{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R745",
  "content_hash": null,
  "slug": "ssclt-claim-strict-through-1000",
  "type": "claim",
  "title": "All 492 comparisons through n=1000 are strict increases",
  "summary": "Exact coefficient extraction and integer comparison find no counterexample between admissible indices 16 and 1000.",
  "relevance": "For Eventual monotonicity in a signed subset-sum local limit, record ssclt-claim-strict-through-1000 (“All 492 comparisons through n=1000 are strict increases”) records a bound, answer, status fact, or structural consequence. The record states: Exact coefficient extraction and integer comparison find no counterexample between admissible indices 16 and 1000.",
  "relevance_source": "recorded",
  "body": "The exhaustive replay constructs every coefficient polynomial through \\(F_{1000}\\) and extracts \\(C_n\\) at each of the 500 positive admissible indices up to 1000. It checks the sign of the cleared integer margin for every adjacent pair.\n\nAll 492 comparisons beginning at \\(n=16\\) are positive. The normalized endpoints include\n\\[\nA_{16}=0.775498980775123\\ldots,\n\\]\n\\[\nA_{999}=0.797525249765113\\ldots,\n\\qquad\nA_{1000}=0.797525608979770\\ldots.\n\\]\nAs a check on the earlier behavior, the complete list of decreases through 1000 is\n\\[\n3\\to4,\\qquad 8\\to11,\\qquad 15\\to16.\n\\]\nThe count at \\(n=200\\) is\n`780463610226751719065842218999070243255558586796769387244`,\nmatching the candidate's prior computation.",
  "status": "supported",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "all consecutive admissible indices a<b with 16<=a<b<=1000",
    "bounds": {
      "minimum_n": {
        "min": 16,
        "max": 16
      },
      "maximum_n": {
        "min": 1000,
        "max": 1000
      },
      "comparisons": {
        "min": 492,
        "max": 492
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://cs.uwaterloo.ca/journals/JIS/VOL16/Sullivan/sullivan8.html",
      "locator": "Independent exact computation in ssclt-artifact-bitpacked-dp, executed 2026-07-24"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://cs.uwaterloo.ca/journals/JIS/VOL16/Sullivan/sullivan8.html",
    "locator": "Independent exact computation in ssclt-artifact-bitpacked-dp, executed 2026-07-24"
  },
  "models": [],
  "relations": [
    {
      "slug": "R744",
      "title": "Each monotonicity comparison reduces to an integer inequality",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R741",
      "title": "Bit-packed exact subset-sum computation through n=1000",
      "object_type": "artifact",
      "relation": "verifies",
      "direction": "incoming"
    },
    {
      "slug": "R743",
      "title": "The all-n monotonicity claim remains unresolved in this audit",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "signed-subset-sum-local-clt-monotone",
      "title": "signed subset sum local clt monotone",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}