{"slug":"oip-invariant-3-33-symmetry-conservation","title":"Invariant 3.3 — 3.3 Symmetry ↔ conservation","body":"# Invariant: 3.3 Symmetry ↔ conservation\n\n### 3.3 Symmetry ↔ conservation\nEvery 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.\n\n---\n\n## Corpus map\n- Same invariant, other planes: [Catalogue node C03](/a/oip-node-c03-symmetry-conservation) · [Encyclopedia C03](/a/convergence-encyclopedia-c03)\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":"Every continuous symmetry yields a conserved quantity.","section":"### 3.3 Symmetry ↔ conservation","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Core statement of the invariant linking symmetry to conservation."},{"id":"c2","text":"The dual of the invariant is symmetry-breaking.","section":"### 3.3 Symmetry ↔ conservation","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Specifies the paired concept for the invariant."},{"id":"c3","text":"The tier of the invariant is T0 (theorem).","section":"### 3.3 Symmetry ↔ conservation","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Classifies the invariant's formal status."},{"id":"c4","text":"The scale of the invariant is quantum → cosmic.","section":"### 3.3 Symmetry ↔ conservation","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Defines the range of applicability."},{"id":"c5","text":"The invariant maps to A₁ and A₃.","section":"### 3.3 Symmetry ↔ conservation","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Specifies explicit mappings for the invariant."},{"id":"c6","text":"The same invariant appears in other planes at Catalogue node C03 and Encyclopedia C03.","section":"## Corpus map","tier":"anecdotal","source_ids":[],"source_status":"unsourced","why_material":"Documents cross-references within the corpus."},{"id":"c7","text":"The inventory hub for the invariant is Convergence Catalogue — Public Article.","section":"## Corpus map","tier":"anecdotal","source_ids":[],"source_status":"unsourced","why_material":"Documents the central reference point in the corpus."}],"sources":[],"prov":{"model":"Fable 5 (Claude Code)","action":"write"}}