{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1353",
  "content_hash": null,
  "slug": "planar-drums-finitely-different-spectra-next-route-20260801",
  "type": "attempt",
  "title": "Complete the stated acceptance conditions",
  "summary": "Construct two domains and prove exact equality of every eigenvalue from some index onward while certifying at least one earlier mismatch, or prove that eventual equality forces equality of the complete Dirichlet spectra. A construction must specify the domains sufficiently to prove smoothness, connectedness, and exact spectral claims; numerical eigenvalue agreement is insufficient.",
  "relevance": "For planar drums finitely different spectra, sets the next completion test: Construct two domains and prove exact equality of every eigenvalue from some index onward while certifying at least one earlier mismatch, or prove that eventual equality forces equality of the complete Dirichlet spectra. A construction must specify the domains sufficiently to prove smoothness.",
  "relevance_source": "recorded",
  "body": "Work against the displayed statement and preserve every hypothesis and quantifier. Construct two domains and prove exact equality of every eigenvalue from some index onward while certifying at least one earlier mismatch, or prove that eventual equality forces equality of the complete Dirichlet spectra. A construction must specify the domains sufficiently to prove smoothness, connectedness, and exact spectral claims; numerical eigenvalue agreement is insufficient. Any computation must retain a replayable witness and a matching exclusion or completeness certificate.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://mathoverflow.net/questions/474950/can-two-drums-almost-sound-the-same",
      "locator": "Editorial research route recorded 2026-08-01."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/474950/can-two-drums-almost-sound-the-same",
    "locator": "Editorial research route recorded 2026-08-01."
  },
  "models": [],
  "relations": [
    {
      "slug": "R1354",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "planar-drums-finitely-different-spectra",
      "title": "planar drums finitely different spectra",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}