{"_self":{"principle":"Self-explaining payload — no external context required. This _self block describes what you are reading and where to look next.","widget":"article_topology","feature":"topology","name":"Article topology","what":"Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER.","contains":"claims, sources, anecdotes, question_graph slice","slug":"convergence-encyclopedia-c03","urls":{"read":"https://miscsubjects.com/api/articles/convergence-encyclopedia-c03/topology"},"how_to_use":"Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER.","write":null,"imessage":null,"router_tag":null,"proof_chain":[{"step":1,"claim":"Articles are voxel graphs of tiered claims, not prose blobs.","verify":"https://miscsubjects.com/api/articles/constitution"},{"step":2,"claim":"Claims link to hash-chained sources via source_ids.","verify":"https://miscsubjects.com/api/articles/convergence-encyclopedia-c03/sources"},{"step":3,"claim":"Ask reads topology; ingest/claim append to ledger.","verify":"https://miscsubjects.com/api/protocol"},{"step":4,"claim":"Models queue growth: populate → collaborate → repair → reflex.","verify":"https://miscsubjects.com/api/protocol/grow"},{"step":5,"claim":"Graph proves its own shape (reflex) and $/claim (yield).","verify":"https://miscsubjects.com/graph.html?layer=reflex"},{"step":6,"claim":"Full feature index + _explain on every API response.","verify":"https://miscsubjects.com/api/articles/system-map"}],"related_features":[{"id":"ask","name":"Ask protocol","what":"Answer only from topology; creates question_node with gaps and ingest_hint.","urls":{"read":"https://miscsubjects.com/api/articles/convergence-encyclopedia-c03/prompts","write":"https://miscsubjects.com/api/protocol/ask"}},{"id":"graph_topology","name":"Cross-article graph","what":"Merged claims/sources across condition+stack slugs for one question.","urls":{"read":"https://miscsubjects.com/api/articles/convergence-encyclopedia-c03/graph-topology?question=..."}},{"id":"question_graph","name":"Question graph","what":"Ask nodes (questions + gaps) and evidence_ingest nodes (pasted model output).","urls":{"read":"https://miscsubjects.com/api/articles/convergence-encyclopedia-c03/question-graph","write":"https://miscsubjects.com/api/protocol/ask"}},{"id":"voxels","name":"Voxel graph","what":"Claims as atoms, sources as edges (supported_by, posted_by). Per-claim provenance.","urls":{"read":"https://miscsubjects.com/api/articles/convergence-encyclopedia-c03/voxels","write":"https://miscsubjects.com/api/protocol/claim"}}],"system_map":"https://miscsubjects.com/api/articles/system-map","system_map_markdown":"https://miscsubjects.com/api/articles/system-map?format=markdown","not_medical_advice":true},"_explain":{"feature":"topology","name":"Article topology","what":"Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER.","why":"Every feature is auditable collective intelligence","how":"Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER.","model":null,"verifies":null,"urls":{"read":"https://miscsubjects.com/api/articles/convergence-encyclopedia-c03/topology"},"imessage":null,"router":null,"related":[{"id":"ask","what":"Answer only from topology; creates question_node with gaps and ingest_hint."},{"id":"graph_topology","what":"Merged claims/sources across condition+stack slugs for one question."},{"id":"question_graph","what":"Ask nodes (questions + gaps) and evidence_ingest nodes (pasted model output)."},{"id":"voxels","what":"Claims as atoms, sources as edges (supported_by, posted_by). Per-claim provenance."}],"not_medical_advice":true},"slug":"convergence-encyclopedia-c03","title":"Convergence Encyclopedia: C03 — Symmetry ↔ Conservation","register":"oip_protocol","tags":["OIP","convergence-encyclopedia","node"],"updated_at":"2026-07-04T05:00:56.619Z","body_excerpt":"**F1 — Tier.** T0 (mathematical theorem — Noether’s first theorem).\n\n**F2 — Sources.** \n- Noether, E. (1918). “Invariante Variationsprobleme.” Nachrichten von der Gesellschaft der Wissenschaften zu Gottingen, Mathematisch-Physikalische Klasse, 235–257.\n- Lie, S. (1888–1893). Theorie der Transformationsgruppen. 3 vols. Leipzig: Teubner.\n- Gauge theory framework: Weyl, H. (1918). “Gravitation und Elektrizitat.” Sitzungsberichte der Preussischen Akademie der Wissenschaften, 465–480; Yang, C.N. & Mills, R.L. (1954). “Conservation of isotopic spin and isotopic gauge invariance.” Physical Review, 96(1), 191–195.\n\n**F3 — Domains.** Core physics — classical mechanics, electromagnetism, general relativity, quantum field theory, particle physics.\n\n**F4 — Scale.** All scales where physical law applies.\n\n**F5 — Falsifier.** n/a (mathematical theorem). Noether’s theorem is proven; it cannot be falsified. The physical applicability — whether nature’s Lagrangians carry the required symmetries — is an empirical matter, but the theorem itself stands.\n\n**F6 — Rival (strongest form).** The symmetry-conservation link is a mathematical identity, not a physical claim. It tells us nothing about which symmetries nature actually possesses — it merely formalizes the consequences of symmetries we posit. The deep question is why nature has the symmetries it does; Noether’s theorem answers the consequence, not the cause. (Wigner 1967 Symmetries and Reflections; standard position in philosophy of physics.)\n\n**F7 — Independence.** Mathematical proof — universal by construction. The theorem applies wherever the premises (action principle + differentiable symmetry) hold. Independence is not at issue; this is a T0 node.\n\n**F8 — Pattern type.** Mathematical.\n\n**F9 — Maps.** A1 (foundational structure), A3 (pattern-dynamics).\n\n---\n\n## Corpus map\n- Previous: [Convergence Encyclopedia: C02](/a/convergence-encyclopedia-c02)\n- Next: [Convergence Encyclopedia: C04](/a/convergence-encyclopedia-c04)\n- Encyclopedia start: [The Schema](/a/convergence-encyclopedia-schema)\n- Same node, other planes: [Catalogue node C03](/a/oip-node-c03-symmetry-conservation) · [Catalogue hub](/a/oip-convergence-public-article)\n- Edges touching C03: [convergence edge 3](/a/oip-convergence-edge-3) · [disconfirming edge 4](/a/oip-disconfirming-edge-4)\n- Kin corpora: [Total Structure](/a/oip-total-structure) · [Signature of the Grain](/a/oip-sog-preamble-axioms)","ranking":"safety-first (interaction_risk/limitations), then quote-gated effective_weight","claims":[],"sources":[],"anecdotal_sources":[],"scientific_sources":[],"user_reports":[],"related_articles":[],"question_graph":{"slug":"convergence-encyclopedia-c03","questions":[],"evidence":[],"edges":[],"counts":{"questions":0,"evidence":0,"edges":0}},"honesty":{"active_claims":0,"retracted_claims":0,"cut_claims":0,"challenges":0,"scrub_events":0,"note":"Retracted/cut claims stay on ledger but are excluded from ask unless ?include_inactive=1"},"counts":{"claims":0,"claims_total":0,"sources":0,"anecdotal":0,"scientific":0,"user_reports":0,"questions":0,"evidence_ingests":0}}