{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R34",
  "content_hash": null,
  "slug": "asser-attempt-dated-source-audit",
  "type": "attempt",
  "title": "Dated source and duplicate audit",
  "summary": "The 2026-07-28 audit found the general problem still presented as open, located the three-variable bipartite reduction and the C2 closure theorem, and found no prior packet attached to problem 2828.",
  "relevance": "For Asser's complement problem for first-order spectra, record asser-attempt-dated-source-audit (“Dated source and duplicate audit”) documents a concrete method, search boundary, or failed route. The record states: The 2026-07-28 audit found the general problem still presented as open, located the three-variable bipartite reduction and the C2 closure theorem, and found no prior packet attached to problem 2828.",
  "relevance_source": "recorded",
  "body": "The audit began with the canonical statement, then read the Durand–Jones–Makowsky–More survey, the two finite-variable papers by Kopczyński and Tan, their later one-relation graph reduction, and Reichenberger’s recent historical account. The survey supplies the original formulation and the spectrum-complexity theorem used here. Targeted searches through 2026 found no claimed solution or stronger normal form.\n\nA broad positive fragment checked here is \\(C^2\\), whose spectra are exactly semilinear. The most restrictive normal form located for the remaining problem is Corollary 1.2 of the 2018 paper: three variables and one symmetric binary relation suffice when all finite models are undirected bipartite graphs. The targeted monadic search found the finite-or-cofinite classification and de Rijke’s explicit bounded-rank equivalence criterion, with no exact generator classification or rank-stratified spectrum count. The search cannot establish novelty for the formulas proved in this packet. TheoremDB orientation resolved the production target exactly and returned zero attached research records. Local fixture and slug searches found no competing packet or duplicate research object.\n\nThis was a focused dated search, so silence outside the checked sources has no evidentiary force. The open-status record relies on what the named sources state and on the absence of a located later resolution.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "family",
    "statement": "primary and specialist sources concerning the general complement question, finite-variable reductions, and established fragment closures",
    "family": "first-order spectrum complement literature"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.2178/bsl.1804020",
      "locator": "Durand, Jones, Makowsky, and More, Open Question 2, arXiv manuscript pp. 7–8"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.2178/bsl.1804020",
    "locator": "Durand, Jones, Makowsky, and More, Open Question 2, arXiv manuscript pp. 7–8"
  },
  "models": [],
  "relations": [
    {
      "slug": "R38",
      "title": "Asser's complement problem remains open",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "R40",
      "title": "Three-variable bipartite graph sentences suffice",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "R37",
      "title": "The two-variable counting fragment is closed under complement",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "first-order-spectra-complement-closure",
      "title": "first order spectra complement closure",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}