{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R499",
  "content_hash": null,
  "slug": "mdsc-attempt-published-code-neighborhood",
  "type": "attempt",
  "title": "Search exact mixed-dimension extensions near the published 333-code",
  "summary": "The exact search reconstructs the code, closes its direct-extension problem, and checks every replacement that deletes at most five original planes. The local maximum remains 334.",
  "relevance": "For Exact mixed-dimension subspace-code number A_2(7,4), record mdsc-attempt-published-code-neighborhood (“Search exact mixed-dimension extensions near the published 333-code”) documents a concrete method, search boundary, or failed route. The record states: The exact search reconstructs the code, closes its direct-extension problem, and checks every replacement that deletes at most five original planes.",
  "relevance_source": "recorded",
  "body": "The search first verifies the Appendix C orbit data and all pairwise distances. It then enumerates every subspace of F₂⁷ in canonical reduced row echelon form. Direct extension leaves only F₂⁷. For the replacement search, each outside subspace carries its exact set of conflicting original planes. Every union of blocker sets of size at most five is checked, followed by direct enumeration of all mutually compatible additions. The search closes this bounded neighborhood and leaves the unrestricted problem open.",
  "status": "completed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "the direct-extension and radius-five replacement neighborhoods of the specific published 333-plane code",
    "bounds": {
      "ambient_subspaces": {
        "min": 29212,
        "max": 29212
      },
      "deleted_starting_codewords": {
        "min": 0,
        "max": 5
      },
      "starting_code_size": {
        "min": 333,
        "max": 333
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1708.06224",
      "locator": "Appendix C reconstruction and exact bounded search in mdsc-artifact-exact-f2-seven-census"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1708.06224",
    "locator": "Appendix C reconstruction and exact bounded search in mdsc-artifact-exact-f2-seven-census"
  },
  "relations": [
    {
      "slug": "R497",
      "title": "Exact F₂⁷ census, Appendix C replay, and Singer-orbit search",
      "object_type": "artifact",
      "relation": "uses",
      "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"
    }
  ]
}