{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R89",
  "content_hash": null,
  "slug": "c31m-claim-exact-lower-witness",
  "type": "claim",
  "title": "An exact integer witness attains ratio 1.3303042705991634737...",
  "summary": "All active radii and the squared norm quotient are verified with rational arithmetic.",
  "relevance": "For Sharp L2 norm of the centered maximal operator on C_31, record c31m-claim-exact-lower-witness (“An exact integer witness attains ratio 1.3303042705991634737...”) records a bound, answer, status fact, or structural consequence. The record states: All active radii and the squared norm quotient are verified with rational arithmetic.",
  "relevance_source": "recorded",
  "body": "In cyclic coordinate order, take\n\\[\n\\begin{aligned}\nx={}&(60240784093944,71756706270677,71756706270677,69429053137658,\\\\\n&69429053137658,124946197568962,124946197568962,634350542282289,\\\\\n&220384421138340,634350542282289,124946197568962,124946197568962,\\\\\n&69429053137658,69429053137658,71756706270677,71756706270677,\\\\\n&60240784093944,60240784093944,53164211021439,53164211021439,\\\\\n&49020565351307,49020565351307,47095643667602,47095643667602,\\\\\n&47095643667602,47095643667602,49020565351307,49020565351307,\\\\\n&53164211021439,53164211021439,60240784093944).\n\\end{aligned}\n\\]\nExact comparison of the sixteen averages at every coordinate selects the radii\n\\[\n(9,8,7,6,5,4,1,0,1,0,1,4,5,6,7,8,9,10,11,12,13,15,15,15,15,15,15,13,12,11,10).\n\\]\nThere are no ties. Direct rational summation gives\n\\[\n\\frac{\\|Mx\\|_2^2}{\\|x\\|_2^2}\n=\\frac{95224622960985697907125617859822805279079620426252}{53808054668649331334697257108564850111138302100375}.\n\\]\nThis quotient exceeds \\((1.3303042705)^2\\) by exact integer comparison.",
  "status": "established",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "one explicit nonnegative integer vector on C_31, with every one of its 496 centered averages compared exactly",
    "bounds": {
      "cycle_order": {
        "min": 31,
        "max": 31
      },
      "coordinates": {
        "min": 31,
        "max": 31
      },
      "averages_checked": {
        "min": 496,
        "max": 496
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2005.03146",
      "locator": "The integer witness and all active-radius comparisons are replayed in c31m-artifact-exact-replay"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2005.03146",
    "locator": "The integer witness and all active-radius comparisons are replayed in c31m-artifact-exact-replay"
  },
  "relations": [
    {
      "slug": "R87",
      "title": "The L2 norm lies between 1.33030427059916347 and 1.63067915195310467",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R85",
      "title": "Exact lower-witness and upper-certificate replay",
      "object_type": "artifact",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "c31-centered-maximal-l2-norm",
      "title": "c31 centered maximal l2 norm",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}