{
  "status": "PASS",
  "checks": 7135,
  "groups": {
    "PSD versus all principal minors": 729,
    "negative quadratic direction": 705,
    "exact nullity": 24,
    "kernel annihilation": 38,
    "supplied interval Gram coefficient identity": 224,
    "one coefficient mutation rejected": 224,
    "supplementary rational value checks": 1344,
    "positive atom prefix feasibility": 810,
    "supplied rational atoms all moments": 810,
    "localizer integral identity": 1620,
    "unique support zeros contain all atoms": 450,
    "third-moment endpoint uniqueness": 2,
    "third-moment endpoint measure": 2,
    "complete third-moment interval": 21,
    "outside third-moment interval": 2,
    "fourth-moment dual polynomial identities": 25,
    "complete fourth-moment interval": 25,
    "upper endpoint three-node measure": 1,
    "positive Hankel with singular localizer": 1,
    "two complete rational root brackets": 2,
    "equal-weight quadratic-root recurrence moments": 1,
    "lower endpoint zero-square uniqueness": 1,
    "quadratic annihilator all supplied moments": 7,
    "parameter family exact Gram acceptance": 6,
    "negative parameter root-pair witness": 6,
    "actual quadratic degree after cancellation": 1,
    "attained minimum primal point and square lower bound": 1,
    "two terminal infeasible tables": 2,
    "all available elementary differences pass false table": 6,
    "affine lower moments": 1,
    "affine upper moments": 1,
    "affine lower dual polynomial": 2,
    "affine upper dual polynomial": 2,
    "affine endpoint uniqueness": 2,
    "same complete uniform prefix finite representative": 1,
    "zero measure every order": 9,
    "collapsed interval unique even at degree zero": 9,
    "collapsed interval mismatch witness": 8,
    "degree-zero positive mass nondegenerate interval": 1,
    "negative mass": 1,
    "zero mass nonzero high moment": 1,
    "zero and constant Gram contracts": 1,
    "out-of-support supplied atom refused": 1,
    "invalid contract refused": 5
  },
  "third_moment_interval": [
    "2/9",
    "5/18"
  ],
  "fourth_moment_interval": [
    "7/36",
    "5/24"
  ],
  "quadratic_root_brackets": [
    [
      "1/5",
      "1/4"
    ],
    [
      "3/4",
      "4/5"
    ]
  ],
  "lower_quadratic_pair_moments": [
    "1",
    "1/2",
    "1/3",
    "1/4",
    "7/36"
  ],
  "upper_three_atom_moments": [
    "1",
    "1/2",
    "1/3",
    "1/4",
    "5/24"
  ],
  "parameter_condition": "gamma >= 0",
  "p1_minimum": "1/144",
  "p1_minimizer": "1/2",
  "scope": "Exact supplied Gram/moment/atom certificates and complete low-degree endpoints; no general SDP optimization or algebraic root solver."
}