{"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)","hero":null,"images":[],"style":{},"tags":["philosophy","oip","catalogue","invariant","systems-theory"],"model":null,"ledger":null,"embeds":[],"widgets":[],"home":true,"claims":[],"sources":[],"reviews":[],"extra":{"kind":"corpus","corpus_map":{"prev":"oip-invariant-2-32-least-action-variational-principles","next":"oip-invariant-4-34-symmetry-breaking-bifurcation","hub":"oip-convergence-public-article","series":"catalogue-inventory-invariants","position":3,"of":22}},"register":"oip_protocol","status":"published","revisions":3,"contributions":[],"provenance":[{"ts":"2026-07-04T04:33:53.465Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"b3530229c0c4fdae053ed70c5d1be32affb60db2ed8d5cd514a5f9103a1ae2e3"},{"ts":"2026-07-04T05:01:51.438Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"b3530229c0c4fdae053ed70c5d1be32affb60db2ed8d5cd514a5f9103a1ae2e3","hash":"5e9b5115f35398e49ee9f91d8c4b794c8d7d508cc11123eac4fb161ae1ea9879"}],"energy":{"passes":2,"tokens_in":0,"tokens_out":0,"tokens_total":0,"cost_usd":0,"models":{"claude-fable-5":2},"head":"5e9b5115f35398e49ee9f91d8c4b794c8d7d508cc11123eac4fb161ae1ea9879"},"posted_at":"2026-07-04T02:40:23.228Z","created_at":"2026-07-04T02:40:23.228Z","updated_at":"2026-07-04T05:01:51.438Z","machine":{"shape":"article.machine/v1","slug":"oip-invariant-3-33-symmetry-conservation","kind":"corpus","read":{"human":"https://miscsubjects.com/a/oip-invariant-3-33-symmetry-conservation","json":"https://miscsubjects.com/api/articles/oip-invariant-3-33-symmetry-conservation","bundle":"https://miscsubjects.com/api/articles/oip-invariant-3-33-symmetry-conservation/bundle?format=markdown"},"traversal":{"prev":{"slug":"oip-invariant-2-32-least-action-variational-principles","human":"https://miscsubjects.com/a/oip-invariant-2-32-least-action-variational-principles","json":"https://miscsubjects.com/api/articles/oip-invariant-2-32-least-action-variational-principles"},"next":{"slug":"oip-invariant-4-34-symmetry-breaking-bifurcation","human":"https://miscsubjects.com/a/oip-invariant-4-34-symmetry-breaking-bifurcation","json":"https://miscsubjects.com/api/articles/oip-invariant-4-34-symmetry-breaking-bifurcation"},"hub":{"slug":"oip-convergence-public-article","human":"https://miscsubjects.com/a/oip-convergence-public-article","json":"https://miscsubjects.com/api/articles/oip-convergence-public-article"},"series":"catalogue-inventory-invariants","position":3,"of":22},"ledger":{"claims":0,"sources":0,"contributions":0,"revisions":3,"objections_url":"https://miscsubjects.com/api/articles/oip-invariant-3-33-symmetry-conservation/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=oip-invariant-3-33-symmetry-conservation","proof_rule":"An action is proven by its ledger receipt, never by a 200 or a description."},"standard":{"writing":"peptide standard: logical prose, zero decorative wording, every material assertion atomized as a claim with a tier and a source (or explicitly unsourced)","claim_tiers":["human","preclinical","anecdotal","mechanistic","speculative","system"],"verbatim_law":"source text is prose-preserving — attack via objections, never rewrite the author's words"},"terminal":{"how":"Any model may emit these commands; 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