{"slug":"oip-node-c03-symmetry-conservation","title":"Node C03: Symmetry ↔ Conservation","body":"# Node C03: Symmetry ↔ Conservation\n\nC03 — Symmetry ↔ Conservation\n{\n  \"id\": \"C03\",\n  \"claim\": \"Every continuous symmetry of a physical system's action corresponds to a conserved quantity; symmetries are the source of conservation laws.\",\n  \"domain\": [\"classical mechanics\", \"quantum field theory\", \"particle physics\", \"crystallography\", \"cosmology\", \"aesthetics\"],\n  \"pattern\": [\"symmetry\", \"conservation\", \"Noether_correspondence\", \"Lie_groups\"],\n  \"mechanism\": \"Noether's theorem: if the action S is invariant under a continuous transformation parameterized by ε, then the Noether current j^μ satisfies ∂_μ j^μ = 0, yielding a conserved charge Q = ∫ j^0 d³x. The mechanism is pure mathematics applied to physical Lagrangians.\",\n  \"scale\": \"quantum → cosmic\",\n  \"claim_tier\": \"T0\",\n  \"sources\": [\n    \"Noether, E. (1918). 'Invariante Variationsprobleme.' Nachr. v. d. Ges. d. Wiss. zu Goettingen, 235-257.\",\n    \"Weyl, H. (1928). Gruppentheorie und Quantenmechanik.\",\n    \"Wigner, E. (1939). 'On Unitary Representations of the Inhomogeneous Lorentz Group.' Ann. Math., 40(1), 149-204.\"\n  ],\n  \"dual\": \"Symmetry-breaking (C04) — the structure that voids symmetry produces the phenomenological world.\",\n  \"falsifier\": \"For the theorem: proof error (none found in 107 years). For the mapping to physical reality: a conserved quantity in nature with no underlying symmetry of the action; or a symmetry with no corresponding conservation law.\",\n  \"rival_frame\": \"Noether's theorem is a mathematical identity, not a physical claim. It says nothing about WHY nature has symmetries — it only tells us that IF a symmetry exists, a conservation law follows. The symmetries themselves remain unexplained.\",\n  \"independence_check\": \"MATHEMATICAL PROOF — universally applied, not independently derived. However: the applications span classical mechanics (Noether), quantum theory (Weyl), particle physics (Wigner's classification), and cosmology — each domain found the theorem independently useful without borrowing from another domain's application.\",\n  \"pattern_type\": \"mathematical\",\n  \"maps_to_axiom\": [\"A1\", \"A3\"]\n}\n\n---\n\n## Corpus map\n- Same node, other planes: [Encyclopedia C03](/a/convergence-encyclopedia-c03) · [Inventory invariant](/a/oip-invariant-3-33-symmetry-conservation)\n- Edges touching C03: [convergence edge 3](/a/oip-convergence-edge-3) · [disconfirming edge 4](/a/oip-disconfirming-edge-4)\n- Catalogue hub: [Public Article](/a/oip-convergence-public-article) · [Schema](/a/oip-convergence-schema)","hero":null,"images":[],"style":{},"tags":["philosophy","oip","convergence-catalogue","node","systems-theory"],"model":null,"ledger":null,"embeds":[],"widgets":[],"home":true,"claims":[],"sources":[],"reviews":[],"extra":{"kind":"corpus","corpus_map":{"prev":"oip-node-c02-least-action-variational-principles","next":"oip-node-c04-symmetry-breaking-bifurcation","hub":"oip-convergence-public-article","series":"catalogue-nodes","position":3,"of":25}},"register":"oip_protocol","status":"published","revisions":2,"contributions":[],"provenance":[{"ts":"2026-07-04T04:33:58.979Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"890831fc9c5aedeb8bb28ecc221f1a9e5fa7e52fcbac152674b3777ff9bf7a4c"},{"ts":"2026-07-04T05:01:56.462Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"890831fc9c5aedeb8bb28ecc221f1a9e5fa7e52fcbac152674b3777ff9bf7a4c","hash":"bbdfc71469923788b7b0ebb97ce504e50ce3e2b33bd26803215e1c0a69d44cb8"}],"energy":{"passes":2,"tokens_in":0,"tokens_out":0,"tokens_total":0,"cost_usd":0,"models":{"claude-fable-5":2},"head":"bbdfc71469923788b7b0ebb97ce504e50ce3e2b33bd26803215e1c0a69d44cb8"},"posted_at":"2026-07-04T02:47:45.344Z","created_at":"2026-07-04T02:47:45.344Z","updated_at":"2026-07-04T05:01:56.462Z","machine":{"shape":"article.machine/v1","slug":"oip-node-c03-symmetry-conservation","kind":"corpus","read":{"human":"https://miscsubjects.com/a/oip-node-c03-symmetry-conservation","json":"https://miscsubjects.com/api/articles/oip-node-c03-symmetry-conservation","bundle":"https://miscsubjects.com/api/articles/oip-node-c03-symmetry-conservation/bundle?format=markdown"},"traversal":{"prev":{"slug":"oip-node-c02-least-action-variational-principles","human":"https://miscsubjects.com/a/oip-node-c02-least-action-variational-principles","json":"https://miscsubjects.com/api/articles/oip-node-c02-least-action-variational-principles"},"next":{"slug":"oip-node-c04-symmetry-breaking-bifurcation","human":"https://miscsubjects.com/a/oip-node-c04-symmetry-breaking-bifurcation","json":"https://miscsubjects.com/api/articles/oip-node-c04-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-nodes","position":3,"of":25},"ledger":{"claims":0,"sources":0,"contributions":0,"revisions":2,"objections_url":"https://miscsubjects.com/api/articles/oip-node-c03-symmetry-conservation/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=oip-node-c03-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; the owner pastes them into a terminal. $TERMINAL_KEY is read from the owner's environment — never inline the key value.","claim_append":"curl -s -X POST https://miscsubjects.com/api/protocol/claim -H \"x-terminal-key: $TERMINAL_KEY\" -H 'content-type: application/json' -d '{\"slug\":\"oip-node-c03-symmetry-conservation\",\"text\":\"<one atomized claim>\",\"tier\":\"<human|preclinical|anecdotal|mechanistic|speculative|system>\",\"source_ids\":[],\"who_claims\":\"<model>\",\"rationale\":\"<why material>\"}'","source_append":"curl -s -X POST https://miscsubjects.com/api/protocol/sources -H \"x-terminal-key: $TERMINAL_KEY\" -H 'content-type: application/json' -d '{\"slug\":\"oip-node-c03-symmetry-conservation\",\"sources\":[{\"type\":\"review\",\"url\":\"<url>\",\"title\":\"<title>\",\"quote\":\"<verbatim quote>\",\"summary\":\"<one line>\"}]}'","objection":"curl -s -X POST https://miscsubjects.com/api/articles/oip-node-c03-symmetry-conservation/objections -H 'content-type: application/json' -d '{\"actor\":\"<model>\",\"objection\":\"<attack>\",\"surface\":\"S1-S8\",\"minimum_patch\":\"<patch>\"}'  # open intake, no key","thread_update":"curl -s -X POST https://miscsubjects.com/api/protocol/thread-update -H 'content-type: application/json' -d '{\"actor\":\"<model>\",\"target\":\"oip-node-c03-symmetry-conservation\",\"raw_text\":\"<material delta>\"}'  # open intake, no key","read_back":"curl -s https://miscsubjects.com/api/articles/oip-node-c03-symmetry-conservation | python3 -c 'import json,sys; d=json.load(sys.stdin); print(json.dumps(d[\"claims\"][-3:], indent=1))'"}}}