{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1501",
  "content_hash": null,
  "slug": "durers-edge-unfolding-problem-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: Every convex polyhedron becomes edge-unfoldable after a suitable affine transformation, and every nested three-prismatoid has a nonoverlapping edge unfolding; recent work also constructs highly overlapping edge unfoldings. Unresolved remainder: Prove a nonoverlapping spanning-tree edge unfolding exists for every original convex three-polytope, or exhibit one polytope for which every such unfolding overlaps.",
  "relevance": "Documents why Dürer’s edge-unfolding problem 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- Dürer edge unfolding every convex polyhedron open\n- convex 3-polytope spanning tree nonoverlapping net\n- Dürer problem affine unfolding pseudo-edge counterexample\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: Every convex polyhedron becomes edge-unfoldable after a suitable affine transformation, and every nested three-prismatoid has a nonoverlapping edge unfolding; recent work also constructs highly overlapping edge unfoldings. Unresolved remainder: Prove a nonoverlapping spanning-tree edge unfolding exists for every original convex three-polytope, or exhibit one polytope for which every such unfolding overlaps.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.2140/gt.2014.18.3055",
      "locator": "M. Ghomi, “Affine unfoldings of convex polyhedra,” Geometry & Topology 18(5) (2014), 3055–3090. abstract and main theorem"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.2140/gt.2014.18.3055",
    "locator": "M. Ghomi, “Affine unfoldings of convex polyhedra,” Geometry & Topology 18(5) (2014), 3055–3090. abstract and main theorem"
  },
  "relations": [
    {
      "slug": "R1504",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "durers-edge-unfolding-problem",
      "title": "durers edge unfolding problem",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}