{"slug":"oip-invariant-4-34-symmetry-breaking-bifurcation","title":"Invariant 3.4 — 3.4 Symmetry-breaking / bifurcation","body":"# Invariant: 3.4 Symmetry-breaking / bifurcation\n\n### 3.4 Symmetry-breaking / bifurcation\nStructure, mass, and form arise when a symmetry *breaks*. **Sources:** Landau; Anderson; Higgs; Prigogine (bifurcation); morphogenesis. **Domains:** cosmology, phase transitions, developmental biology. **Dual:** symmetry (§3.3). **Tier:** T1. **Falsifier:** structure appearing with no prior symmetric state. **Maps:** A₁, A₇. *(Note: §3.3 and §3.4 are a `dual-of` pair — the two are the engine of \"difference → form.\")*\n\n---\n\n## Corpus map\n- Same invariant, other planes: [Catalogue node C04](/a/oip-node-c04-symmetry-breaking-bifurcation) · [Encyclopedia C04](/a/convergence-encyclopedia-c04)\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":"Structure, mass, and form arise when a symmetry breaks.","section":"### 3.4 Symmetry-breaking / bifurcation","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Core assertion defining the invariant mechanism of form emergence."},{"id":"c2","text":"§3.3 and §3.4 form a dual-of pair that functions as the engine of difference to form.","section":"### 3.4 Symmetry-breaking / bifurcation","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Explicit relational definition between paired invariants."},{"id":"c3","text":"A falsifier of the invariant is structure appearing with no prior symmetric state.","section":"### 3.4 Symmetry-breaking / bifurcation","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Provides the test condition for the claim."}],"sources":[],"prov":{"model":"Fable 5 (Claude Code)","action":"write"}}