": true
    },
    {
      "name": "Refinement diagnostic, case 1",
      "passed": true
    },
    {
      "name": "Archived physical coefficients replay, case 2",
      "passed": true
    },
    {
      "name": "Refinement diagnostic, case 2",
      "passed": true
    },
    {
      "name": "Archived physical coefficients replay, case 3",
      "passed": true
    },
    {
      "name": "Refinement diagnostic, case 3",
      "passed": true
    },
    {
      "name": "Archived physical coefficients replay, case 4",
      "passed": true
    },
    {
      "name": "Refinement diagnostic, case 4",
      "passed": true
    },
    {
      "name": "Archived physical coefficients replay, case 5",
      "passed": true
    },
    {
      "name": "Refinement diagnostic, case 5",
      "passed": true
    },
    {
      "name": "Archived physical coefficients replay, case 6",
      "passed": true
    },
    {
      "name": "Refinement diagnostic, case 6",
      "passed": true
    },
    {
      "name": "Archived physical coefficients replay, case 7",
      "passed": true
    },
    {
      "name": "Refinement diagnostic, case 7",
      "passed": true
    },
    {
      "name": "Archived physical coefficients replay, case 8",
      "passed": true
    },
    {
      "name": "Refinement diagnostic, case 8",
      "passed": true
    },
    {
      "name": "Archived physical coefficients replay, case 9",
      "passed": true
    },
    {
      "name": "Refinement diagnostic, case 9",
      "passed": true
    }
  ],
  "checkCount": 296,
  "passed": true
}