{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R86",
  "content_hash": null,
  "slug": "c31m-attempt-primary-literature-check",
  "type": "attempt",
  "title": "Finite-graph norm literature gives context but no C_31 value",
  "summary": "Gonzalez-Riquelme and Madrid study the same graph-ball operator and derive exact L2 norms for complete and star graphs.",
  "relevance": "For Sharp L2 norm of the centered maximal operator on C_31, record c31m-attempt-primary-literature-check (“Finite-graph norm literature gives context but no C_31 value”) documents a concrete method, search boundary, or failed route. The record states: Gonzalez-Riquelme and Madrid study the same graph-ball operator and derive exact L2 norms for complete and star graphs.",
  "relevance_source": "recorded",
  "body": "Gonzalez-Riquelme and Madrid define the centered maximal operator on a finite graph by taking averages over graph-metric balls. This specializes to the operator in the candidate record when the graph is \\(C_{31}\\). Their L2 results give exact formulas for complete graphs and star graphs. The paper supplies no corresponding cycle formula. A focused search by the cycle notation, graph name, and operator norm found nearby variation results, while the exact \\(C_{31}\\) constant remained unlocated. Novelty therefore remains unverified.",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "primary literature located for exact L2 norms of centered Hardy-Littlewood maximal operators on finite graphs, with attention to the cycle C_31",
    "bounds": {
      "cycle_order": {
        "min": 31,
        "max": 31
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2005.03146",
      "locator": "Cristian Gonzalez-Riquelme and Jose Madrid, Sharp inequalities for maximal operators on finite graphs, arXiv:2005.03146, definition (1.1) and section 1.3"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2005.03146",
    "locator": "Cristian Gonzalez-Riquelme and Jose Madrid, Sharp inequalities for maximal operators on finite graphs, arXiv:2005.03146, definition (1.1) and section 1.3"
  },
  "relations": [
    {
      "slug": "R87",
      "title": "The L2 norm lies between 1.33030427059916347 and 1.63067915195310467",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "c31-centered-maximal-l2-norm",
      "title": "c31 centered maximal l2 norm",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}