{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R91",
  "content_hash": null,
  "slug": "c7p5-attempt-current-frontier-audit",
  "type": "attempt",
  "title": "The checked sources leave 368 unresolved",
  "summary": "The newest preprint still identifies 367 as the largest known fifth-power code, while its capacity improvement comes from 134,753 words in dimension ten.",
  "relevance": "For A 368-word code in the fifth strong power of the 7-cycle, record c7p5-attempt-current-frontier-audit (“The checked sources leave 368 unresolved”) documents a concrete method, search boundary, or failed route. The record states: The newest preprint still identifies 367 as the largest known fifth-power code, while its capacity improvement comes from 134,753 words in dimension ten.",
  "relevance_source": "recorded",
  "body": "Polak and Schrijver give the explicit 367-word code and list\n\\[\n367\\leq\\alpha(C_7^{\\boxtimes5})\\leq401.\n\\]\nTheir Section 3 reports failed searches for 368 and states that no three-for-four exchange around their incumbent succeeds. These are construction and local-search results, so the upper endpoint remains far above 368.\n\nItty, Rosin, Carstensen, and Reichman submitted arXiv:2607.21517v1 on 2026-07-23. Its Introduction and Section 3.1 still call 367 the largest known independent set in the fifth power. Their new bound uses 134,753 words in the tenth power. The paper's public repository includes `R367.txt` as the fifth-power base and supplies no 368-word file.\n\nThe checked primary sources and associated repository contain no 368-word witness and no global exclusion of one. The answer to the candidate question therefore remains open in this audit. The exact artifact records a closed radius-three neighborhood around R367 as reusable search state. It supplies no global bound.",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "source audit for a 368-word independent set in the fifth strong power of C7 through 2026-07-24",
    "bounds": {
      "cycle_length": {
        "min": 7,
        "max": 7
      },
      "strong_power": {
        "min": 5,
        "max": 5
      },
      "target_cardinality": {
        "min": 368,
        "max": 368
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2607.21517",
      "locator": "Nathaniel Itty, Christopher D. Rosin, Chase Carstensen, and Daniel Reichman, Improved lower bounds for the Shannon capacity of odd cycles, arXiv:2607.21517v1, submitted 2026-07-23, Introduction, Table 1, Section 3.1 (7-Cycle C7), and Data and Code Availability; Polak and Schrijver, Information Processing Letters 143 (2019), Table 1, Section 3, and Appendix"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2607.21517",
    "locator": "Nathaniel Itty, Christopher D. Rosin, Chase Carstensen, and Daniel Reichman, Improved lower bounds for the Shannon capacity of odd cycles, arXiv:2607.21517v1, submitted 2026-07-23, Introduction, Table 1, Section 3.1 (7-Cycle C7), and Data and Code Availability; Polak and Schrijver, Information Processing Letters 143 (2019), Table 1, Section 3, and Appendix"
  },
  "relations": [
    {
      "slug": "R92",
      "title": "The certified lower bound is 367 words",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "c7-fifth-power-independent-368",
      "title": "c7 fifth power independent 368",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}