{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R552",
  "content_hash": null,
  "slug": "nonagon-tree-attempt-literature-audit",
  "type": "attempt",
  "title": "Literature gives general circle bounds but no exact nonagon value",
  "summary": "The closest papers study minimum-dilation trees, star centers, and asymptotic bounds for equally spaced circle points.",
  "relevance": "For Minimum spanning-tree dilation on the regular nonagon, record nonagon-tree-attempt-literature-audit (“Literature gives general circle bounds but no exact nonagon value”) documents a concrete method, search boundary, or failed route. The record states: The closest papers study minimum-dilation trees, star centers, and asymptotic bounds for equally spaced circle points.",
  "relevance_source": "recorded",
  "body": "Cheong, Haverkort, and Lee prove that computing a minimum-dilation spanning tree is NP-hard for general planar point sets. Eppstein and Wortman give algorithms for evaluating a star and choosing its center, including the case where the center must be an input point.\n\nAronov, de Berg, Cheong, Gudmundsson, Haverkort, Smid, and Vigneron use equally spaced circle points to obtain a linear lower bound for sparse geometric graphs. Buchin, Rehs, and Scheele revisit the same family. Their 2025 paper records the tree lower bound \\(2n/\\pi-1\\) from Aronov and coauthors and proves a tree upper bound\n\\[\n\\frac{2n}{\\pi}+\\frac{\\pi}{2n}.\n\\]\nThese bounds frame the present value without specifying the optimum for nine points.\n\nSearches for the title terms together with `nonagon`, `regular 9-gon`, and `nine equally spaced points` found no paper stating the exact nine-point tree value. This is a focused prior-art check, so the originality of the exact value remains unverified.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "focused search for geometric-spanner results on minimum-dilation trees and equally spaced points on a circle through 2026-07-24",
    "bounds": {
      "polygon_vertices": {
        "min": 9,
        "max": 9
      },
      "search_year": {
        "min": 2026,
        "max": 2026
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.4230/LIPIcs.SoCG.2025.26",
      "locator": "Buchin, Rehs, and Scheele, Geometric Spanners of Bounded Tree-Width, SoCG 2025, section 6.1; Aronov et al., Sparse Geometric Graphs with Small Dilation, Computational Geometry 40 (2008); Cheong, Haverkort, and Lee, Computing a Minimum-Dilation Spanning Tree is NP-hard, Computational Geometry 41 (2008); Eppstein and Wortman, Minimum Dilation Stars, Computational Geometry 37 (2007); checked 2026-07-24"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.4230/LIPIcs.SoCG.2025.26",
    "locator": "Buchin, Rehs, and Scheele, Geometric Spanners of Bounded Tree-Width, SoCG 2025, section 6.1; Aronov et al., Sparse Geometric Graphs with Small Dilation, Computational Geometry 40 (2008); Cheong, Haverkort, and Lee, Computing a Minimum-Dilation Spanning Tree is NP-hard, Computational Geometry 41 (2008); Eppstein and Wortman, Minimum Dilation Stars, Computational Geometry 37 (2007); checked 2026-07-24"
  },
  "relations": [
    {
      "slug": "R553",
      "title": "The minimum nonagon tree dilation is 2+4 cos(pi/9)",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "regular-nonagon-tree-dilation",
      "title": "regular nonagon tree dilation",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}