{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R541",
  "content_hash": null,
  "slug": "ms200-claim-verified-71-set",
  "type": "claim",
  "title": "A 71-element multiplicative Sidon set",
  "summary": "Exact enumeration confirms that every one of the set's 2,556 unordered pair products is different.",
  "relevance": "For Largest multiplicative Sidon subset of the first 200 integers, record ms200-claim-verified-71-set (“A 71-element multiplicative Sidon set”) records a bound, answer, status fact, or structural consequence. The record states: Exact enumeration confirms that every one of the set's 2,556 unordered pair products is different.",
  "relevance_source": "recorded",
  "body": "The set\n\\[\n\\begin{split}\nA=\\{&1,12,17,31,35,40,41,43,49,52,54,55,58,71,73,81,83,86,89,96,\\\\\n&101,103,107,109,113,114,117,118,119,121,125,127,131,133,134,137,\\\\\n&138,139,143,145,148,149,151,153,157,158,159,163,164,167,168,170,\\\\\n&173,174,176,179,181,182,183,184,185,186,188,191,193,194,195,197,\\\\\n&198,199,200\\}\n\\end{split}\n\\]\nhas 71 elements. Direct integer enumeration of all pairs \\(a\\le b\\) in \\(A\\) produces 2,556 products and 2,556 distinct values. Thus \\(A\\) is multiplicative Sidon under the question's convention, which includes squares.\n\nThe canonical space-separated set has SHA-256 digest `87c37bb973034570880b4c3a868eaf2a20ab69d25872f48a545fe2e9a0716db3`. The sorted product list has digest `2c893b6f16e7f5b02675d9d78bf06467300d5437d6729334d35473e816cc5c20`.",
  "status": "established",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "all unordered pairs with repetition from the displayed 71-element subset of 1 through 200",
    "bounds": {
      "set_size": {
        "min": 71,
        "max": 71
      },
      "unordered_pairs": {
        "min": 2556,
        "max": 2556
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1808.06182",
      "locator": "Candidate construction exhaustively replayed in ms200-artifact-construction-and-lp"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1808.06182",
    "locator": "Candidate construction exhaustively replayed in ms200-artifact-construction-and-lp"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R540",
      "title": "The certified interval is 71 through 145",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "multiplicative-sidon-200",
      "title": "multiplicative sidon 200",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}