{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R87",
  "content_hash": null,
  "slug": "c31m-claim-certified-norm-interval",
  "type": "claim",
  "title": "The L2 norm lies between 1.33030427059916347 and 1.63067915195310467",
  "summary": "An exact integer witness reproduces the candidate lower bound, while a closed-form diagonal certificate supplies a universal upper bound.",
  "relevance": "For Sharp L2 norm of the centered maximal operator on C_31, record c31m-claim-certified-norm-interval (“The L2 norm lies between 1.33030427059916347 and 1.63067915195310467”) records a bound, answer, status fact, or structural consequence. The record states: An exact integer witness reproduces the candidate lower bound, while a closed-form diagonal certificate supplies a universal upper bound.",
  "relevance_source": "recorded",
  "body": "Let \\(N_{31}\\) denote the requested norm. Exact rational evaluation of the integer vector in c31m-claim-exact-lower-witness gives\n\\[\n\\sqrt{\\frac{95224622960985697907125617859822805279079620426252}{53808054668649331334697257108564850111138302100375}}\n\\leq N_{31}.\n\\]\nThe lower endpoint is\n\\[\n1.3303042705991634737558623603323047716\\ldots.\n\\]\nThe weighted Cauchy-Schwarz argument in c31m-claim-diagonal-upper-certificate proves\n\\[\nN_{31}\\leq \\sqrt{\\frac{1916477}{720720}}\n=1.6306791519531046652193954473854436190\\ldots.\n\\]\nThus the candidate's reported value is a certified lower bound to ten decimal places. This entry leaves the exact norm and the complete active-pattern exclusion open.",
  "status": "established",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "the centered Hardy-Littlewood maximal operator over all graph-metric balls of the cycle C_31",
    "bounds": {
      "cycle_order": {
        "min": 31,
        "max": 31
      },
      "minimum_radius": {
        "min": 0,
        "max": 0
      },
      "maximum_radius": {
        "min": 15,
        "max": 15
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2005.03146",
      "locator": "Exact standard-library replay in c31m-artifact-exact-replay"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2005.03146",
    "locator": "Exact standard-library replay in c31m-artifact-exact-replay"
  },
  "relations": [
    {
      "slug": "R89",
      "title": "An exact integer witness attains ratio 1.3303042705991634737...",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R88",
      "title": "A weighted Cauchy-Schwarz certificate gives N_31 squared at most 1916477/720720",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R86",
      "title": "Finite-graph norm literature gives context but no C_31 value",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "c31-centered-maximal-l2-norm",
      "title": "c31 centered maximal l2 norm",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}