{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R504",
  "content_hash": null,
  "slug": "mdsc-claim-published-code-radius-five-closed",
  "type": "claim",
  "title": "Deleting at most five published planes still cannot beat 334",
  "summary": "An exact replacement search covers every code obtainable by deleting at most five planes from the published 333-code and adding arbitrary compatible subspaces. It optimizes over every normalized deletion set, and the largest size in this neighborhood is 334.",
  "relevance": "For Exact mixed-dimension subspace-code number A_2(7,4), record mdsc-claim-published-code-radius-five-closed (“Deleting at most five published planes still cannot beat 334”) records a bound, answer, status fact, or structural consequence. The record states: An exact replacement search covers every code obtainable by deleting at most five planes from the published 333-code and adding arbitrary compatible subspaces.",
  "relevance_source": "recorded",
  "body": "For every ambient subspace outside the published code, the replay records which original planes violate distance 4. The counts for blocker-set sizes 0 through 5 are 1, 12, 16, 416, 1,784, and 3,087. Closing these blocker sets under unions of size at most 5 gives 37,591 removal sets. A deletion set can be replaced by the union of the blockers of its chosen additions. This retains every addition and restores any original plane whose deletion served no compatibility constraint, so normalized blocker unions contain an optimum. Padding a normalized witness with unused deletions gives the exact-deletion maxima. At most 11 candidate additions are eligible for any one normalized set, and direct subset enumeration checks their mutual distances. The best size is 334. With exactly five deletions the best size is 333. The output records four selected optimal witnesses with canonical encodings, individual SHA-256 digests, and aggregate digest e694fe602c2f0977efa1224876e9e61e312b1b5e9f07472e79f72849bbb0eb9f.",
  "status": "supported",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "all codes formed by deleting at most five words from the specific 333-plane Appendix C code and adjoining any mutually compatible subspaces of F_2^7",
    "bounds": {
      "starting_code_size": {
        "min": 333,
        "max": 333
      },
      "deleted_starting_codewords": {
        "min": 0,
        "max": 5
      },
      "ambient_subspaces_checked": {
        "min": 29212,
        "max": 29212
      },
      "removal_sets_checked": {
        "min": 37591,
        "max": 37591
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "locator": "Exact replacement search in mdsc-artifact-exact-f2-seven-census, executed 2026-07-28 UTC"
    },
    "runtime_seconds": 6.27,
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Exact replacement search in mdsc-artifact-exact-f2-seven-census, executed 2026-07-28 UTC"
  },
  "relations": [
    {
      "slug": "R497",
      "title": "Exact F₂⁷ census, Appendix C replay, and Singer-orbit search",
      "object_type": "artifact",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R500",
      "title": "Extend the exact replacement search through six deletions",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "mixed-dimension-subspace-code-f2-7-d4",
      "title": "mixed dimension subspace code f2 7 d4",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}