{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1503",
  "content_hash": null,
  "slug": "durers-edge-unfolding-problem-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "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.",
  "relevance": "For Dürer’s edge-unfolding problem, record durers-edge-unfolding-problem-claim-literature-frontier (“Strongest checked neighboring result”) records a bound, answer, status fact, or structural consequence. The record states: 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.",
  "relevance_source": "recorded",
  "body": "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\nThis leaves the following boundary unresolved: Prove a nonoverlapping spanning-tree edge unfolding exists for every original convex three-polytope, or exhibit one polytope for which every such unfolding overlaps. The distinction is retained here so a restricted theorem, finite computation, or neighboring case is not presented as a solution of the full target.",
  "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"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1504",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "durers-edge-unfolding-problem",
      "title": "durers edge unfolding problem",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}