{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R530",
  "content_hash": null,
  "slug": "minimal105-claim-literature-boundary-through-sixteen",
  "type": "claim",
  "title": "The proved type classification stops at weight sixteen",
  "summary": "Christie, Dykema, and Klep prove the type classification through weight 16; the current revision labels the implemented extension through weight 21 conjectural.",
  "relevance": "For Minimal vanishing sums of distinct 105th roots, record minimal105-claim-literature-boundary-through-sixteen (“The proved type classification stops at weight sixteen”) records a bound, answer, status fact, or structural consequence. The record states: Christie, Dykema, and Klep prove the type classification through weight 16; the current revision labels the implemented extension through weight 21 conjectural.",
  "relevance_source": "recorded",
  "body": "Theorem 3.3 of arXiv:2008.11268v2 lists the types of all minimal vanishing sums of weight at most 16, up to rotation, and proves that they have height 1. The weight-16 table includes an all-odd relative-order-105 type \\((R_7:1+\\nu_3:(R_5:R_3))\\). Section 4 and Appendix B describe an algorithmic list through weight 21. The current revision calls those later conclusions conjectural because the implementation has not been formally verified.\n\nTable 1 cannot be used as a literal exhaustive filter for a fixed ambient conductor. Its weight-14 row places type \\((R_7:(R_5:4R_3))\\), including parity \\((14,0)\\), under displayed relative order 210, while the Lam-Leung construction realizes the relevant all-odd sum using 105th roots. The type table and this packet's fixed-conductor affine-orbit enumeration answer different classification questions.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the source's proved type list through weight 16 and conjectural implemented extension at weights 17 through 21",
    "bounds": {
      "weight": {
        "min": 1,
        "max": 21
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2008.11268",
      "locator": "Louis Christie, Kenneth J. Dykema, and Igor Klep, Classifying minimal vanishing sums of roots of unity, arXiv:2008.11268v2, Definition of relative order, Theorem 3.3, Table 1, Section 4, and Appendix B"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2008.11268",
    "locator": "Louis Christie, Kenneth J. Dykema, and Igor Klep, Classifying minimal vanishing sums of roots of unity, arXiv:2008.11268v2, Definition of relative order, Theorem 3.3, Table 1, Section 4, and Appendix B"
  },
  "models": [],
  "relations": [
    {
      "slug": "R529",
      "title": "Audit the literature and current TheoremDB state",
      "object_type": "attempt",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R531",
      "title": "There are seven affine-Galois orbits through weight nineteen",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "minimal-vanishing-105th-root-sums",
      "title": "minimal vanishing 105th root sums",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}