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79134ea | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | {
"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."
]
} |