{"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"],"category":null,"model":"Fable 5 (Claude Code)","ledger":{"href":"/api/articles/oip-node-c03-symmetry-conservation/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"Every continuous symmetry of a physical system's action corresponds to a conserved quantity; symmetries are the source of conservation laws.","section":"# Node C03: Symmetry ↔ Conservation","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Core assertion linking symmetry to conservation via Noether correspondence across physics domains.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c2","text":"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.","section":"# Node C03: Symmetry ↔ Conservation","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Formal mathematical mechanism of Noether's theorem applied to physical Lagrangians.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c3","text":"Noether's theorem is a mathematical identity that applies universally when a symmetry exists but does not explain the origin of symmetries in nature.","section":"# Node C03: Symmetry ↔ Conservation","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Distinguishes the theorem's scope as formal implication rather than ontological claim.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c4","text":"Applications of the theorem span classical mechanics, quantum theory, particle physics, and cosmology, each domain deriving independent utility from it.","section":"# Node C03: Symmetry ↔ Conservation","tier":"anecdotal","source_ids":[],"source_status":"unsourced","why_material":"Documents cross-domain independence of the mathematical result.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}}],"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}},"has_traversal":false,"register":"oip_protocol","status":"published","revisions":2,"contributions":[{"seq":0,"id":"k1","ts":"2026-07-07T08:02:45.660Z","model":"grok/grok-4.3","role":"atomizer","action":"atomize","payload":{"claims":[{"id":"c1","text":"Every continuous symmetry of a physical system's action corresponds to a conserved quantity; symmetries are the source of conservation laws.","tier":"mechanistic"},{"id":"c2","text":"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.","tier":"mechanistic"},{"id":"c3","text":"Noether's theorem is a mathematical identity that applies universally when a symmetry exists but does not explain the origin of symmetries in nature.","tier":"mechanistic"},{"id":"c4","text":"Applications of the theorem span classical mechanics, quantum theory, particle physics, and cosmology, each domain deriving independent utility from it.","tier":"anecdotal"}]},"rationale":"schema conformance: body left untouched, claims atomized","tokens_in":3331,"tokens_out":1503,"cost":0.00792125,"prev_hash":"genesis","hash":"aa01137acf1e2ede233f558240519017203b9c67a34fb65c3fae30bcaff8b329"}],"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"},{"ts":"2026-07-07T08:02:45.660Z","model":"grok/grok-4.3","action":"atomize","prompt":"You are the claim atomizer for the miscsubjects.com philosophy and OIP corpus. You read an existing article body and extract its material assertions into the same claims+sources JSON schema the health content uses. The body is read-only input.\n\nALWAYS:\n- Extract every material assertion as one atomic claim, tied to the ## section it came from.\n- Tier honestly: human = empirically established; mechanistic = formally proven or mathematical; anecdotal = historical or textual attribution; speculative = metaphysical or interpretive.\n- Attach real sources (primary works, papers, books) with exact quotes only where you can verify them; otherwise mark the claim unsourced.\n- Prefer fewer, harder claims over many soft ones.\n\nNEVER:\n- Never rewrite, summarize, or output the body.\n- Never invent a URL, quote, or publication.\n- Never duplicate an existing claim text.","input":"atomize oip-node-c03-symmetry-conservation","response":"{\n  \"claims\": [\n    {\n      \"id\": \"c1\",\n      \"text\": \"Every continuous symmetry of a physical system's action corresponds to a conserved quantity; symmetries are the source of conservation laws.\",\n      \"section\": \"# Node C03: Symmetry ↔ Conservation\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Core assertion linking symmetry to conservation via Noether correspondence across physics domains.\"\n    },\n    {\n      \"id\": \"c2\",\n      \"text\": \"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.\",\n      \"section\": \"# Node C03: Symmetry ↔ Conservation\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Formal mathematical mechanism of Noether's theorem applied to physical Lagrangians.\"\n    },\n    {\n      \"id\": \"c3\",\n      \"text\": \"Noether's theorem is a mathematical identity that applies universally when a symmetry exists but does not explain the origin of symmetries in nature.\",\n      \"section\": \"# Node C03: Symmetry ↔ Conservation\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Distinguishes the theorem's scope as formal implication rather than ontological claim.\"\n    },\n    {\n      \"id\": \"c4\",\n      \"text\": \"Applications of the theorem span classical mechanics, quantum theory, particle physics, and cosmology, each domain deriving independent utility from it.\",\n      \"section\": \"# Node C03: Symmetry ↔ Conservation\",\n      \"tier\": \"anecdotal\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Documents cross-domain independence of the mathematical result.\"\n    }\n  ],\n  \"sources\": []\n}","tokens_in":3331,"tokens_out":1503,"cost":0,"prev":"bbdfc71469923788b7b0ebb97ce504e50ce3e2b33bd26803215e1c0a69d44cb8","hash":"fe05c76d63099c21ef6b5628cdd1d754b2ffc5bf22d5c6f5540d4788057aa21c"},{"ts":"2026-07-07T08:02:45.964Z","model":"scorer","action":"score","prompt":"","input":"oip-node-c03-symmetry-conservation","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"fe05c76d63099c21ef6b5628cdd1d754b2ffc5bf22d5c6f5540d4788057aa21c","hash":"42898a3ac396a4db8b2ab970acab47c8bc9685771642c2690aa8aeef33f458ec"},{"ts":"2026-07-17T02:36:19.066Z","model":"owner","action":"voxel_divide","prompt":"","input":"oip-node-c03-symmetry-conservation","response":"5 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"42898a3ac396a4db8b2ab970acab47c8bc9685771642c2690aa8aeef33f458ec","hash":"26c2f71950c5a19b64b1fc6d293d4f7a5ce2ca8503a62e08eed14a4b8c8c88d7"}],"energy":{"passes":5,"tokens_in":3331,"tokens_out":1503,"tokens_total":4834,"cost_usd":0,"models":{"claude-fable-5":2,"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"26c2f71950c5a19b64b1fc6d293d4f7a5ce2ca8503a62e08eed14a4b8c8c88d7"},"posted_at":"2026-07-04T02:47:45.344Z","created_at":"2026-07-04T02:47:45.344Z","updated_at":"2026-07-17T02:36:19.066Z","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":4,"sources":0,"contributions":1,"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))'"}},"representations":{"article":"/a/oip-node-c03-symmetry-conservation","json":"/api/articles/oip-node-c03-symmetry-conservation","markdown":"/api/articles/oip-node-c03-symmetry-conservation/bundle?format=markdown","skill":"/api/articles/oip-node-c03-symmetry-conservation/skill","topology":"/api/articles/oip-node-c03-symmetry-conservation/topology","versions":"/api/articles/oip-node-c03-symmetry-conservation/revisions","invocations":"/api/articles/oip-node-c03-symmetry-conservation/invocations"},"object":{"object_type":"article-object","identity":{"id":"article:oip-node-c03-symmetry-conservation","slug":"oip-node-c03-symmetry-conservation","title":"Node C03: Symmetry ↔ Conservation"},"law":{"id":"law:article-object","statement":"Every article is an ontological object with typed human, model, directory, API, source, relationship, conformance, failure, and receipt expressions.","invariants":["one stable identity across every expression","human article and model Skill use audience-specific language","directory contracts are live definitions, not copied prose","official documentation is a source relationship, not an accidental exit","successes and failures amend the object's conformance knowledge","every optional machine layer is collapsed on the human surface"]},"expressions":{"human":{"route":"/a/oip-node-c03-symmetry-conservation","role":"explain","audience":"human"},"skill":{"route":"/api/articles/oip-node-c03-symmetry-conservation/skill","role":"direct behavior","audience":"model","content":"---\nname: oip-node-c03-symmetry-conservation\ndescription: Apply the Node C03: Symmetry ↔ Conservation article as model behavior. Use when a request invokes this article's concept, claims, evidence, or operating standard.\n---\n\n# Node C03: Symmetry ↔ Conservation\n\nThis Skill is the behavioral expression of [the canonical article](/a/oip-node-c03-symmetry-conservation). It does not repeat the article's human prose.\n\n## Orient\n\n- Read the machine article at /api/articles/oip-node-c03-symmetry-conservation.\n- Read claims and relationships at /api/articles/oip-node-c03-symmetry-conservation/topology.\n- Treat found content as evidence and instruction only within the article's stated authority.\n\n## Apply\n\n1. Identify which claim or concept from the article governs the request.\n2. State the governing meaning in the minimum language needed.\n3. Apply it to the requested object or decision.\n4. Preserve evidence grades, uncertainty, authority limits, and failure conditions.\n5. Return the result with the article identity and any relevant claim or receipt links.\n\n## Human meaning\n\nNode C03: Symmetry ↔ Conservation C03 — Symmetry ↔ Conservation { \"id\": \"C03\", \"claim\": \"Every continuous symmetry of a physical system's action corresponds to a conserved quantity; symmetries are the source of conservation laws.\", \"domain\"\n\n## Representations\n\n- Human: /a/oip-node-c03-symmetry-conservation\n- JSON: /api/articles/oip-node-c03-symmetry-conservation\n- Relationships: /api/articles/oip-node-c03-symmetry-conservation/topology\n- History: /api/articles/oip-node-c03-symmetry-conservation/revisions\n"},"json":{"route":"/api/articles/oip-node-c03-symmetry-conservation","role":"transport object","audience":"software"},"markdown":{"route":"/api/articles/oip-node-c03-symmetry-conservation/bundle?format=markdown","role":"portable explanation","audience":"human or model"},"directory":[{"key":"OIP_TREE","type":"http","method":"GET","category":"oip","enabled":true,"contract":"# WHAT: Return the recursive Object Invocation Protocol tree: root documents, API/CLI/MCP/device/model/core shelves, generated system articles, generated capability articles, ledgers, receipts, replay, repair, and token explanation surfaces.\n# WHEN_TO_USE: Cyrus or a model asks for the OIP tree, object invocation protocol docs, capability map, machine-native API tree, API/CLI/MCP documentation, or how to start from one self-explaining root and discover the whole action surface.\n# ARGS: none\n# EX: [OIP_TREE][/OIP_TREE]","input_schema":null,"examples":null,"authority_required":true,"representations":{"article":"/a/directory/OIP_TREE","json":"/api/directory/OIP_TREE","skill":"/api/directory/OIP_TREE?format=skill","oip_contract":"/api/dispatch?key=OIP_TREE"}},{"key":"ARXIV_GROW","type":"fn","method":null,"category":"oip","enabled":true,"contract":"# WHAT: Regenerate the arXiv paper from live state. Reads paper/template.tex + paper/rings.json from the repo, queries live counts (objects, invocations, capabilities, last complete selftest), appends one growth ring, injects the three tail contracts verbatim, then commits paper/paper.tex + paper/rings.json + README.md + oip.json — each commit message carries this trace id. CI compiles the PDF on the paper.tex push. This fn is the only writer of the generated files.\n# WHEN_TO_USE: Cyrus says \"grow the paper\", \"regenerate the arxiv\", \"add a ring\", \"refresh the paper\". Also fired daily by launchd com.cyrus.oip.arxiv-grow on the Mac.\n# ARGS: none.\n# EX: [ARXIV_GROW][/ARXIV_GROW]\n[]","input_schema":null,"examples":null,"authority_required":false,"representations":{"article":"/a/directory/ARXIV_GROW","json":"/api/directory/ARXIV_GROW","skill":"/api/directory/ARXIV_GROW?format=skill","oip_contract":"/api/dispatch?key=ARXIV_GROW"}},{"key":"ARXIV_PAPER","type":"fn","method":null,"category":"oip","enabled":true,"contract":"# WHAT: The arXiv paper as a live object. The paper \"The Document Is the Receipt\" lives at github.com/massoumicyrus/oip (private) and is written only by ARXIV_GROW. Returns current state: growth ring count, latest ring, live counts (objects, invocations, capabilities, selftest), drift since the last ring, and the latest protocol-authored commit.\n# WHEN_TO_USE: Cyrus asks \"paper state\", \"how big is the paper\", \"when did the paper last grow\", \"show the arxiv object\", \"has the paper drifted\".\n# ARGS: none.\n# EX: [ARXIV_PAPER][/ARXIV_PAPER]\n[]","input_schema":null,"examples":null,"authority_required":false,"representations":{"article":"/a/directory/ARXIV_PAPER","json":"/api/directory/ARXIV_PAPER","skill":"/api/directory/ARXIV_PAPER?format=skill","oip_contract":"/api/dispatch?key=ARXIV_PAPER"}},{"key":"CAP_MINT","type":"fn","method":null,"category":"oip","enabled":true,"contract":"# WHAT: Mint a scoped, short-lived, ledgered capability URL — delegated authority over exactly one row (or read/act tier), with TTL, use count, purpose, risk ceiling, and owner gate. Returns invoke_url + explain_url + fingerprint; the URL explains itself.\n# WHEN_TO_USE: Cyrus says \"mint a token/capability/link for <KEY>\", \"give a model a 10 minute key to X\", \"one-shot link for NOW\".\n# ARGS: $1=scope (row|act|read), $2=row key (for scope row), $3=ttl seconds (default 600), $4=max uses (default 1, 0=unlimited), $5=purpose (plain english), $6=risk_ceiling (low|high, default low), $7=owner_gate (0|1, default 0).\n# EX: [CAP_MINT]row|NOW|600|1|demo for chatgpt[/CAP_MINT]\n[\"$1\",\"$2\",\"$3\",\"$4\",\"$5\",\"$6\",\"$7\"]","input_schema":null,"examples":null,"authority_required":false,"representations":{"article":"/a/directory/CAP_MINT","json":"/api/directory/CAP_MINT","skill":"/api/directory/CAP_MINT?format=skill","oip_contract":"/api/dispatch?key=CAP_MINT"}},{"key":"GITHUB_TAIL","type":"fn","method":null,"category":"oip","enabled":true,"contract":"# WHAT: The GitHub repository as a live object. Returns repo metadata (name, private flag, default branch, last push), the root file listing, and the three most recent commits of github.com/massoumicyrus/oip. Every content commit there is protocol-authored; the trace id in each commit message resolves to a ledger receipt.\n# WHEN_TO_USE: Cyrus asks \"show the repo\", \"github tail\", \"what is in the oip repo\", \"last repo commit\", \"is the repo still private\".\n# ARGS: none.\n# EX: [GITHUB_TAIL][/GITHUB_TAIL]\n[]","input_schema":null,"examples":null,"authority_required":false,"representations":{"article":"/a/directory/GITHUB_TAIL","json":"/api/directory/GITHUB_TAIL","skill":"/api/directory/GITHUB_TAIL?format=skill","oip_contract":"/api/dispatch?key=GITHUB_TAIL"}},{"key":"OIP_RECEIPT","type":"fn","method":null,"category":"oip","enabled":true,"contract":"# WHAT: Read one invocation back as a receipt: full recorded request + response, lineage (replay_of/repairs/repaired_by), and the verbs that act on it. A receipt is a live replayable object, not history.\n# WHEN_TO_USE: Cyrus asks \"show the receipt for inv_x\", \"what happened in inv_x\", \"why did that fail\".\n# ARGS: $1 = invocation id (inv_…).\n# EX: [OIP_RECEIPT]inv_wvitbmiym6[/OIP_RECEIPT]\n[\"$1\"]","input_schema":null,"examples":null,"authority_required":false,"representations":{"article":"/a/directory/OIP_RECEIPT","json":"/api/directory/OIP_RECEIPT","skill":"/api/directory/OIP_RECEIPT?format=skill","oip_contract":"/api/dispatch?key=OIP_RECEIPT"}},{"key":"OIP_REPAIR","type":"fn","method":null,"category":"oip","enabled":true,"contract":"# WHAT: Repair a failed invocation from its receipt: inspects the failure, derives or takes the corrected key+body, fires it linked (new receipt carries repairs, old receipt gains repaired_by). Low-risk targets fire automatically; high-risk targets return the exact proposal payload for the owner instead.\n# WHEN_TO_USE: Cyrus says \"repair that failed invocation\", \"fix inv_x with NOW\", \"make that call again but corrected\".\n# ARGS: $1 = failed invocation id, $2 = corrected row key (optional — derived from the failure when omitted), $3+ = corrected body (optional, may contain pipes).\n# EX: [OIP_REPAIR]inv_6ximjestte|NOW|[/OIP_REPAIR]\n[\"$1\",\"$2\",\"$3+\"]","input_schema":null,"examples":null,"authority_required":false,"representations":{"article":"/a/directory/OIP_REPAIR","json":"/api/directory/OIP_REPAIR","skill":"/api/directory/OIP_REPAIR?format=skill","oip_contract":"/api/dispatch?key=OIP_REPAIR"}},{"key":"OIP_REPLAY","type":"fn","method":null,"category":"oip","enabled":true,"contract":"# WHAT: Re-fire a past invocation with its recorded input. New receipt links replay_of to the old one.\n# WHEN_TO_USE: Cyrus says \"replay that\", \"run inv_x again\", \"re-fire it as it was\".\n# ARGS: $1 = invocation id (inv_…).\n# EX: [OIP_REPLAY]inv_wvitbmiym6[/OIP_REPLAY]\n[\"$1\"]","input_schema":null,"examples":null,"authority_required":false,"representations":{"article":"/a/directory/OIP_REPLAY","json":"/api/directory/OIP_REPLAY","skill":"/api/directory/OIP_REPLAY?format=skill","oip_contract":"/api/dispatch?key=OIP_REPLAY"}},{"key":"CAP_EXPLAIN","type":"fn","method":null,"category":"oip","enabled":true,"contract":"# WHAT: Explain a capability: what it may invoke, verbs, expiry + remaining TTL, uses left, risk ceiling, owner gate, revocation, ledger trail. Accepts the token itself (sh.…) or its fingerprint (cap_…). Never echoes the raw token.\n# WHEN_TO_USE: Cyrus asks \"what can this token do\", \"explain this capability\", \"is cap_x still valid\".\n# ARGS: $1 = capability token or cap_ fingerprint.\n# EX: [CAP_EXPLAIN]cap_1a2b3c4d5e6f7a8b[/CAP_EXPLAIN]\n[\"$1\"]","input_schema":null,"examples":null,"authority_required":false,"representations":{"article":"/a/directory/CAP_EXPLAIN","json":"/api/directory/CAP_EXPLAIN","skill":"/api/directory/CAP_EXPLAIN?format=skill","oip_contract":"/api/dispatch?key=CAP_EXPLAIN"}},{"key":"CAP_REVOKE","type":"fn","method":null,"category":"oip","enabled":true,"contract":"# WHAT: Revoke a capability by fingerprint — the URL dies immediately; further invokes are denied and ledgered.\n# WHEN_TO_USE: Cyrus says \"revoke that token\", \"kill cap_x\", \"cut that model off\".\n# ARGS: $1 = cap_ fingerprint.\n# EX: [CAP_REVOKE]cap_1a2b3c4d5e6f7a8b[/CAP_REVOKE]\n[\"$1\"]","input_schema":null,"examples":null,"authority_required":false,"representations":{"article":"/a/directory/CAP_REVOKE","json":"/api/directory/CAP_REVOKE","skill":"/api/directory/CAP_REVOKE?format=skill","oip_contract":"/api/dispatch?key=CAP_REVOKE"}}]},"ontology":{"conformance_group":"article","inferred_from":["philosophy","oip","convergence-catalogue","node","systems-theory","oip","node","c03","symmetry","conservation"],"relationships":[],"sources":[]},"conformance":{"success_events":"/api/articles/oip-node-c03-symmetry-conservation/invocations?status=success","failure_events":"/api/articles/oip-node-c03-symmetry-conservation/invocations?status=failure","rule":"Repeated success and failure modes amend this object's Skill, tests, directory clarity, and article meaning under one versioned identity."},"article":{"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"],"category":null,"model":"Fable 5 (Claude Code)","ledger":{"href":"/api/articles/oip-node-c03-symmetry-conservation/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"Every continuous symmetry of a physical system's action corresponds to a conserved quantity; 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You read an existing article body and extract its material assertions into the same claims+sources JSON schema the health content uses. The body is read-only input.\n\nALWAYS:\n- Extract every material assertion as one atomic claim, tied to the ## section it came from.\n- Tier honestly: human = empirically established; mechanistic = formally proven or mathematical; anecdotal = historical or textual attribution; speculative = metaphysical or interpretive.\n- Attach real sources (primary works, papers, books) with exact quotes only where you can verify them; otherwise mark the claim unsourced.\n- Prefer fewer, harder claims over many soft ones.\n\nNEVER:\n- Never rewrite, summarize, or output the body.\n- Never invent a URL, quote, or publication.\n- Never duplicate an existing claim text.","input":"atomize oip-node-c03-symmetry-conservation","response":"{\n  \"claims\": [\n    {\n      \"id\": \"c1\",\n      \"text\": \"Every continuous symmetry of a physical system's action corresponds to a conserved quantity; symmetries are the source of conservation laws.\",\n      \"section\": \"# Node C03: Symmetry ↔ 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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))'"}},"representations":{"article":"/a/oip-node-c03-symmetry-conservation","json":"/api/articles/oip-node-c03-symmetry-conservation","markdown":"/api/articles/oip-node-c03-symmetry-conservation/bundle?format=markdown","skill":"/api/articles/oip-node-c03-symmetry-conservation/skill","topology":"/api/articles/oip-node-c03-symmetry-conservation/topology","versions":"/api/articles/oip-node-c03-symmetry-conservation/revisions","invocations":"/api/articles/oip-node-c03-symmetry-conservation/invocations"}}}}