{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1504",
  "content_hash": null,
  "slug": "durers-edge-unfolding-problem-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring 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. Exact 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": "For Dürer’s edge-unfolding problem, record durers-edge-unfolding-problem-claim-status-20260801 (“Current status and exact unresolved remainder”) records a bound, answer, status fact, or structural consequence. The record states: OPEN as checked on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The problem was checked as open on 2026-08-01.\n\nThe strongest neighboring result found in the cited sources is: 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.\n\nThe exact unresolved remainder is: Prove a nonoverlapping spanning-tree edge unfolding exists for every original convex three-polytope, or exhibit one polytope for which every such unfolding overlaps.\n\nA complete resolution must meet the following acceptance conditions:\n- For a proof, construct or establish a valid spanning tree for every convex three-polytope and prove injectivity on face interiors.\n- For a disproof, give explicit coordinates and faces for one convex polytope and exhaust or structurally exclude every spanning-tree edge unfolding.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "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": "R1503",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1501",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1502",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "durers-edge-unfolding-problem",
      "title": "durers edge unfolding problem",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}