{"slug":"oip-node-c04-symmetry-breaking-bifurcation","title":"Node C04: Symmetry-Breaking / Bifurcation","body":"# Node C04: Symmetry-Breaking / Bifurcation\n\nC04 — Symmetry-Breaking / Bifurcation\n{\n  \"id\": \"C04\",\n  \"claim\": \"Structure, mass, and form arise when a symmetry of the underlying equations is not shared by the solution; the vacuum/state picks a direction.\",\n  \"domain\": [\"cosmology\", \"condensed matter physics\", \"developmental biology\", \"particle physics\", \"pattern formation\"],\n  \"pattern\": [\"symmetry_breaking\", \"bifurcation\", \"phase_transition\", \"spontaneous_structure\"],\n  \"mechanism\": \"A system described by symmetric equations can settle into an asymmetric ground state when a control parameter crosses a critical value. The Higgs mechanism: SU(2)×U(1) gauge symmetry is spontaneously broken, giving mass to W and Z bosons. In development: reaction-diffusion systems break translational symmetry to produce stripes/spots.\",\n  \"scale\": \"quantum → cosmic\",\n  \"claim_tier\": \"T1\",\n  \"sources\": [\n    \"Landau, L.D. (1937). 'On the Theory of Phase Transitions.' Phys. Z. Sowjetunion, 11, 26-47.\",\n    \"Anderson, P.W. (1958). 'Coherent Excited States in the Theory of Superconductivity.' Phys. Rev., 112(6), 1900-1916.\",\n    \"Higgs, P.W. (1964). 'Broken Symmetries and the Masses of Gauge Bosons.' Phys. Rev. Lett., 13(16), 508-509.\",\n    \"Turing, A.M. (1952). 'The Chemical Basis of Morphogenesis.' Phil. Trans. R. Soc. Lond. B, 237, 37-72.\"\n  ],\n  \"dual\": \"Symmetry (C03) — the symmetric state that precedes and explains the broken one.\",\n  \"falsifier\": \"Observation of structure appearing without any prior symmetric state — i.e., structure that never passed through a higher-symmetry phase and has no underlying symmetric description.\",\n  \"rival_frame\": \"Structure emerges from local interactions without any symmetry-breaking phase transition. The 'breaking' is descriptive, not causal — a posteriori labeling of what interactions produced, not a mechanism that explains.\",\n  \"independence_check\": \"HIGH. Landau (condensed matter, USSR) worked from thermodynamics of phase transitions. Higgs (particle physics, Edinburgh) worked from gauge theory of electroweak unification. Turing (mathematical biology, Manchester) worked from reaction-diffusion equations. Three fields, three nations, three mathematical frameworks, same pattern: symmetric laws, asymmetric solutions.\",\n  \"pattern_type\": \"structural\",\n  \"maps_to_axiom\": [\"A1\", \"A7\"]\n}\n\n---\n\n## Corpus map\n- Same node, other planes: [Encyclopedia C04](/a/convergence-encyclopedia-c04) · [Inventory invariant](/a/oip-invariant-4-34-symmetry-breaking-bifurcation)\n- Edges touching C04: [convergence edge 10](/a/oip-convergence-edge-10)\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-c03-symmetry-conservation","next":"oip-node-c05-criticality-edge-of-chaos-power-laws","hub":"oip-convergence-public-article","series":"catalogue-nodes","position":4,"of":25}},"register":"oip_protocol","status":"published","revisions":2,"contributions":[],"provenance":[{"ts":"2026-07-04T04:33:59.523Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"183e12ff07a6046ed71cbe23a7e05e55cc75a80f19b860e21bc176fbdb438ee5"},{"ts":"2026-07-04T05:01:56.963Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"183e12ff07a6046ed71cbe23a7e05e55cc75a80f19b860e21bc176fbdb438ee5","hash":"34a6f0e12819a16aa2691b3cda21bab17ee3362bcea365567d7fe1b5bbf0c2ca"}],"energy":{"passes":2,"tokens_in":0,"tokens_out":0,"tokens_total":0,"cost_usd":0,"models":{"claude-fable-5":2},"head":"34a6f0e12819a16aa2691b3cda21bab17ee3362bcea365567d7fe1b5bbf0c2ca"},"posted_at":"2026-07-04T02:47:46.064Z","created_at":"2026-07-04T02:47:46.064Z","updated_at":"2026-07-04T05:01:56.963Z","machine":{"shape":"article.machine/v1","slug":"oip-node-c04-symmetry-breaking-bifurcation","kind":"corpus","read":{"human":"https://miscsubjects.com/a/oip-node-c04-symmetry-breaking-bifurcation","json":"https://miscsubjects.com/api/articles/oip-node-c04-symmetry-breaking-bifurcation","bundle":"https://miscsubjects.com/api/articles/oip-node-c04-symmetry-breaking-bifurcation/bundle?format=markdown"},"traversal":{"prev":{"slug":"oip-node-c03-symmetry-conservation","human":"https://miscsubjects.com/a/oip-node-c03-symmetry-conservation","json":"https://miscsubjects.com/api/articles/oip-node-c03-symmetry-conservation"},"next":{"slug":"oip-node-c05-criticality-edge-of-chaos-power-laws","human":"https://miscsubjects.com/a/oip-node-c05-criticality-edge-of-chaos-power-laws","json":"https://miscsubjects.com/api/articles/oip-node-c05-criticality-edge-of-chaos-power-laws"},"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":4,"of":25},"ledger":{"claims":0,"sources":0,"contributions":0,"revisions":2,"objections_url":"https://miscsubjects.com/api/articles/oip-node-c04-symmetry-breaking-bifurcation/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=oip-node-c04-symmetry-breaking-bifurcation","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-c04-symmetry-breaking-bifurcation\",\"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-c04-symmetry-breaking-bifurcation\",\"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-c04-symmetry-breaking-bifurcation/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-c04-symmetry-breaking-bifurcation\",\"raw_text\":\"<material delta>\"}'  # open intake, no key","read_back":"curl -s https://miscsubjects.com/api/articles/oip-node-c04-symmetry-breaking-bifurcation | python3 -c 'import json,sys; d=json.load(sys.stdin); print(json.dumps(d[\"claims\"][-3:], indent=1))'"}}}