{"slug":"convergence-c10","verification":{"valid":false,"broken_at":0,"reason":"prev mismatch"},"count":5,"sources":[{"id":"mandelbrot-1967","type":"primary","url":"/a/mandelbrot-1967","title":"Mandelbrot (1967, 1982) — How Long Is the Coast of Britain? / The Fractal Geometry of Nature","quote":"The coast has no fixed length. It has a dimension.","summary":"Introduced fractal geometry and fractional dimension; showed that natural coastlines, turbulence, and prices exhibit statistical self-similarity across scales.","claim_ids":["c1","c2","c7"],"quality_score":0.95},{"id":"kleiber-1932","type":"primary","url":"","title":"Kleiber (1932) — Body Size and Metabolism","quote":"The data fell on a straight line. The slope was 0.74. Not 0.67. Not 0.85. Three-quarters.","summary":"Published in Hilgardia; measured 13 mammals and found metabolic rate scales with mass^0.74, now known as Kleiber's law.","claim_ids":["c3"],"quality_score":0.9},{"id":"wbe-1997","type":"primary","url":"","title":"West, Brown & Enquist (1997) — A General Model for the Origin of Allometric Scaling Laws in Biology","quote":"They derived Kleiber's 3/4 from first principles. The same math predicts lungs, rivers, and respiratory trees.","summary":"Published in Science; derived 3/4 metabolic scaling from fractal space-filling transport networks and energy minimization.","claim_ids":["c3","c4"],"quality_score":0.85},{"id":"wilson-1971","type":"primary","url":"/a/wilson-1971","title":"Wilson (1971, 1982 Nobel) — Renormalization Group and Critical Phenomena","quote":"He showed that near phase transitions, the same scaling rules apply regardless of material.","summary":"Solved critical phenomena using renormalization group theory; proved universality classes and scale invariance at phase transitions.","claim_ids":["c5"],"quality_score":0.95},{"id":"bak-1987","type":"primary","url":"/a/bak-1987","title":"Bak, Tang & Wiesenfeld (1987) — Self-Organized Criticality","quote":"The avalanches followed power laws. Small slips were common. Big collapses were rare. No characteristic scale existed.","summary":"Introduced SOC: systems naturally evolve to critical states producing power-law distributions without external tuning.","claim_ids":["c6"],"quality_score":0.85}]}