{"slug":"paper-feigenbaum-m-j-1979-the-universal-metric-properties-of-nonlinear-transformations","verification":{"valid":true,"entries":2,"head":"94fb4de0d5e9d4b234081d9cc458df36ece1562d85e2284ef1a43b6cde3e2c77"},"count":2,"sources":[{"id":"s1","type":"other","url":"https://link.springer.com/article/10.1007/BF01107909","title":"The universal metric properties of nonlinear transformations","quote":"A hierarchy of universal functions g_τ(X) exists, each descriptive of the same local structure but at levels of a cluster of 2^τ points.","summary":"Primary 1979 paper establishing Feigenbaum constants and functional equations.","claim_ids":["c1","c2","c3","c4"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-10T11:44:41.334Z","link_status":"ok","quote_status":"unverified","prev":"genesis","hash":"9bd00fc0cc44e99387f3be56ac6b812b333dedb09b2a2ca77b92771333bd02ee"},{"id":"s2","type":"other","url":"https://en.wikipedia.org/wiki/Feigenbaum_constants","title":"Feigenbaum constants","quote":"Two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map.","summary":"Verified summary of constants and their origin in Feigenbaum's work.","claim_ids":["c1"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-10T11:44:41.334Z","link_status":"ok","quote_status":"unverified","prev":"9bd00fc0cc44e99387f3be56ac6b812b333dedb09b2a2ca77b92771333bd02ee","hash":"94fb4de0d5e9d4b234081d9cc458df36ece1562d85e2284ef1a43b6cde3e2c77"}]}