{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R477",
  "content_hash": null,
  "slug": "lwf101-attempt-literature-identification",
  "type": "attempt",
  "title": "Finite-field root bounds give context rather than this fixed value",
  "summary": "Primary literature treats sparse finite-field polynomials broadly; no table for this Littlewood family was located.",
  "relevance": "This records a line of attack on the target problem, including what it establishes and where it stops.",
  "relevance_source": "derived",
  "body": "Kelley proves coefficient-independent bounds for the number of nonzero roots of a \\(t\\)-nomial over \\(\\mathbb F_q\\), with stronger conclusions when the polynomial does not vanish on a large multiplicative coset. A degree-30 Littlewood polynomial has 31 nonzero terms, so the ordinary degree bound already gives 30 roots and is sharper for this small fixed instance. A focused search combining Littlewood polynomials, finite-field roots, \\(\\mathbb F_{101}\\), and degree 30 did not locate a published enumeration or the value 12. Publication novelty remains unverified.",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "universal",
    "statement": "published bounds for roots of restricted-coefficient and sparse polynomials over finite fields"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1112/S1461157016000334",
      "locator": "Zander Kelley, Roots of Sparse Polynomials over a Finite Field, LMS Journal of Computation and Mathematics 19 (2016), 196-204"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1112/S1461157016000334",
    "locator": "Zander Kelley, Roots of Sparse Polynomials over a Finite Field, LMS Journal of Computation and Mathematics 19 (2016), 196-204"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R478",
      "title": "The exact maximum number of roots is 12",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "littlewood-f101-max-roots-30",
      "title": "littlewood f101 max roots 30",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}