{"slug":"oip-convergence-edge-9","head_index":3,"current":{"title":"Convergence Edge 9: Branching ↔ Networks","updated_at":"2026-07-04T05:01:38.410Z"},"revisions":[{"n":0,"ts":"2026-07-04T02:54:05.892Z","title":"Convergence Edge 9: Edge 9: C16 (Branching) recurs-with C11 (Networks) - Shared pattern: Hierarchical connectivity; few large channels, many small ones; optimal transport through tree-like structures - Domain distance: Physiology/Geology → Sociology/Technology (large) - Derivation independence: HIGH. Murray (physiology, 1926) derived the law from blood flow. Horton (geology, 1945) found stream ordering. Barabasi (physics, 1999) found hub-and-spoke in scale-free networks. The tree structure of branching transport and the hub structure of scale-free networks are geometric duals: both minimize average path length given connectivity constraints. - Convergence strength (1–10): 7 - Note: The convergence is in the optimization structure: both are solutions to the problem of connecting many points to one source with minimum cost. One is continuous (branching), one is discrete (network).","status":"published","bytes":0,"hash":"336b869132174d55d2458f74a47ced865cfc54701a6e9d721bded3a828d171ba"},{"n":1,"ts":"2026-07-04T03:33:05.603Z","title":"Convergence Edge 9: Edge 9: C16 (Branching) recurs-with C11 (Networks) - Shared pattern: Hierarchical connectivity; few large channels, many small ones; optimal transport through tree-like structures - Domain distance: Physiology/Geology → Sociology/Technology (large) - Derivation independence: HIGH. Murray (physiology, 1926) derived the law from blood flow. Horton (geology, 1945) found stream ordering. Barabasi (physics, 1999) found hub-and-spoke in scale-free networks. The tree structure of branching transport and the hub structure of scale-free networks are geometric duals: both minimize average path length given connectivity constraints. - Convergence strength (1–10): 7 - Note: The convergence is in the optimization structure: both are solutions to the problem of connecting many points to one source with minimum cost. One is continuous (branching), one is discrete (network).","status":"published","bytes":871,"hash":"af3d749f3c541ff9997cb5707c76b8c561dd65a69590fc61ce230a39d2a16342"},{"n":2,"ts":"2026-07-04T04:33:39.506Z","title":"Convergence Edge 9: Branching ↔ Networks","status":"published","bytes":1702,"hash":"db2d9e09f635ac5960c0509c5bf5d46e40ba9440d327479d22414557eb3d8c37"}]}