{
  "status": "PASS",
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  "all_cyclic_offset_case_count": 154918,
  "offset_validation": "All edge subsets and graph components checked explicitly; geometric rotation equivariance transfers complete base sampled-interval-union certificates to every cyclic offset.",
  "scope": "Exact component-budget frontier for interior uniform-normal audits.",
  "arithmetic": "Exact integer edge counts plus geometric analytic formulas evaluated in float64.",
  "proof_dependency": {
    "authors": [
      "D. Z. Du",
      "F. K. Hwang",
      "J. F. Weng"
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    "title": "Steiner minimal trees for regular polygons",
    "journal": "Discrete & Computational Geometry",
    "year": 1987,
    "volume": 2,
    "pages": "65-84",
    "doi": "10.1007/BF02187871",
    "primary_url": "https://doi.org/10.1007/BF02187871",
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