{"slug":"oip-invariant-5-35-criticality-edge-of-chaos-power-laws","title":"Invariant 3.5 — 3.5 Criticality / edge of chaos / power laws","body":"# Invariant: 3.5 Criticality / edge of chaos / power laws\n\n### 3.5 Criticality / edge of chaos / power laws\nThe richest behavior sits between frozen order and noise. **Sources:** Per Bak (self-organized criticality); Kauffman & Langton (edge of chaos); Wilson (renormalization group); Mandelbrot, Zipf, Pareto (power laws). **Domains:** sandpiles, earthquakes, brains (neuronal avalanches), markets, cities, language. **Scale:** molecular → civilization. **Dual:** rigid lattice / pure randomness (the two death-states). **Tier:** T1 core, T2 for claims of ubiquity. **Falsifier:** a living/adaptive system provably tuned far from criticality. **Maps:** A₂, A₇; this is your \"bounded chaos.\"\n\n---\n\n## Corpus map\n- Same invariant, other planes: [Catalogue node C05](/a/oip-node-c05-criticality-edge-of-chaos-power-laws) · [Encyclopedia C05](/a/convergence-encyclopedia-c05)\n- Inventory hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article)","register":"oip_protocol","tags":["philosophy","oip","catalogue","invariant","systems-theory"],"category":null,"style":{},"claims":[{"id":"c1","text":"The richest behavior sits between frozen order and noise.","section":"### 3.5 Criticality / edge of chaos / power laws","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Core definition of the invariant's location in state space."}],"sources":[],"prov":{"model":"Fable 5 (Claude Code)","action":"write"}}