{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R660",
  "content_hash": null,
  "slug": "rm28-attempt-dated-source-audit",
  "type": "attempt",
  "title": "A 2026-07-28 source audit confirms the current 88 to 96 interval",
  "summary": "A dated audit of six primary or specialist sources found current support for 88 <= rho(2,8) <= 96; the 2026 sources still treat 88 as a lower or relative cubic value.",
  "relevance": "For Covering radius of the second-order Reed-Muller code RM(2,8), record rm28-attempt-dated-source-audit (“A 2026-07-28 source audit confirms the current 88 to 96 interval”) documents a concrete method, search boundary, or failed route. The record states: A dated audit of six primary or specialist sources found current support for 88 <= rho(2,8) <= 96; the 2026 sources still treat 88 as a lower or relative cubic value.",
  "relevance_source": "recorded",
  "body": "The audit checked the IEEE proceedings paper of Brier and Langevin, Wang's final 2019 paper, Gillot and Langevin's 2023 paper and specialist project page, Gao's January 2026 paper, and arXiv:2607.02365v1. Queries included `RM(2,8) covering radius`, `rho(2,8)`, and `second-order nonlinearity 8 variables`, with date filters and targeted searches of arXiv, DOI records, and the Toulon project pages. Brier and Langevin give the displayed distance-88 cubic and the split-by-one-variable quotient method. Wang supplies \\(\\rho(2,7)=40\\), hence the current recursive upper bound 96. The 2023 paper and February 2024 project page display 88 through 96 and call the full case open. Gao's 2026 introduction still cites 88 as a lower bound obtained from the cubic classification. Khoruzhii, Gelß, and Pokutta distinguish the relative cubic value from the full radius in July 2026. The audit located no source that closes the full interval. This is a dated search report rather than an absence theorem.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "a dated audit of six primary or specialist source items concerning rho(2,8)",
    "bounds": {
      "publication_year": {
        "min": 2003,
        "max": 2026
      },
      "source_items_checked": {
        "min": 6,
        "max": 6
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://langevin.univ-tln.fr/project/covering/covering.html",
      "locator": "Current specialist table and methodology, cross-checked against the source list in metadata on 2026-07-28"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://langevin.univ-tln.fr/project/covering/covering.html",
    "locator": "Current specialist table and methodology, cross-checked against the source list in metadata on 2026-07-28"
  },
  "models": [],
  "relations": [
    {
      "slug": "R662",
      "title": "The full covering radius satisfies 88 <= rho(2,8) <= 96",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "R664",
      "title": "The relative cubic covering radius equals 88",
      "object_type": "claim",
      "relation": "reports",
      "direction": "outgoing"
    },
    {
      "slug": "R663",
      "title": "An eight-term cubic has exact second-order nonlinearity 88",
      "object_type": "claim",
      "relation": "reports",
      "direction": "outgoing"
    },
    {
      "slug": "reed-muller-rm2-8-covering-radius",
      "title": "reed muller rm2 8 covering radius",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}