{"slug":"convergence-c04","verification":{"valid":false,"broken_at":0,"reason":"prev mismatch"},"count":5,"sources":[{"id":"prigogine-1977","type":"primary","url":"https://miscsubjects.com/api/articles/prigogine-1977","title":"Dissipative structures and far-from-equilibrium order","quote":"They proved that dissipative systems break symmetry spontaneously. A chemical soup far from equilibrium builds structure. It exports entropy. It organizes itself.","summary":"Prigogine and Lefever's 1968 proof that non-equilibrium chemical systems spontaneously organize by breaking symmetry and exporting entropy","claim_ids":["C1","C5"],"quality_score":0.92},{"id":"turing-1936","type":"primary","url":"https://miscsubjects.com/api/articles/turing-1936","title":"The mathematical basis of pattern formation","quote":"He built reaction-diffusion equations. He showed that uniform chemicals self-organize into patterns. Stripes on a zebra. Spots on a leopard. The digits on your hand. All from a sphere breaking symmetry.","summary":"Turing's 1952 paper on morphogenesis via reaction-diffusion, demonstrating pattern formation from broken symmetry in uniform chemical systems","claim_ids":["C4"],"quality_score":0.93},{"id":"wilson-1971","type":"primary","url":"https://miscsubjects.com/api/articles/wilson-1971","title":"Renormalization group and critical phenomena","quote":"He showed that at criticality, correlation length diverges to infinity. The system forgets its microscopic details. Only the symmetry and dimensionality matter.","summary":"Wilson's renormalization group framework unifying critical phenomena across different physical systems via symmetry and dimensionality","claim_ids":["C1","C3"],"quality_score":0.94},{"id":"bak-1987","type":"primary","url":"https://miscsubjects.com/api/articles/bak-1987","title":"Self-organized criticality and emergent structure","quote":"They added grains to a lattice. At a critical slope, avalanches occur. The avalanches follow power laws. The system self-organizes to criticality. It does not need tuning. It finds the critical point itself.","summary":"Bak, Tang, and Wiesenfeld's sandpile model showing spontaneous symmetry-breaking at self-organized critical points without external tuning","claim_ids":["C6"],"quality_score":0.88},{"id":"noether-1918","type":"adjacent","url":"https://miscsubjects.com/api/articles/noether-1918","title":"Symmetry and conservation laws","quote":"The Higgs field settles into a nonzero vacuum expectation value. Three forces split from one. Particles acquire mass. The W and Z bosons grow heavy. The photon stays massless.","summary":"The article maps Noether's symmetry-conservation linkage to the Higgs mechanism's electroweak symmetry-breaking and mass generation","claim_ids":["C2"],"quality_score":0.85}]}