{"slug":"convergence-c11","verification":{"valid":false,"broken_at":0,"reason":"prev mismatch"},"count":5,"sources":[{"id":"watts-1998","type":"primary","url":"https://miscsubjects.com/a/watts-1998","title":"Watts & Strogatz (1998) — Collective dynamics of 'small-world' networks","quote":"They rewired a few edges in a regular lattice. Clustering stayed high. Path length collapsed. The math is exact. This is theorem, not metaphor.","summary":"Foundational paper introducing the small-world network model, proving that rewiring a small fraction of edges in a regular lattice preserves high clustering while dramatically reducing path length.","claim_ids":["c1","c2"],"quality_score":0.95},{"id":"barabasi-1999","type":"primary","url":"https://miscsubjects.com/a/barabasi-1999","title":"Barabasi & Albert (1999) — Emergence of scaling in random networks","quote":"They proved preferential attachment births power laws. Growth plus inequality in links equals scale-free topology. This is statistical physics. This is not sociology.","summary":"Foundational paper on scale-free networks proving that preferential attachment produces power-law degree distributions, with empirical confirmation across internet topology, protein networks, and metabolic networks.","claim_ids":["c1","c3","c4","c5","c6","c8"],"quality_score":0.95},{"id":"granovetter-1973","type":"primary","url":"https://miscsubjects.com/a/granovetter-1973","title":"Granovetter (1973) — The Strength of Weak Ties","quote":"People found jobs through acquaintances. Not close friends. Weak ties bridge clusters. They carry novel information across social distance.","summary":"Sociological study demonstrating that weak social ties (acquaintances) bridge otherwise disconnected clusters and carry novel information, a key mechanism in small-world social networks.","claim_ids":["c4"],"quality_score":0.9},{"id":"prigogine-1977","type":"adjacent","url":"https://miscsubjects.com/a/prigogine-1977","title":"Prigogine (1977) — Dissipative structures: order maintained by gradient flow","quote":"Networks are dissipative structures. They persist only while gradients flow. A river delta exists while water flows. The internet exists while electricity flows. Your brain exists while glucose flows.","summary":"Nobel-winning work on dissipative structures: ordered systems that persist only while energy gradients flow through them, providing a thermodynamic framework for network existence.","claim_ids":["c7"],"quality_score":0.75},{"id":"shannon-1948","type":"adjacent","url":"https://miscsubjects.com/a/shannon-1948","title":"Shannon (1948) — A mathematical theory of communication","quote":"Each link is a channel. Each node is a switch. The network topology determines how much information can flow. Small-world topology maximizes information flow per connection.","summary":"Foundational information theory paper establishing that network topology constrains information flow capacity, with small-world structures optimizing flow per connection.","claim_ids":["c7"],"quality_score":0.8}]}