{"slug":"oip-pattern-4-pattern-4-symmetry-the-compression-solution","verification":{"valid":true,"entries":1,"head":"b1948ffb691ded26941689ac9a5ab18721d245507ed52e43e65d642c772d8e75"},"count":1,"sources":[{"id":"s1","type":"other","url":"","title":"Honeycomb conjecture proof","quote":"","summary":"Proven by Hales in 1999 that hexagonal tiling minimizes perimeter for equal-area partition of the plane.","author":"","publisher":"","date":"","claim_ids":["c20"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-07T07:47:54.686Z","link_status":"invalid","quote_status":"na","prev":"genesis","hash":"b1948ffb691ded26941689ac9a5ab18721d245507ed52e43e65d642c772d8e75"}]}