{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1636",
  "content_hash": null,
  "slug": "lloyd-polynomial-integral-root-classification-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: The MathOverflow page has zero answers. Literature gives strong nonexistence conditions and classifications tied to perfect codes, but the dated search did not locate a classification of every parameter triple having the stated integral-root property. Exact unresolved remainder: Give a necessary-and-sufficient classification of all triples (q,n,t), with a proof that every listed polynomial has the required roots and every omitted triple fails at least one requirement. A computational component must use exact rational polynomial arithmetic and provide certificates for factorization, root integrality, distinctness, and the finite parameter ranges it eliminates.",
  "relevance": "For Integral-root classification for Lloyd polynomials, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: The MathOverflow page has zero answers. Literature gives strong nonexistence conditions and classifications tied to perfect codes, but the dated search did not locate a classification of every parameter triple having the stated integral-root property.\n\nExact unresolved remainder: Give a necessary-and-sufficient classification of all triples (q,n,t), with a proof that every listed polynomial has the required roots and every omitted triple fails at least one requirement. A computational component must use exact rational polynomial arithmetic and provide certificates for factorization, root integrality, distinctness, and the finite parameter ranges it eliminates.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1006/jcta.1996.0038",
      "locator": "main theorems restricting integral zeros of Krawtchouk polynomials"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1006/jcta.1996.0038",
    "locator": "main theorems restricting integral zeros of Krawtchouk polynomials"
  },
  "relations": [
    {
      "slug": "R1338",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "lloyd-polynomial-integral-root-classification",
      "title": "lloyd polynomial integral root classification",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}