---
slug: oip-convergence-edge-10
title: Convergence Edge 10: Symmetry-Breaking ↔ Attractors
canonical: https://miscsubjects.com/a/oip-convergence-edge-10
---

**C04** (Symmetry-Breaking) recurs-with **C23** (Attractors)

**Shared pattern:** A symmetric state becomes unstable; the system must choose among equivalent broken states; different initial conditions fall into the same attractor basins

**Domain distance:** Particle physics/Cosmology → Dynamical systems/Meteorology (large)

**Derivation independence:** HIGH. Higgs (particle physics, 1964) showed gauge symmetry breaking gives mass. Landau (condensed matter, 1937) showed phase transitions break symmetry. Lorenz (meteorology, 1963) found strange attractors where symmetric equations produce asymmetric trajectories. Thom (topology, 1972) classified catastrophe types from symmetry-breaking. Four fields, same mathematics (bifurcation theory), same pattern: symmetric laws, asymmetric outcomes.

**Convergence strength (1–10):** 9

**Note:** This is the most mathematically precise convergence in the catalogue. Both nodes are instances of bifurcation theory. The symmetry-breaking of the Higgs mechanism and the symmetry-breaking of a convecting fluid cell are the same mathematical operation on different Hamiltonians.

Summary Table: Cross-Domain Convergence Edges

---

## Corpus map
- C04 (Symmetry-Breaking): [C04 in the Encyclopedia](/a/convergence-encyclopedia-c04) · [C04 in the Catalogue](/a/oip-node-c04-symmetry-breaking-bifurcation)
- C23 (Attractors): [C23 in the Encyclopedia](/a/convergence-encyclopedia-c23) · [C23 in the Catalogue](/a/oip-node-c23-attractors-dynamical-systems)
- Convergence edges: [1](/a/oip-convergence-edge-1) · [2](/a/oip-convergence-edge-2) · [3](/a/oip-convergence-edge-3) · [4](/a/oip-convergence-edge-4) · [5](/a/oip-convergence-edge-5) · [6](/a/oip-convergence-edge-6) · [7](/a/oip-convergence-edge-7) · [8](/a/oip-convergence-edge-8) · [9](/a/oip-convergence-edge-9) · [10](/a/oip-convergence-edge-10)
- Catalogue hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article) · [The Schema](/a/oip-convergence-schema)
