{
  "version": "1.0.0",
  "date": "2026-11-01",
  "construction": "Original square grids, a three-region partition, and concentric polygon rings generated by build-four-color.py.",
  "adjacency": "Two polygons are neighbors only when collinear sides overlap by a positive length; a single point is not an edge.",
  "calculation": "For each map, enumerate assignments in lexicographic order for k=1,2,3,4. Reject any matching adjacent pair. Stop at the first valid assignment.",
  "minimum": "Every assignment with fewer colors is exhausted; the first valid assignment is an upper-bound witness. Short mathematical explanations are supplied per map.",
  "tolerance": "Coordinates rounded to 4 decimals; collinearity and overlap tolerance 1e-5. No nearly coincident edges occur in this pack.",
  "validation": "Reproduction independently re-derives adjacency from the polygons, checks polygon area/overlap and compares computed minimum colors to stored results.",
  "limitations": [
    "This finite exercise set does not prove the four color theorem.",
    "The outside of each diagram is excluded from this activity.",
    "Each labeled region is connected; no islands share a country identity.",
    "No learning-outcome or age-suitability study was performed."
  ],
  "corrections": "https://coloringpagegenerator.net/contact"
}