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the rival frame holds that branching emerges from geometric necessity (dimensionality + conservation laws) rather than optimization.","tier":"speculative","weight":0.75,"status":"active","source_ids":["bejan-1996"],"posted_by":null,"who_claims":null,"edges":[{"type":"supported_by","target":"bejan-1996","source_type":"primary","hash":null}]},{"id":"c7","text":"Murray's law fails in turbulence, electrical conduction, and lightning; Horton's laws describe rivers, not lungs; the convergence is real but the mechanisms are not identical.","tier":"system","weight":0.8,"status":"active","source_ids":["murray-1926","horton-1945"],"posted_by":null,"who_claims":null,"edges":[{"type":"supported_by","target":"murray-1926","source_type":"primary","hash":null},{"type":"supported_by","target":"horton-1945","source_type":"primary","hash":null}]},{"id":"c8","text":"The convergence of branching patterns across four fields (physiology, geology, mechanical engineering, theoretical biology), four nations, and seven decades, with no borrowing chain, constitutes evidence of a substrate-independent principle.","tier":"system","weight":0.8,"status":"active","source_ids":["murray-1926","horton-1945","bejan-1996"],"posted_by":null,"who_claims":null,"edges":[{"type":"supported_by","target":"murray-1926","source_type":"primary","hash":null},{"type":"supported_by","target":"horton-1945","source_type":"primary","hash":null},{"type":"supported_by","target":"bejan-1996","source_type":"primary","hash":null}]}],"sources":[{"id":"murray-1926","type":"primary","url":"https://pubmed.ncbi.nlm.nih.gov/16587418/","title":"Murray 1926 PNAS - The Physiological Principle of Minimum Work Applied to the Angle of Branching of Arteries","quote":"He opened dogs and measured their arteries. 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