# Invariant 3.3 — 3.3 Symmetry ↔ conservation

slug: oip-invariant-3-33-symmetry-conservation · https://miscsubjects.com/a/oip-invariant-3-33-symmetry-conservation · tags: philosophy, oip, catalogue, invariant, systems-theory · updated 2026-07-17T02:36:16.784Z

# Invariant: 3.3 Symmetry ↔ conservation

### 3.3 Symmetry ↔ conservation
Every continuous symmetry yields a conserved quantity. **Sources:** Noether's theorem; Lie/group theory; gauge theory; Curie's principle. **Domains:** physics core, crystallography, particle physics, aesthetics. **Scale:** quantum → cosmic. **Dual:** symmetry-breaking (below). **Tier:** T0 (theorem). **Falsifier:** n/a for the theorem; for a *mapping*, a conserved quantity with no symmetry. **Maps:** A₁, A₃.

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## Corpus map
- Same invariant, other planes: [Catalogue node C03](/a/oip-node-c03-symmetry-conservation) · [Encyclopedia C03](/a/convergence-encyclopedia-c03)
- Inventory hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article)