{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R57",
  "content_hash": null,
  "slug": "bbmb-attempt-literature-audit",
  "type": "attempt",
  "title": "The focused literature search found broader digit-sum results",
  "summary": "Work on binary digit sums along arithmetic progressions supplies context, while the stated small-multiplier bound was not located.",
  "relevance": "For Sharp multipliers for balanced binary products, record bbmb-attempt-literature-audit (“The focused literature search found broader digit-sum results”) documents a concrete method, search boundary, or failed route. The record states: Work on binary digit sums along arithmetic progressions supplies context, while the stated small-multiplier bound was not located.",
  "relevance_source": "recorded",
  "body": "Spiegelhofer and Stoll study the binary sum-of-digits function \\(s_2\\) along arithmetic progressions. Their Theorem 1.1 proves full complexity, up to a shift, for finite tuples of digit-sum differences. Their elementary discussion also points out the carry difficulty introduced by multiplication by 3.\n\nFocused searches for balanced binary multiples, prescribed binary weight in a residue class, and the exact bound \\(2^{m-1}+1\\) found no primary source stating this candidate. The cited paper concerns eventual digit-sum patterns and gives no multiplier of the required size. The novelty and universal status of the candidate remain unverified.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1909.08849",
      "locator": "Lukas Spiegelhofer and Thomas Stoll, The sum-of-digits function on arithmetic progressions, Theorem 1.1, Lemma 1.2, and the carry discussion in section 1"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1909.08849",
    "locator": "Lukas Spiegelhofer and Thomas Stoll, The sum-of-digits function on arithmetic progressions, Theorem 1.1, Lemma 1.2, and the carry discussion in section 1"
  },
  "models": [],
  "relations": [
    {
      "slug": "R56",
      "title": "A carry-free criterion reduces part of the search to popcounts",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "balanced-binary-multiplier-bound",
      "title": "balanced binary multiplier bound",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}