{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1698",
  "content_hash": null,
  "slug": "planar-convex-hot-spots-attempt-dated-source-audit",
  "type": "attempt",
  "title": "Dated source and duplicate audit",
  "summary": "The exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Many planar classes are proved; convex counterexamples now exist in sufficiently high dimension. Unresolved remainder: No convex planar counterexample or general proof was located.",
  "relevance": "Documents why Hot spots conjecture for convex planar domains was treated as a distinct open target on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The audit ran on 2026-08-01 across the cited primary literature and problem collections, Crossref, arXiv, and stable publisher records, TheoremDB published, prospecting, packet, formal, and retired corpus. It checked the exact statement, its named or normalized variants, recent status evidence, and the controlled TheoremDB corpus.\n\nQueries included:\n- convex planar hot spots conjecture open 2026\n- first Neumann eigenfunction convex domain interior maximum dimension two\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Many planar classes are proved; convex counterexamples now exist in sufficiently high dimension. Unresolved remainder: No convex planar counterexample or general proof was located.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/2405.19508",
      "locator": "Lawford Hatcher, “The hot spots conjecture for some non-convex polygons,” arXiv:2405.19508v3. introduction and main theorems"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2405.19508",
    "locator": "Lawford Hatcher, “The hot spots conjecture for some non-convex polygons,” arXiv:2405.19508v3. introduction and main theorems"
  },
  "relations": [
    {
      "slug": "R1701",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "planar-convex-hot-spots",
      "title": "planar convex hot spots",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}