{"_self":{"principle":"Self-explaining payload — no external context required. This _self block describes what you are reading and where to look next.","widget":"article_voxels","feature":"voxels","name":"Voxel graph","what":"Claims as atoms, sources as edges (supported_by, posted_by). Per-claim provenance.","contains":"claim voxels + source edges","slug":"bak-1987","urls":{"read":"https://miscsubjects.com/api/articles/bak-1987/voxels","write":"https://miscsubjects.com/api/protocol/claim"},"how_to_use":"Claims as atoms, sources as edges (supported_by, posted_by). 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Rev. Lett. 59, 381, 1987)","quote":"We argue and demonstrate numerically that dynamical systems with extended spatial degrees of freedom naturally evolve into self-organized critical structures of states which are barely stable. We suggest that this self-organized criticality is the common underlying mechanism behind the phenonomenon of 1/f noise and the behavior of the sandpile.","summary":"The original 1987 letter that introduced the concept of self-organized criticality (SOC). It presents a simple sandpile cellular automaton, shows numerically that it evolves into a barely stable critical state, and proposes SOC as the explanation for 1/f noise and avalanche dynamics.","claim_ids":["c1","c2","c3","c6"]},{"id":"src2","type":"primary","url":"https://doi.org/10.1103/PhysRevA.38.364","title":"Self-Organized Criticality (Phys. Rev. A 38, 364, 1988)","quote":"When z_i ≥ z_c: z_i → z_i - 4, neighbors z_j → z_j + 1.","summary":"The extended 1988 paper providing the full mathematical treatment of the sandpile model, precise update rules, and detailed numerical results for avalanche statistics in multiple dimensions.","claim_ids":["c2"]},{"id":"src3","type":"adjacent","url":"https://doi.org/10.1523/JNEUROSCI.23-35-11167.2003","title":"Beggs & Plenz (2003) — Neuronal avalanches in neocortical circuits","quote":"","summary":"Empirical follow-up study finding cortical avalanches with power-law size distributions, cited in the article as evidence that SOC-like statistics appear in neural tissue. Provides biological instantiation of the grain pattern.","claim_ids":["c4"]},{"id":"src4","type":"rival","url":"https://doi.org/10.1126/science.286.5439.509","title":"Barabási & Albert (1999) — Emergence of scaling in random networks","quote":"","summary":"Demonstrates that power-law (scale-free) distributions can emerge from preferential attachment without any threshold-driven critical dynamics. Serves as a direct rival mechanism to SOC for explaining observed power laws.","claim_ids":["c5"]},{"id":"src5","type":"adjacent","url":"https://miscsubjects.com/article/grain-the-no-go-theorems","title":"GRAIN — The No-Go Theorems","quote":"","summary":"Internal GRAIN convergence article cited as a philosophical frame that questions whether power laws always imply criticality and whether 'edge of chaos' is a mechanism or a slogan. 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