{"slug":"oip-catalogue-mapping","title":"The Catalogue: Mapping Invariants to Protocol","body":"# Mapping Invariants to Protocol\n\n5. Mapping the invariants onto the protocol\n\n| Axiom | Invariants that instance it |\n|---|---|\n| **A₀** inversion | Falsification (Popper), Gödel, the negation test |\n| **A₁** polarity | Duality/complementarity (§3.14), symmetry ↔ breaking (§3.3–3.4) |\n| **A₂** the grain | Dissipation (§3.1), least action (§3.2), compression (§3.10), Tao/*wu wei*, maximum power (§3.18) |\n| **A₃** convergence | Physics unification (GUT), free energy (§3.11), emergence (§3.13), Pareto (§3.15), general systems theory |\n| **A₄** the floor | Thermoeconomics/exergy (§3.18), Ostrom's commons (§3.19), coercion-cost |\n| **A₇** signatures | The whole of §3 — but the signal is *compressibility of the convergence* (§3.10) |\n| **A₈** maker-system | Autopoiesis (§3.8), observer/participatory universe (§3.21), strange loops (§3.9) |\n| **A₁₁** the receipt | Information/Landauer (§3.10), ledger, provenance |\n| **A₁₂** recursion | Cybernetics (§3.7), autopoiesis (§3.8), evolutionary epistemology (§3.12) |\n| **T₂** the Ought | Teleology/entelechy/Omega (§3.22) — typed T3, carried, not asserted |\n\n---\n\n##\n\n---\n\n## Corpus map\n- Catalogue hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article)\n- Nodes: [C01](/a/oip-node-c01-gradient-dissipation-far-from-equilibrium-order) · [C02](/a/oip-node-c02-least-action-variational-principles) · [C03](/a/oip-node-c03-symmetry-conservation) · [C04](/a/oip-node-c04-symmetry-breaking-bifurcation) · [C05](/a/oip-node-c05-criticality-edge-of-chaos-power-laws) · [C06](/a/oip-node-c06-information-entropy-compression) · … (25 nodes)\n- Edge series: [Convergence 1](/a/oip-convergence-edge-1) · [Disconfirming 1](/a/oip-disconfirming-edge-1)","hero":null,"images":[],"style":{},"tags":["philosophy","oip","catalogue","systems-theory"],"category":null,"model":"Fable 5 (Claude Code)","ledger":{"href":"/api/articles/oip-catalogue-mapping/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"A₀ inversion is instanced by Falsification (Popper), Gödel, and the negation test.","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c2","text":"A₁ polarity is instanced by Duality/complementarity (§3.14) and symmetry ↔ breaking (§3.3–3.4).","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c3","text":"A₂ the grain is instanced by Dissipation (§3.1), least action (§3.2), compression (§3.10), Tao/wu wei, and maximum power (§3.18).","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c4","text":"A₃ convergence is instanced by Physics unification (GUT), free energy (§3.11), emergence (§3.13), Pareto (§3.15), and general systems theory.","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c5","text":"A₄ the floor is instanced by Thermoeconomics/exergy (§3.18), Ostrom's commons (§3.19), and coercion-cost.","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c6","text":"A₇ signatures is instanced by the whole of §3 with the signal being compressibility of the convergence (§3.10).","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c7","text":"A₈ maker-system is instanced by Autopoiesis (§3.8), observer/participatory universe (§3.21), and strange loops (§3.9).","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c8","text":"A₁₁ the receipt is instanced by Information/Landauer (§3.10), ledger, and provenance.","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c9","text":"A₁₂ recursion is instanced by Cybernetics (§3.7), autopoiesis (§3.8), and evolutionary epistemology (§3.12).","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c10","text":"T₂ the Ought is instanced by Teleology/entelechy/Omega (§3.22), typed T3, carried not asserted.","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c11","text":"The corpus includes a Catalogue hub at Convergence Catalogue — Public Article, 25 nodes C01–C06 and beyond, and Edge series Convergence 1 and Disconfirming 1.","section":"## Corpus map","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Defines the structure and navigation of the OIP corpus.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}}],"sources":[],"reviews":[],"extra":{"kind":"corpus","corpus_map":{"prev":"oip-catalogue-traversal","next":"oip-catalogue-ai-instance","hub":"oip-convergence-public-article","series":"convergence-catalogue","position":5,"of":11}},"has_traversal":false,"register":"oip_protocol","status":"published","revisions":3,"contributions":[{"seq":0,"id":"k1","ts":"2026-07-07T08:30:52.540Z","model":"grok/grok-4.3","role":"atomizer","action":"atomize","payload":{"claims":[{"id":"c1","text":"A₀ inversion is instanced by Falsification (Popper), Gödel, and the negation test.","tier":"speculative"},{"id":"c2","text":"A₁ polarity is instanced by Duality/complementarity (§3.14) and symmetry ↔ breaking (§3.3–3.4).","tier":"speculative"},{"id":"c3","text":"A₂ the grain is instanced by Dissipation (§3.1), least action (§3.2), compression (§3.10), Tao/wu wei, and maximum power (§3.18).","tier":"speculative"},{"id":"c4","text":"A₃ convergence is instanced by Physics unification (GUT), free energy (§3.11), emergence (§3.13), Pareto (§3.15), and general systems theory.","tier":"speculative"},{"id":"c5","text":"A₄ the floor is instanced by Thermoeconomics/exergy (§3.18), Ostrom's commons (§3.19), and coercion-cost.","tier":"speculative"},{"id":"c6","text":"A₇ signatures is instanced by the whole of §3 with the signal being compressibility of the convergence (§3.10).","tier":"speculative"},{"id":"c7","text":"A₈ maker-system is instanced by Autopoiesis (§3.8), observer/participatory universe (§3.21), and strange loops (§3.9).","tier":"speculative"},{"id":"c8","text":"A₁₁ the receipt is instanced by Information/Landauer (§3.10), ledger, and provenance.","tier":"speculative"},{"id":"c9","text":"A₁₂ recursion is instanced by Cybernetics (§3.7), autopoiesis (§3.8), and evolutionary epistemology (§3.12).","tier":"speculative"},{"id":"c10","text":"T₂ the Ought is instanced by Teleology/entelechy/Omega (§3.22), typed T3, carried not asserted.","tier":"speculative"},{"id":"c11","text":"The corpus includes a Catalogue hub at Convergence Catalogue — Public Article, 25 nodes C01–C06 and beyond, and Edge series Convergence 1 and Disconfirming 1.","tier":"speculative"}]},"rationale":"schema conformance: body left untouched, claims atomized","tokens_in":3223,"tokens_out":2117,"cost":0.00932125,"prev_hash":"genesis","hash":"5c89cb9305e87f22d7d03306e241a62ac5f7bee0f569de92995011dda341feb2"}],"provenance":[{"ts":"2026-07-04T04:33:30.252Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"c7e0941b6760703005291bdcc9859a331d253191baeaa9be97614ba2ffeb3183"},{"ts":"2026-07-04T05:01:30.651Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"c7e0941b6760703005291bdcc9859a331d253191baeaa9be97614ba2ffeb3183","hash":"8c83adf18dc55783dd702c0474b6e7fe7e063cae9ff288c379918048604807f1"},{"ts":"2026-07-07T08:30:52.540Z","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-catalogue-mapping","response":"{\n  \"claims\": [\n    {\n      \"id\": \"c1\",\n      \"text\": \"A₀ inversion is instanced by Falsification (Popper), Gödel, and the negation test.\",\n      \"section\": \"5. Mapping the invariants onto the protocol\",\n      \"tier\": \"speculative\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Maps core axiom to specific invariant instances in the protocol.\"\n    },\n    {\n      \"id\": \"c2\",\n      \"text\": \"A₁ polarity is instanced by Duality/complementarity (§3.14) and symmetry ↔ breaking (§3.3–3.4).\",\n      \"section\": \"5. Mapping the invariants onto the protocol\",\n      \"tier\": \"speculative\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Maps core axiom to specific invariant instances in the protocol.\"\n    },\n    {\n      \"id\": \"c3\",\n      \"text\": \"A₂ the grain is instanced by Dissipation (§3.1), least action (§3.2), compression (§3.10), Tao/wu wei, and maximum power (§3.18).\",\n      \"section\": \"5. Mapping the invariants onto the protocol\",\n      \"tier\": \"speculative\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Maps core axiom to specific invariant instances in the protocol.\"\n    },\n    {\n      \"id\": \"c4\",\n      \"text\": \"A₃ convergence is instanced by Physics unification (GUT), free energy (§3.11), emergence (§3.13), Pareto (§3.15), and general systems theory.\",\n      \"section\": \"5. Mapping the invariants onto the protocol\",\n      \"tier\": \"speculative\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Maps core axiom to specific invariant instances in the protocol.\"\n    },\n    {\n      \"id\": \"c5\",\n      \"text\": \"A₄ the floor is instanced by Thermoeconomics/exergy (§3.18), Ostrom's commons (§3.19), and coercion-cost.\",\n      \"section\": \"5. Mapping the invariants onto the protocol\",\n      \"tier\": \"speculative\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Maps core axiom to specific invariant instances in","tokens_in":3223,"tokens_out":2117,"cost":0,"prev":"8c83adf18dc55783dd702c0474b6e7fe7e063cae9ff288c379918048604807f1","hash":"c42e7e88a76dd030dc90c5a9494a4545dda209c1914d3fad6bf7e5ab01911712"},{"ts":"2026-07-07T08:30:52.864Z","model":"scorer","action":"score","prompt":"","input":"oip-catalogue-mapping","response":"[{\"claim_id\":\"c1\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"},{\"claim_id\":\"c2\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"},{\"claim_id\":\"c3\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"},{\"claim_id\":\"c4\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"},{\"claim_id\":\"c5\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"},{\"claim_id\":\"c6\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"},{\"claim_id\":\"c7\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"},{\"claim_id\":\"c8\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"},{\"claim_id\":\"c9\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"},{\"claim_id\":\"c10\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"},{\"claim_id\":\"c11\",\"old_weight\":0.1,\"new_weight\":0.1,\"status\":\"cut\"}]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"c42e7e88a76dd030dc90c5a9494a4545dda209c1914d3fad6bf7e5ab01911712","hash":"744ba41d16930e4512308dbf75569def5fc127c4fe88eb2eef82f009d31a7812"},{"ts":"2026-07-17T02:36:05.612Z","model":"owner","action":"voxel_divide","prompt":"","input":"oip-catalogue-mapping","response":"8 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"744ba41d16930e4512308dbf75569def5fc127c4fe88eb2eef82f009d31a7812","hash":"c086acac1f01ed7f7b64c33abe7d0fb60df0f159ba6aaca86a74f8a057e5425c"}],"energy":{"passes":5,"tokens_in":3223,"tokens_out":2117,"tokens_total":5340,"cost_usd":0,"models":{"claude-fable-5":2,"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"c086acac1f01ed7f7b64c33abe7d0fb60df0f159ba6aaca86a74f8a057e5425c"},"posted_at":"2026-07-04T02:40:41.104Z","created_at":"2026-07-04T02:40:41.104Z","updated_at":"2026-07-17T02:36:05.612Z","machine":{"shape":"article.machine/v1","slug":"oip-catalogue-mapping","kind":"corpus","read":{"human":"https://miscsubjects.com/a/oip-catalogue-mapping","json":"https://miscsubjects.com/api/articles/oip-catalogue-mapping","bundle":"https://miscsubjects.com/api/articles/oip-catalogue-mapping/bundle?format=markdown"},"traversal":{"prev":{"slug":"oip-catalogue-traversal","human":"https://miscsubjects.com/a/oip-catalogue-traversal","json":"https://miscsubjects.com/api/articles/oip-catalogue-traversal"},"next":{"slug":"oip-catalogue-ai-instance","human":"https://miscsubjects.com/a/oip-catalogue-ai-instance","json":"https://miscsubjects.com/api/articles/oip-catalogue-ai-instance"},"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":"convergence-catalogue","position":5,"of":11},"ledger":{"claims":11,"sources":0,"contributions":1,"revisions":3,"objections_url":"https://miscsubjects.com/api/articles/oip-catalogue-mapping/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=oip-catalogue-mapping","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-catalogue-mapping\",\"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-catalogue-mapping\",\"sources\":[{\"type\":\"review\",\"url\":\"<url>\",\"title\":\"<title>\",\"quote\":\"<verbatim quote>\",\"summary\":\"<one line>\"}]}'","objection":"curl -s -X POST https://miscsubjects.com/api/articles/oip-catalogue-mapping/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-catalogue-mapping\",\"raw_text\":\"<material delta>\"}'  # open intake, no key","read_back":"curl -s https://miscsubjects.com/api/articles/oip-catalogue-mapping | python3 -c 'import json,sys; d=json.load(sys.stdin); print(json.dumps(d[\"claims\"][-3:], indent=1))'"}},"representations":{"article":"/a/oip-catalogue-mapping","json":"/api/articles/oip-catalogue-mapping","markdown":"/api/articles/oip-catalogue-mapping/bundle?format=markdown","skill":"/api/articles/oip-catalogue-mapping/skill","topology":"/api/articles/oip-catalogue-mapping/topology","versions":"/api/articles/oip-catalogue-mapping/revisions","invocations":"/api/articles/oip-catalogue-mapping/invocations"},"object":{"object_type":"article-object","identity":{"id":"article:oip-catalogue-mapping","slug":"oip-catalogue-mapping","title":"The Catalogue: Mapping Invariants to Protocol"},"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-catalogue-mapping","role":"explain","audience":"human"},"skill":{"route":"/api/articles/oip-catalogue-mapping/skill","role":"direct behavior","audience":"model","content":"---\nname: oip-catalogue-mapping\ndescription: Apply the The Catalogue: Mapping Invariants to Protocol article as model behavior. Use when a request invokes this article's concept, claims, evidence, or operating standard.\n---\n\n# The Catalogue: Mapping Invariants to Protocol\n\nThis Skill is the behavioral expression of [the canonical article](/a/oip-catalogue-mapping). It does not repeat the article's human prose.\n\n## Orient\n\n- Read the machine article at /api/articles/oip-catalogue-mapping.\n- Read claims and relationships at /api/articles/oip-catalogue-mapping/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\nMapping Invariants to Protocol 5. Mapping the invariants onto the protocol Axiom Invariants that instance it --- --- A₀ inversion Falsification Popper , Gödel, the negation test A₁ polarity Duality/complementarity §3.14 , symmetry ↔ breakin\n\n## Representations\n\n- Human: /a/oip-catalogue-mapping\n- JSON: /api/articles/oip-catalogue-mapping\n- Relationships: /api/articles/oip-catalogue-mapping/topology\n- History: /api/articles/oip-catalogue-mapping/revisions\n"},"json":{"route":"/api/articles/oip-catalogue-mapping","role":"transport object","audience":"software"},"markdown":{"route":"/api/articles/oip-catalogue-mapping/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. 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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","catalogue","systems-theory","oip","catalogue","mapping"],"relationships":[],"sources":[]},"conformance":{"success_events":"/api/articles/oip-catalogue-mapping/invocations?status=success","failure_events":"/api/articles/oip-catalogue-mapping/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-catalogue-mapping","title":"The Catalogue: Mapping Invariants to Protocol","body":"# Mapping Invariants to Protocol\n\n5. Mapping the invariants onto the protocol\n\n| Axiom | Invariants that instance it |\n|---|---|\n| **A₀** inversion | Falsification (Popper), Gödel, the negation test |\n| **A₁** polarity | Duality/complementarity (§3.14), symmetry ↔ breaking (§3.3–3.4) |\n| **A₂** the grain | Dissipation (§3.1), least action (§3.2), compression (§3.10), Tao/*wu wei*, maximum power (§3.18) |\n| **A₃** convergence | Physics unification (GUT), free energy (§3.11), emergence (§3.13), Pareto (§3.15), general systems theory |\n| **A₄** the floor | Thermoeconomics/exergy (§3.18), Ostrom's commons (§3.19), coercion-cost |\n| **A₇** signatures | The whole of §3 — but the signal is *compressibility of the convergence* (§3.10) |\n| **A₈** maker-system | Autopoiesis (§3.8), observer/participatory universe (§3.21), strange loops (§3.9) |\n| **A₁₁** the receipt | Information/Landauer (§3.10), ledger, provenance |\n| **A₁₂** recursion | Cybernetics (§3.7), autopoiesis (§3.8), evolutionary epistemology (§3.12) |\n| **T₂** the Ought | Teleology/entelechy/Omega (§3.22) — typed T3, carried, not asserted |\n\n---\n\n##\n\n---\n\n## Corpus map\n- Catalogue hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article)\n- Nodes: [C01](/a/oip-node-c01-gradient-dissipation-far-from-equilibrium-order) · [C02](/a/oip-node-c02-least-action-variational-principles) · [C03](/a/oip-node-c03-symmetry-conservation) · [C04](/a/oip-node-c04-symmetry-breaking-bifurcation) · [C05](/a/oip-node-c05-criticality-edge-of-chaos-power-laws) · [C06](/a/oip-node-c06-information-entropy-compression) · … (25 nodes)\n- Edge series: [Convergence 1](/a/oip-convergence-edge-1) · [Disconfirming 1](/a/oip-disconfirming-edge-1)","hero":null,"images":[],"style":{},"tags":["philosophy","oip","catalogue","systems-theory"],"category":null,"model":"Fable 5 (Claude Code)","ledger":{"href":"/api/articles/oip-catalogue-mapping/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"A₀ inversion is instanced by Falsification (Popper), Gödel, and the negation test.","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c2","text":"A₁ polarity is instanced by Duality/complementarity (§3.14) and symmetry ↔ breaking (§3.3–3.4).","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c3","text":"A₂ the grain is instanced by Dissipation (§3.1), least action (§3.2), compression (§3.10), Tao/wu wei, and maximum power (§3.18).","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c4","text":"A₃ convergence is instanced by Physics unification (GUT), free energy (§3.11), emergence (§3.13), Pareto (§3.15), and general systems theory.","section":"5. Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c5","text":"A₄ the floor is instanced by Thermoeconomics/exergy (§3.18), Ostrom's commons (§3.19), and coercion-cost.","section":"5. 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Mapping the invariants onto the protocol","tier":"speculative","source_ids":[],"source_status":"unsourced","why_material":"Maps core axiom to specific invariant instances in the protocol.","evidence_basis":"atomized","weight":0.1,"status":"cut","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c10","text":"T₂ the Ought is instanced by Teleology/entelechy/Omega (§3.22), typed T3, carried not asserted.","section":"5. 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