{
  "schema_version": 1,
  "project": "Hsin-Heart Exact 84",
  "status": "candidate_theorem_unreviewed",
  "canonical_problem": "Maximum size of F subset C([21],13) with pairwise intersections in {7,9}",
  "equivalent_problem": "Maximum size of B subset C([21],8) with pairwise intersections in {2,4}",
  "johnson_notation": "A(J^{21,8},{4,6})",
  "claims": [
    {
      "id": "C1",
      "statement": "The exact maximum is 84.",
      "status": "claimed_verified_by_package",
      "machine_check": "verification/hsin84_final_verify.py"
    },
    {
      "id": "C2",
      "statement": "Every non-PG(2,4) maximal doubly-even [21,9] core admits at most 81 compatible weight-8 words.",
      "status": "claimed_verified_by_package"
    },
    {
      "id": "C3",
      "statement": "Every valid family of size at least 82 lies in and spans the PG(2,4) [21,9,8] core.",
      "status": "claimed_proof_plus_certificates"
    },
    {
      "id": "C4",
      "statement": "Every 84-family is parametrized by one incident-line choice at each point of PG(2,4).",
      "status": "claimed_human_proof"
    },
    {
      "id": "C5",
      "statement": "There are 5^21 extremizers inside a fixed labelled PG(2,4) core.",
      "status": "claimed_corollary"
    }
  ],
  "caveats": [
    "Not independently peer reviewed.",
    "Novelty search found no exact prior theorem but cannot guarantee global priority.",
    "Classical code/design/finite-geometry ingredients are prior art and cited."
  ]
}