{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R502",
  "content_hash": null,
  "slug": "mdsc-claim-current-interval-334-388",
  "type": "claim",
  "title": "The dated interval is 334 ≤ A₂(7,4) ≤ 388",
  "summary": "A published 333-plane code extends to 334 by adjoining the whole space, and the published semidefinite bound is 388. The exact value remains unresolved among the 55 integers in this interval.",
  "relevance": "For Exact mixed-dimension subspace-code number A_2(7,4), record mdsc-claim-current-interval-334-388 (“The dated interval is 334 ≤ A₂(7,4) ≤ 388”) records a bound, answer, status fact, or structural consequence. The record states: A published 333-plane code extends to 334 by adjoining the whole space, and the published semidefinite bound is 388.",
  "relevance_source": "recorded",
  "body": "Heinlein, Kiermaier, Kurz, and Wassermann give 333 three-dimensional subspaces of F₂⁷ with minimum subspace distance 4. The whole space has distance 4 from every three-space, so adjoining it gives 334 mixed-dimension codewords. Heinlein and Ihringer prove the upper bound 388 by semidefinite programming. The current online subspace-code table still displays 334–388 for these parameters. A dated search on 2026-07-28 found no later primary result that closes either side of the interval.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the maximum size A_2(7,4) of a binary mixed-dimension subspace code with minimum subspace distance 4",
    "bounds": {
      "field_order": {
        "min": 2,
        "max": 2
      },
      "ambient_dimension": {
        "min": 7,
        "max": 7
      },
      "minimum_subspace_distance": {
        "min": 4,
        "max": 4
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1809.09352v2",
      "locator": "Heinlein et al., arXiv:1708.06224v5, Theorem 2 on PDF p. 2 and Appendix C on pp. 16-18; Heinlein and Ihringer, arXiv:1809.09352v2, Introduction and Theorem 1.1 on PDF p. 2; Subspace Codes bounds table, A_2(7,4), checked 2026-07-28"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1809.09352v2",
    "locator": "Heinlein et al., arXiv:1708.06224v5, Theorem 2 on PDF p. 2 and Appendix C on pp. 16-18; Heinlein and Ihringer, arXiv:1809.09352v2, Introduction and Theorem 1.1 on PDF p. 2; Subspace Codes bounds table, A_2(7,4), checked 2026-07-28"
  },
  "relations": [
    {
      "slug": "R501",
      "title": "Audit the primary sources, current bounds table, and production record",
      "object_type": "attempt",
      "relation": "reports",
      "direction": "incoming"
    },
    {
      "slug": "R503",
      "title": "The published 333-plane code has a unique one-word extension",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R505",
      "title": "The SDP upper bound is 388, with an integer-only fallback of 394",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "mixed-dimension-subspace-code-f2-7-d4",
      "title": "mixed dimension subspace code f2 7 d4",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}