{"slug":"oip-node-c06-information-entropy-compression","title":"Node C06: Information / Entropy / Compression","body":"# Node C06: Information / Entropy / Compression\n\nC06 — Information / Entropy / Compression\n{\n  \"id\": \"C06\",\n  \"claim\": \"Order is compressibility; physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit; information is physical.\",\n  \"domain\": [\"communications engineering\", \"statistical mechanics\", \"quantum computing\", \"machine_learning\", \"molecular_biology\"],\n  \"pattern\": [\"entropy_as_information\", \"Landauer_bound\", \"MaxEnt\", \"compression\"],\n  \"mechanism\": \"Shannon entropy H = -Σ p_i log p_i measures information content. Boltzmann entropy S = k ln W counts microstates. Landauer: erasing one bit of information requires dissipation of at least kT ln(2) of heat — information destruction is irreversible and physical. Kolmogorov complexity: the shortest program that produces a string is its information content.\",\n  \"scale\": \"quantum → cosmic\",\n  \"claim_tier\": \"T0/T1\",\n  \"sources\": [\n    \"Shannon, C.E. (1948). 'A Mathematical Theory of Communication.' Bell System Tech. J., 27, 379-423, 623-656.\",\n    \"Landauer, R. (1961). 'Irreversibility and Heat Generation in the Computing Process.' IBM J. Res. Dev., 5(3), 183-191.\",\n    \"Jaynes, E.T. (1957). 'Information Theory and Statistical Mechanics.' Phys. Rev., 106(4), 620-630.\",\n    \"Kolmogorov, A.N. (1965). 'Three Approaches to the Quantitative Definition of Information.' Probl. Peredachi Inf., 1(1), 3-11.\",\n    \"Bennett, C.H. (1982). 'The Thermodynamics of Computation.' Int. J. Theor. Phys., 21(12), 905-940.\"\n  ],\n  \"dual\": \"Noise / incompressibility — maximum entropy, no pattern to encode.\",\n  \"falsifier\": \"Information erasure below the Landauer bound (dissipation < kT ln(2) per bit) in a physically realizable process; or information processing with no physical substrate.\",\n  \"rival_frame\": \"Information is a human construct mapped onto physics. The Landauer bound is a calculation about a specific model of computation, not a fundamental physical limit. 'Information is physical' is a metaphorical extension of thermodynamic vocabulary to abstract domains.\",\n  \"independence_check\": \"HIGH. Shannon (Bell Labs, 1948) derived entropy from communication engineering — minimizing transmission cost. Boltzmann/Gibbs (statistical mechanics, 1870s-1900s) derived entropy from counting gas microstates. Landauer (IBM, 1961) derived the bound from thermodynamics of computation. Kolmogorov (Soviet mathematics, 1965) derived complexity from algorithmic theory. Four fields, four nations, four decades, unified result: information and entropy are the same quantity.\",\n  \"pattern_type\": \"mathematical\",\n  \"maps_to_axiom\": [\"A2\", \"A11\", \"A7\"]\n}\n\n---\n\n## Corpus map\n- Same node, other planes: [Encyclopedia C06](/a/convergence-encyclopedia-c06) · [Inventory invariant](/a/oip-invariant-10-310-information-entropy-compression)\n- Edges touching C06: [convergence edge 5](/a/oip-convergence-edge-5)\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-c06-information-entropy-compression/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"Order is compressibility.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Core assertion equating order with a fundamental property of information.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c2","text":"Physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"States the Landauer bound as a physical limit on information destruction.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c3","text":"Information is physical.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Unifies information theory with physical laws.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c4","text":"Shannon entropy H = -Σ p_i log p_i measures information content.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Formal definition linking probability to information measure.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c5","text":"Boltzmann entropy S = k ln W counts microstates.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Links statistical mechanics entropy to counting of states.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c6","text":"Erasing one bit of information requires dissipation of at least kT ln(2) of heat.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Specifies the energetic cost of irreversible information erasure.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c7","text":"Kolmogorov complexity is the length of the shortest program that produces a string.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Defines algorithmic information content.","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-c05-criticality-edge-of-chaos-power-laws","next":"oip-c07-feedback-cybernetics","hub":"oip-convergence-public-article","series":"catalogue-nodes","position":6,"of":25}},"has_traversal":false,"register":"oip_protocol","status":"published","revisions":2,"contributions":[{"seq":0,"id":"k1","ts":"2026-07-07T08:01:00.449Z","model":"grok/grok-4.3","role":"atomizer","action":"atomize","payload":{"claims":[{"id":"c1","text":"Order is compressibility.","tier":"mechanistic"},{"id":"c2","text":"Physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit.","tier":"mechanistic"},{"id":"c3","text":"Information is physical.","tier":"mechanistic"},{"id":"c4","text":"Shannon entropy H = -Σ p_i log p_i measures information content.","tier":"mechanistic"},{"id":"c5","text":"Boltzmann entropy S = k ln W counts microstates.","tier":"mechanistic"},{"id":"c6","text":"Erasing one bit of information requires dissipation of at least kT ln(2) of heat.","tier":"mechanistic"},{"id":"c7","text":"Kolmogorov complexity is the length of the shortest program that produces a string.","tier":"mechanistic"}]},"rationale":"schema conformance: body left untouched, claims atomized","tokens_in":3443,"tokens_out":2088,"cost":0.00952375,"prev_hash":"genesis","hash":"db345b646db8e44de17469158a997a90dfea727e170f12bca379a80dae78db01"}],"provenance":[{"ts":"2026-07-04T04:34:00.635Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"a8367c42d14e96c1240f88e628f3b19b8bdd85a4c6c5f48aa9ee2d112f983cc8"},{"ts":"2026-07-04T05:01:57.984Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"a8367c42d14e96c1240f88e628f3b19b8bdd85a4c6c5f48aa9ee2d112f983cc8","hash":"35cbbeaad6b8bcc294088246bb12b68149b7fcd6b3db698a4bf455a203cd195b"},{"ts":"2026-07-07T08:01:00.449Z","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-c06-information-entropy-compression","response":"{\n  \"claims\": [\n    {\n      \"id\": \"c1\",\n      \"text\": \"Order is compressibility.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Core assertion equating order with a fundamental property of information.\"\n    },\n    {\n      \"id\": \"c2\",\n      \"text\": \"Physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"States the Landauer bound as a physical limit on information destruction.\"\n    },\n    {\n      \"id\": \"c3\",\n      \"text\": \"Information is physical.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Unifies information theory with physical laws.\"\n    },\n    {\n      \"id\": \"c4\",\n      \"text\": \"Shannon entropy H = -Σ p_i log p_i measures information content.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Formal definition linking probability to information measure.\"\n    },\n    {\n      \"id\": \"c5\",\n      \"text\": \"Boltzmann entropy S = k ln W counts microstates.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Links statistical mechanics entropy to counting of states.\"\n    },\n    {\n      \"id\": \"c6\",\n      \"text\": \"Erasing one bit of information requires dissipation of at least kT ln(2) of heat.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Speci","tokens_in":3443,"tokens_out":2088,"cost":0,"prev":"35cbbeaad6b8bcc294088246bb12b68149b7fcd6b3db698a4bf455a203cd195b","hash":"b7b671a394e66a6675ac5ce827c122f85b3c329ae9a5f2215b80f0b90fda1dab"},{"ts":"2026-07-07T08:01:00.762Z","model":"scorer","action":"score","prompt":"","input":"oip-node-c06-information-entropy-compression","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"b7b671a394e66a6675ac5ce827c122f85b3c329ae9a5f2215b80f0b90fda1dab","hash":"2cadc86aeec587f3f75c660caea3a85d3f3fb168a57d6e513ab32132a327e256"},{"ts":"2026-07-17T02:36:19.774Z","model":"owner","action":"voxel_divide","prompt":"","input":"oip-node-c06-information-entropy-compression","response":"5 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"2cadc86aeec587f3f75c660caea3a85d3f3fb168a57d6e513ab32132a327e256","hash":"5a3c55268c351d39871017be9c8531dafc6776cd008eefcf7639e200246f94b7"}],"energy":{"passes":5,"tokens_in":3443,"tokens_out":2088,"tokens_total":5531,"cost_usd":0,"models":{"claude-fable-5":2,"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"5a3c55268c351d39871017be9c8531dafc6776cd008eefcf7639e200246f94b7"},"posted_at":"2026-07-04T02:47:47.540Z","created_at":"2026-07-04T02:47:47.540Z","updated_at":"2026-07-17T02:36:19.774Z","machine":{"shape":"article.machine/v1","slug":"oip-node-c06-information-entropy-compression","kind":"corpus","read":{"human":"https://miscsubjects.com/a/oip-node-c06-information-entropy-compression","json":"https://miscsubjects.com/api/articles/oip-node-c06-information-entropy-compression","bundle":"https://miscsubjects.com/api/articles/oip-node-c06-information-entropy-compression/bundle?format=markdown"},"traversal":{"prev":{"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"},"next":{"slug":"oip-c07-feedback-cybernetics","human":"https://miscsubjects.com/a/oip-c07-feedback-cybernetics","json":"https://miscsubjects.com/api/articles/oip-c07-feedback-cybernetics"},"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":6,"of":25},"ledger":{"claims":7,"sources":0,"contributions":1,"revisions":2,"objections_url":"https://miscsubjects.com/api/articles/oip-node-c06-information-entropy-compression/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=oip-node-c06-information-entropy-compression","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-c06-information-entropy-compression\",\"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-c06-information-entropy-compression\",\"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-c06-information-entropy-compression/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-c06-information-entropy-compression\",\"raw_text\":\"<material delta>\"}'  # open intake, no key","read_back":"curl -s https://miscsubjects.com/api/articles/oip-node-c06-information-entropy-compression | python3 -c 'import json,sys; d=json.load(sys.stdin); print(json.dumps(d[\"claims\"][-3:], indent=1))'"}},"representations":{"article":"/a/oip-node-c06-information-entropy-compression","json":"/api/articles/oip-node-c06-information-entropy-compression","markdown":"/api/articles/oip-node-c06-information-entropy-compression/bundle?format=markdown","skill":"/api/articles/oip-node-c06-information-entropy-compression/skill","topology":"/api/articles/oip-node-c06-information-entropy-compression/topology","versions":"/api/articles/oip-node-c06-information-entropy-compression/revisions","invocations":"/api/articles/oip-node-c06-information-entropy-compression/invocations"},"object":{"object_type":"article-object","identity":{"id":"article:oip-node-c06-information-entropy-compression","slug":"oip-node-c06-information-entropy-compression","title":"Node C06: Information / Entropy / Compression"},"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-c06-information-entropy-compression","role":"explain","audience":"human"},"skill":{"route":"/api/articles/oip-node-c06-information-entropy-compression/skill","role":"direct behavior","audience":"model","content":"---\nname: oip-node-c06-information-entropy-compression\ndescription: Apply the Node C06: Information / Entropy / Compression article as model behavior. Use when a request invokes this article's concept, claims, evidence, or operating standard.\n---\n\n# Node C06: Information / Entropy / Compression\n\nThis Skill is the behavioral expression of [the canonical article](/a/oip-node-c06-information-entropy-compression). It does not repeat the article's human prose.\n\n## Orient\n\n- Read the machine article at /api/articles/oip-node-c06-information-entropy-compression.\n- Read claims and relationships at /api/articles/oip-node-c06-information-entropy-compression/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 C06: Information / Entropy / Compression C06 — Information / Entropy / Compression { \"id\": \"C06\", \"claim\": \"Order is compressibility; physical erasure of information has a minimum thermodynamic cost of kT ln 2 per bit; information is p\n\n## Representations\n\n- Human: /a/oip-node-c06-information-entropy-compression\n- JSON: /api/articles/oip-node-c06-information-entropy-compression\n- Relationships: /api/articles/oip-node-c06-information-entropy-compression/topology\n- History: /api/articles/oip-node-c06-information-entropy-compression/revisions\n"},"json":{"route":"/api/articles/oip-node-c06-information-entropy-compression","role":"transport object","audience":"software"},"markdown":{"route":"/api/articles/oip-node-c06-information-entropy-compression/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","c06","information","entropy","compression"],"relationships":[],"sources":[]},"conformance":{"success_events":"/api/articles/oip-node-c06-information-entropy-compression/invocations?status=success","failure_events":"/api/articles/oip-node-c06-information-entropy-compression/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-c06-information-entropy-compression","title":"Node C06: Information / Entropy / Compression","body":"# Node C06: Information / Entropy / Compression\n\nC06 — Information / Entropy / Compression\n{\n  \"id\": \"C06\",\n  \"claim\": \"Order is compressibility; physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit; information is physical.\",\n  \"domain\": [\"communications engineering\", \"statistical mechanics\", \"quantum computing\", \"machine_learning\", \"molecular_biology\"],\n  \"pattern\": [\"entropy_as_information\", \"Landauer_bound\", \"MaxEnt\", \"compression\"],\n  \"mechanism\": \"Shannon entropy H = -Σ p_i log p_i measures information content. Boltzmann entropy S = k ln W counts microstates. Landauer: erasing one bit of information requires dissipation of at least kT ln(2) of heat — information destruction is irreversible and physical. Kolmogorov complexity: the shortest program that produces a string is its information content.\",\n  \"scale\": \"quantum → cosmic\",\n  \"claim_tier\": \"T0/T1\",\n  \"sources\": [\n    \"Shannon, C.E. (1948). 'A Mathematical Theory of Communication.' Bell System Tech. J., 27, 379-423, 623-656.\",\n    \"Landauer, R. (1961). 'Irreversibility and Heat Generation in the Computing Process.' IBM J. Res. Dev., 5(3), 183-191.\",\n    \"Jaynes, E.T. (1957). 'Information Theory and Statistical Mechanics.' Phys. Rev., 106(4), 620-630.\",\n    \"Kolmogorov, A.N. (1965). 'Three Approaches to the Quantitative Definition of Information.' Probl. Peredachi Inf., 1(1), 3-11.\",\n    \"Bennett, C.H. (1982). 'The Thermodynamics of Computation.' Int. J. Theor. Phys., 21(12), 905-940.\"\n  ],\n  \"dual\": \"Noise / incompressibility — maximum entropy, no pattern to encode.\",\n  \"falsifier\": \"Information erasure below the Landauer bound (dissipation < kT ln(2) per bit) in a physically realizable process; or information processing with no physical substrate.\",\n  \"rival_frame\": \"Information is a human construct mapped onto physics. The Landauer bound is a calculation about a specific model of computation, not a fundamental physical limit. 'Information is physical' is a metaphorical extension of thermodynamic vocabulary to abstract domains.\",\n  \"independence_check\": \"HIGH. Shannon (Bell Labs, 1948) derived entropy from communication engineering — minimizing transmission cost. Boltzmann/Gibbs (statistical mechanics, 1870s-1900s) derived entropy from counting gas microstates. Landauer (IBM, 1961) derived the bound from thermodynamics of computation. Kolmogorov (Soviet mathematics, 1965) derived complexity from algorithmic theory. Four fields, four nations, four decades, unified result: information and entropy are the same quantity.\",\n  \"pattern_type\": \"mathematical\",\n  \"maps_to_axiom\": [\"A2\", \"A11\", \"A7\"]\n}\n\n---\n\n## Corpus map\n- Same node, other planes: [Encyclopedia C06](/a/convergence-encyclopedia-c06) · [Inventory invariant](/a/oip-invariant-10-310-information-entropy-compression)\n- Edges touching C06: [convergence edge 5](/a/oip-convergence-edge-5)\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-c06-information-entropy-compression/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"Order is compressibility.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Core assertion equating order with a fundamental property of information.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c2","text":"Physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"States the Landauer bound as a physical limit on information destruction.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c3","text":"Information is physical.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Unifies information theory with physical laws.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c4","text":"Shannon entropy H = -Σ p_i log p_i measures information content.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Formal definition linking probability to information measure.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c5","text":"Boltzmann entropy S = k ln W counts microstates.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Links statistical mechanics entropy to counting of states.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c6","text":"Erasing one bit of information requires dissipation of at least kT ln(2) of heat.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Specifies the energetic cost of irreversible information erasure.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c7","text":"Kolmogorov complexity is the length of the shortest program that produces a string.","section":"C06 — Information / Entropy / Compression","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Defines algorithmic information content.","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-c05-criticality-edge-of-chaos-power-laws","next":"oip-c07-feedback-cybernetics","hub":"oip-convergence-public-article","series":"catalogue-nodes","position":6,"of":25}},"has_traversal":false,"register":"oip_protocol","status":"published","revisions":2,"contributions":[{"seq":0,"id":"k1","ts":"2026-07-07T08:01:00.449Z","model":"grok/grok-4.3","role":"atomizer","action":"atomize","payload":{"claims":[{"id":"c1","text":"Order is compressibility.","tier":"mechanistic"},{"id":"c2","text":"Physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit.","tier":"mechanistic"},{"id":"c3","text":"Information is physical.","tier":"mechanistic"},{"id":"c4","text":"Shannon entropy H = -Σ p_i log p_i measures information content.","tier":"mechanistic"},{"id":"c5","text":"Boltzmann entropy S = k ln W counts microstates.","tier":"mechanistic"},{"id":"c6","text":"Erasing one bit of information requires dissipation of at least kT ln(2) of heat.","tier":"mechanistic"},{"id":"c7","text":"Kolmogorov complexity is the length of the shortest program that produces a string.","tier":"mechanistic"}]},"rationale":"schema conformance: body left untouched, claims atomized","tokens_in":3443,"tokens_out":2088,"cost":0.00952375,"prev_hash":"genesis","hash":"db345b646db8e44de17469158a997a90dfea727e170f12bca379a80dae78db01"}],"provenance":[{"ts":"2026-07-04T04:34:00.635Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"a8367c42d14e96c1240f88e628f3b19b8bdd85a4c6c5f48aa9ee2d112f983cc8"},{"ts":"2026-07-04T05:01:57.984Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"a8367c42d14e96c1240f88e628f3b19b8bdd85a4c6c5f48aa9ee2d112f983cc8","hash":"35cbbeaad6b8bcc294088246bb12b68149b7fcd6b3db698a4bf455a203cd195b"},{"ts":"2026-07-07T08:01:00.449Z","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-c06-information-entropy-compression","response":"{\n  \"claims\": [\n    {\n      \"id\": \"c1\",\n      \"text\": \"Order is compressibility.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Core assertion equating order with a fundamental property of information.\"\n    },\n    {\n      \"id\": \"c2\",\n      \"text\": \"Physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"States the Landauer bound as a physical limit on information destruction.\"\n    },\n    {\n      \"id\": \"c3\",\n      \"text\": \"Information is physical.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Unifies information theory with physical laws.\"\n    },\n    {\n      \"id\": \"c4\",\n      \"text\": \"Shannon entropy H = -Σ p_i log p_i measures information content.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Formal definition linking probability to information measure.\"\n    },\n    {\n      \"id\": \"c5\",\n      \"text\": \"Boltzmann entropy S = k ln W counts microstates.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Links statistical mechanics entropy to counting of states.\"\n    },\n    {\n      \"id\": \"c6\",\n      \"text\": \"Erasing one bit of information requires dissipation of at least kT ln(2) of heat.\",\n      \"section\": \"C06 — Information / Entropy / Compression\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Speci","tokens_in":3443,"tokens_out":2088,"cost":0,"prev":"35cbbeaad6b8bcc294088246bb12b68149b7fcd6b3db698a4bf455a203cd195b","hash":"b7b671a394e66a6675ac5ce827c122f85b3c329ae9a5f2215b80f0b90fda1dab"},{"ts":"2026-07-07T08:01:00.762Z","model":"scorer","action":"score","prompt":"","input":"oip-node-c06-information-entropy-compression","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"b7b671a394e66a6675ac5ce827c122f85b3c329ae9a5f2215b80f0b90fda1dab","hash":"2cadc86aeec587f3f75c660caea3a85d3f3fb168a57d6e513ab32132a327e256"},{"ts":"2026-07-17T02:36:19.774Z","model":"owner","action":"voxel_divide","prompt":"","input":"oip-node-c06-information-entropy-compression","response":"5 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"2cadc86aeec587f3f75c660caea3a85d3f3fb168a57d6e513ab32132a327e256","hash":"5a3c55268c351d39871017be9c8531dafc6776cd008eefcf7639e200246f94b7"}],"energy":{"passes":5,"tokens_in":3443,"tokens_out":2088,"tokens_total":5531,"cost_usd":0,"models":{"claude-fable-5":2,"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"5a3c55268c351d39871017be9c8531dafc6776cd008eefcf7639e200246f94b7"},"posted_at":"2026-07-04T02:47:47.540Z","created_at":"2026-07-04T02:47:47.540Z","updated_at":"2026-07-17T02:36:19.774Z","machine":{"shape":"article.machine/v1","slug":"oip-node-c06-information-entropy-compression","kind":"corpus","read":{"human":"https://miscsubjects.com/a/oip-node-c06-information-entropy-compression","json":"https://miscsubjects.com/api/articles/oip-node-c06-information-entropy-compression","bundle":"https://miscsubjects.com/api/articles/oip-node-c06-information-entropy-compression/bundle?format=markdown"},"traversal":{"prev":{"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"},"next":{"slug":"oip-c07-feedback-cybernetics","human":"https://miscsubjects.com/a/oip-c07-feedback-cybernetics","json":"https://miscsubjects.com/api/articles/oip-c07-feedback-cybernetics"},"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":6,"of":25},"ledger":{"claims":7,"sources":0,"contributions":1,"revisions":2,"objections_url":"https://miscsubjects.com/api/articles/oip-node-c06-information-entropy-compression/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=oip-node-c06-information-entropy-compression","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-c06-information-entropy-compression\",\"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-c06-information-entropy-compression\",\"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-c06-information-entropy-compression/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-c06-information-entropy-compression\",\"raw_text\":\"<material delta>\"}'  # open intake, no key","read_back":"curl -s https://miscsubjects.com/api/articles/oip-node-c06-information-entropy-compression | python3 -c 'import json,sys; d=json.load(sys.stdin); print(json.dumps(d[\"claims\"][-3:], indent=1))'"}},"representations":{"article":"/a/oip-node-c06-information-entropy-compression","json":"/api/articles/oip-node-c06-information-entropy-compression","markdown":"/api/articles/oip-node-c06-information-entropy-compression/bundle?format=markdown","skill":"/api/articles/oip-node-c06-information-entropy-compression/skill","topology":"/api/articles/oip-node-c06-information-entropy-compression/topology","versions":"/api/articles/oip-node-c06-information-entropy-compression/revisions","invocations":"/api/articles/oip-node-c06-information-entropy-compression/invocations"}}}}