{"_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-c20","urls":{"read":"https://miscsubjects.com/api/articles/convergence-encyclopedia-c20/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-c20/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-c20/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-c20/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-c20/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-c20/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-c20/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-c20","title":"Convergence Encyclopedia: C20 — Universal Computation","register":"oip_protocol","tags":["OIP","convergence-encyclopedia","node"],"updated_at":"2026-07-04T05:01:07.455Z","body_excerpt":"**F1 — Tier.** T0 (mathematical — Church-Turing thesis is a definition of computability); T3 (pancomputationalism — the claim that physical reality is computational is philosophical, not empirical). Load-bearing only at T0.\n\n**F2 — Sources.** \n- Church, A. (1936). “An unsolvable problem of elementary number theory.” American Journal of Mathematics, 58(2), 345–363.\n- Turing, A.M. (1936). “On computable numbers, with an application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society, 42(2), 230–265.\n- Post, E.L. (1936). “Finite combinatory processes — formulation 1.” Journal of Symbolic Logic, 1(3), 103–105.\n- von Neumann, J. (1945). “First draft of a report on the EDVAC.” Moore School of Electrical Engineering, University of Pennsylvania.\n- Wolfram, S. (2002). A New Kind of Science. Wolfram Media. (Principle of computational equivalence — T3.)\n\n**F3 — Domains.** Mathematics (computability theory), computer science (programming languages, architecture), physics (digital physics — T3), philosophy of mind (computationalism).\n\n**F4 — Scale.** Formal (symbolic) → physical (silicon, ~10⁻¹⁰ m) → abstract (Turing machine as mathematical object).\n\n**F5 — Falsifier.** A physical process that cannot be simulated by a Turing machine to arbitrary precision — a “hypercomputer” exploiting physical phenomena beyond computable functions (e.g., Pour-El & Richards 1989 on wave equation computability; speculative quantum gravity computations). Note: The Church-Turing thesis is a hypothesis about physical reality, not a theorem. Its falsification would require demonstrating a physical process that computes a non-recursive function.\n\n**F6 — Rival (strongest form).** The Church-Turing thesis is a hypothesis about physical reality, not a mathematical theorem. It states that any function computable by any physical process is computable by a Turing machine. This is an empirical generalization, not a proof. It has held for all known computational models (lambda calculus, recursive functions, tag systems, cellular automata, quantum circuits — the latter within BQP), but it could in principle be falsified by a physical hypercomputer. (Copeland 2002 “Hypercomputation” Minds and Machines 12:461; Davis 2004 “The myth of hypercomputation” rebuttal.)\n\n**F7 — Independence.** HIGH. Church (logic, Princeton), Turing (mathematics, Cambridge), Post (logic, City College New York) — three independent formulations of computability in 1936, published within months of each other, with no cross-communication. von Neumann’s stored-program architecture (1945) was independent of the logical foundations. Wolfram’s principle of computational equivalence (2002) is a later philosophical extension.\n\n**F8 — Pattern type.** Mathematical.\n\n**F9 — Maps.** A3 (pattern-dynamics).\n\n---\n\n## Corpus map\n- Previous: [Convergence Encyclopedia: C19](/a/convergence-encyclopedia-c19)\n- Next: [Convergence Encyclopedia: C21](/a/convergence-encyclopedia-c21)\n- Encyclopedia start: [The Schema](/a/convergence-encyclopedia-schema)\n- Same node, other planes: [Catalogue node C20](/a/oip-node-c20-universal-computation) · [Catalogue hub](/a/oip-convergence-public-article)\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-c20","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}}