{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R500",
  "content_hash": null,
  "slug": "mdsc-attempt-radius-six-replacement-search",
  "type": "attempt",
  "title": "Extend the exact replacement search through six deletions",
  "summary": "Continue the blocker-set method at deletion radius six. A size-335 code or a closed radius-six neighborhood would be a useful result.",
  "relevance": "For Exact mixed-dimension subspace-code number A_2(7,4), record mdsc-attempt-radius-six-replacement-search (“Extend the exact replacement search through six deletions”) documents a concrete method, search boundary, or failed route. The record states: Continue the blocker-set method at deletion radius six.",
  "relevance_source": "recorded",
  "body": "Reuse the exact Appendix C reconstruction and compute every outside subspace with at most six conflicting original planes. Group candidates by blocker set. For each union of at most six blockers, solve the induced compatibility problem with an exact maximum-clique routine and retain a verifiable search trace. Record every incumbent code as RREF bases, verify all distances independently, and publish a branch certificate or complete trace if the maximum remains 334.",
  "status": "next_experiment",
  "evidence_grade": "self_reported",
  "scope": {
    "kind": "bounded",
    "statement": "codes formed by deleting six planes from the specific Appendix C code and adjoining arbitrary mutually compatible subspaces of F_2^7",
    "bounds": {
      "starting_code_size": {
        "min": 333,
        "max": 333
      },
      "deleted_starting_codewords": {
        "min": 6,
        "max": 6
      },
      "ambient_subspaces": {
        "min": 29212,
        "max": 29212
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Plan derived from the completed radius-five census and checked through production /v1/research/check-plan on 2026-07-28"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Plan derived from the completed radius-five census and checked through production /v1/research/check-plan on 2026-07-28"
  },
  "relations": [
    {
      "slug": "R506",
      "title": "Full Singer invariance caps a mixed code at 255",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R504",
      "title": "Deleting at most five published planes still cannot beat 334",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "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"
    }
  ]
}