{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R529",
  "content_hash": null,
  "slug": "minimal105-attempt-source-and-live-state-audit",
  "type": "attempt",
  "title": "Audit the literature and current TheoremDB state",
  "summary": "A dated audit found strong type and minimum-weight results, corrected a source-version trap, and found no primary source giving the full fixed-conductor affine classification.",
  "relevance": "For Minimal vanishing sums of distinct 105th roots, record minimal105-attempt-source-and-live-state-audit (“Audit the literature and current TheoremDB state”) documents a concrete method, search boundary, or failed route. The record states: A dated audit found strong type and minimum-weight results, corrected a source-version trap, and found no primary source giving the full fixed-conductor affine classification.",
  "relevance_source": "recorded",
  "body": "The audit checked Lam and Leung's paper, both arXiv source revisions of Christie, Dykema, and Klep, and the authors' public code repository. The 2020 v1 manuscript presented the implemented extension through weight 21 as a theorem. The current v2 manuscript expressly treats that extension as conjectural because the implementation was not formally verified. The public repository remains at commit b0563b270dc89ed7ca9e195535a107d5a81cc6dc from 2020-07-28 and predates the v2 correction.\n\nExact web searches on 2026-07-28 for conductor 105, 105th roots, distinct roots, minimal vanishing subsets, and affine or Galois equivalence found no primary source that lists every fixed-conductor affine orbit. This is a dated search result and supplies no proof of absence. Production orient resolved one published, open target, problem 2744, with zero attached research records and no stored statement-integrity advisory. Production check-plan found no stored work covering the exact matrix search, while warning that retrieval was not exhaustive.\n\nThe canonical statement omits an explicit condition that S be nonempty. Standard minimal-vanishing-sum usage has positive weight, and this packet begins at weight 1. A future resolution should add S nonempty to the statement or settle the weight-0 convention separately.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2008.11268",
      "locator": "arXiv:math/9511209v1; arXiv:2008.11268v1 and v2; GitHub repository lchristie/Sums-of-Roots-of-Unity at commit b0563b270dc89ed7ca9e195535a107d5a81cc6dc; production audit dated 2026-07-28 UTC"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2008.11268",
    "locator": "arXiv:math/9511209v1; arXiv:2008.11268v1 and v2; GitHub repository lchristie/Sums-of-Roots-of-Unity at commit b0563b270dc89ed7ca9e195535a107d5a81cc6dc; production audit dated 2026-07-28 UTC"
  },
  "models": [],
  "relations": [
    {
      "slug": "R532",
      "title": "Lam and Leung establish the unique weight-fourteen asymmetric type",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R530",
      "title": "The proved type classification stops at weight sixteen",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "minimal-vanishing-105th-root-sums",
      "title": "minimal vanishing 105th root sums",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}