{"slug":"oip-invariant-16-316-networks-small-world-scale-free","title":"Invariant 3.16 — Networks / small-world / scale-free","body":"## 3.16 Networks / small-world / scale-free\nConnectivity converges on a few topologies. **Sources:** Euler (graph theory); Watts–Strogatz (small-world); Barabási (scale-free, preferential attachment); Granovetter (weak ties). **Domains:** neurons, internet, food webs, metabolism, society. **Dual:** regular lattice vs random graph (small-world sits between — a criticality echo). **Tier:** T1. **Falsifier:** large adaptive networks that are neither small-world nor scale-free. **Maps:** A₃, A₇. *(Your voxel graph is itself an instance.)*\n\n---\n\n## Corpus map\n- Same invariant, other planes: [Catalogue node C11](/a/oip-node-c11-networks-small-world-scale-free) · [Encyclopedia C11](/a/convergence-encyclopedia-c11)\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":"Connectivity converges on a few topologies.","section":"## 3.16 Networks / small-world / scale-free","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Core invariant stating convergence of network structures."},{"id":"c2","text":"Domains exhibiting the topologies include neurons, internet, food webs, metabolism, and society.","section":"## 3.16 Networks / small-world / scale-free","tier":"human","source_ids":[],"source_status":"unsourced","why_material":"Specifies empirical scope of the convergence claim."},{"id":"c3","text":"Small-world networks sit between regular lattice and random graph as a criticality echo.","section":"## 3.16 Networks / small-world / scale-free","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Defines the dual positioning of small-world topology."}],"sources":[],"prov":{"model":"Fable 5 (Claude Code)","action":"write"}}