| { |
| "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." |
| ] |
| } |
