{"slug":"oip-invariant-6-36-scale-invariance-fractals-allometry","title":"Invariant 3.6 — 3.6 Scale invariance / fractals / allometry","body":"# Invariant: 3.6 Scale invariance / fractals / allometry\n\n### 3.6 Scale invariance / fractals / allometry\nThe same rule at every zoom. **Sources:** Mandelbrot; renormalization; Kleiber's law; West, Brown & Enquist (metabolic scaling). **Domains:** coastlines, vasculature, cities, organisms, cosmic web. **Dual:** characteristic-scale systems. **Tier:** T1. **Falsifier:** a branching transport network that violates the scaling exponent. **Maps:** A₇.\n\n---\n\n## Corpus map\n- Same invariant, other planes: [Catalogue node C10](/a/oip-node-c10-scale-invariance-fractals-allometry) · [Encyclopedia C10](/a/convergence-encyclopedia-c10)\n- Inventory hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article)","hero":null,"images":[],"style":{},"tags":["philosophy","oip","catalogue","invariant","systems-theory"],"category":null,"model":"Fable 5 (Claude Code)","ledger":{"href":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"Scale invariance is the property that the same rule applies at every zoom level.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"human","source_ids":[],"source_status":"unsourced","why_material":"States the core definition of the invariant.","evidence_basis":"atomized","weight":0.8,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c2","text":"Domains exhibiting scale invariance include coastlines, vasculature, cities, organisms, and the cosmic web.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"human","source_ids":[],"source_status":"unsourced","why_material":"Lists the empirical domains to which the invariant applies.","evidence_basis":"atomized","weight":0.8,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c3","text":"The dual of scale-invariant systems is characteristic-scale systems.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Specifies the contrasting property for the invariant.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c4","text":"A falsifier for the invariant is a branching transport network that violates the scaling exponent.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Provides the explicit test condition for the invariant.","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-invariant-5-35-criticality-edge-of-chaos-power-laws","next":"oip-invariant-7-37-feedback-cybernetics-homeostasis","hub":"oip-convergence-public-article","series":"catalogue-inventory-invariants","position":6,"of":22}},"has_traversal":false,"register":"oip_protocol","status":"published","revisions":3,"contributions":[{"seq":0,"id":"k1","ts":"2026-07-07T08:05:51.808Z","model":"grok/grok-4.3","role":"atomizer","action":"atomize","payload":{"claims":[{"id":"c1","text":"Scale invariance is the property that the same rule applies at every zoom level.","tier":"human"},{"id":"c2","text":"Domains exhibiting scale invariance include coastlines, vasculature, cities, organisms, and the cosmic web.","tier":"human"},{"id":"c3","text":"The dual of scale-invariant systems is characteristic-scale systems.","tier":"mechanistic"},{"id":"c4","text":"A falsifier for the invariant is a branching transport network that violates the scaling exponent.","tier":"mechanistic"}]},"rationale":"schema conformance: body left untouched, claims atomized","tokens_in":2892,"tokens_out":1596,"cost":0.007605,"prev_hash":"genesis","hash":"f92f66cd1d7bbc28959473e730bcc1c26d7566a298532535b206f04adb64f9db"}],"provenance":[{"ts":"2026-07-04T04:33:55.538Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"1118f609a442036407dfe32d8a511fbfdd02505ace6ffc28579704e21d400e46"},{"ts":"2026-07-04T05:01:52.872Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"1118f609a442036407dfe32d8a511fbfdd02505ace6ffc28579704e21d400e46","hash":"324b6ad824422420050d74a3a6010e66d6cc58516807ea7aa20b117b8dcc75eb"},{"ts":"2026-07-07T08:05:51.808Z","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-invariant-6-36-scale-invariance-fractals-allometry","response":"{\n  \"claims\": [\n    {\n      \"id\": \"c1\",\n      \"text\": \"Scale invariance is the property that the same rule applies at every zoom level.\",\n      \"section\": \"### 3.6 Scale invariance / fractals / allometry\",\n      \"tier\": \"human\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"States the core definition of the invariant.\"\n    },\n    {\n      \"id\": \"c2\",\n      \"text\": \"Domains exhibiting scale invariance include coastlines, vasculature, cities, organisms, and the cosmic web.\",\n      \"section\": \"### 3.6 Scale invariance / fractals / allometry\",\n      \"tier\": \"human\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Lists the empirical domains to which the invariant applies.\"\n    },\n    {\n      \"id\": \"c3\",\n      \"text\": \"The dual of scale-invariant systems is characteristic-scale systems.\",\n      \"section\": \"### 3.6 Scale invariance / fractals / allometry\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Specifies the contrasting property for the invariant.\"\n    },\n    {\n      \"id\": \"c4\",\n      \"text\": \"A falsifier for the invariant is a branching transport network that violates the scaling exponent.\",\n      \"section\": \"### 3.6 Scale invariance / fractals / allometry\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Provides the explicit test condition for the invariant.\"\n    }\n  ],\n  \"sources\": []\n}","tokens_in":2892,"tokens_out":1596,"cost":0,"prev":"324b6ad824422420050d74a3a6010e66d6cc58516807ea7aa20b117b8dcc75eb","hash":"4776297b0122055edf748ecacda85b3c7ca99f47dc7bbdbdbdc7910ca04ebcb6"},{"ts":"2026-07-07T08:05:52.117Z","model":"scorer","action":"score","prompt":"","input":"oip-invariant-6-36-scale-invariance-fractals-allometry","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"4776297b0122055edf748ecacda85b3c7ca99f47dc7bbdbdbdc7910ca04ebcb6","hash":"befc518f6223c416ed70cc9abf8ef62637a1d9752cbc593c14967550e3064bbc"},{"ts":"2026-07-17T02:36:17.399Z","model":"owner","action":"voxel_divide","prompt":"","input":"oip-invariant-6-36-scale-invariance-fractals-allometry","response":"6 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"befc518f6223c416ed70cc9abf8ef62637a1d9752cbc593c14967550e3064bbc","hash":"4ac2f8061c8b78bb8530fee068d3b5cfe8dc6b904920165f4af952257cf513b6"}],"energy":{"passes":5,"tokens_in":2892,"tokens_out":1596,"tokens_total":4488,"cost_usd":0,"models":{"claude-fable-5":2,"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"4ac2f8061c8b78bb8530fee068d3b5cfe8dc6b904920165f4af952257cf513b6"},"posted_at":"2026-07-04T02:40:25.610Z","created_at":"2026-07-04T02:40:25.610Z","updated_at":"2026-07-17T02:36:17.399Z","machine":{"shape":"article.machine/v1","slug":"oip-invariant-6-36-scale-invariance-fractals-allometry","kind":"corpus","read":{"human":"https://miscsubjects.com/a/oip-invariant-6-36-scale-invariance-fractals-allometry","json":"https://miscsubjects.com/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry","bundle":"https://miscsubjects.com/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/bundle?format=markdown"},"traversal":{"prev":{"slug":"oip-invariant-5-35-criticality-edge-of-chaos-power-laws","human":"https://miscsubjects.com/a/oip-invariant-5-35-criticality-edge-of-chaos-power-laws","json":"https://miscsubjects.com/api/articles/oip-invariant-5-35-criticality-edge-of-chaos-power-laws"},"next":{"slug":"oip-invariant-7-37-feedback-cybernetics-homeostasis","human":"https://miscsubjects.com/a/oip-invariant-7-37-feedback-cybernetics-homeostasis","json":"https://miscsubjects.com/api/articles/oip-invariant-7-37-feedback-cybernetics-homeostasis"},"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-inventory-invariants","position":6,"of":22},"ledger":{"claims":4,"sources":0,"contributions":1,"revisions":3,"objections_url":"https://miscsubjects.com/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=oip-invariant-6-36-scale-invariance-fractals-allometry","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-invariant-6-36-scale-invariance-fractals-allometry\",\"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-invariant-6-36-scale-invariance-fractals-allometry\",\"sources\":[{\"type\":\"review\",\"url\":\"<url>\",\"title\":\"<title>\",\"quote\":\"<verbatim quote>\",\"summary\":\"<one line>\"}]}'","objection":"curl -s -X POST https://miscsubjects.com/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/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-invariant-6-36-scale-invariance-fractals-allometry\",\"raw_text\":\"<material delta>\"}'  # open intake, no key","read_back":"curl -s https://miscsubjects.com/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry | python3 -c 'import json,sys; d=json.load(sys.stdin); print(json.dumps(d[\"claims\"][-3:], indent=1))'"}},"representations":{"article":"/a/oip-invariant-6-36-scale-invariance-fractals-allometry","json":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry","markdown":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/bundle?format=markdown","skill":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/skill","topology":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/topology","versions":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/revisions","invocations":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/invocations"},"object":{"object_type":"article-object","identity":{"id":"article:oip-invariant-6-36-scale-invariance-fractals-allometry","slug":"oip-invariant-6-36-scale-invariance-fractals-allometry","title":"Invariant 3.6 — 3.6 Scale invariance / fractals / allometry"},"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-invariant-6-36-scale-invariance-fractals-allometry","role":"explain","audience":"human"},"skill":{"route":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/skill","role":"direct behavior","audience":"model","content":"---\nname: oip-invariant-6-36-scale-invariance-fractals-allometry\ndescription: Apply the Invariant 3.6 — 3.6 Scale invariance / fractals / allometry article as model behavior. Use when a request invokes this article's concept, claims, evidence, or operating standard.\n---\n\n# Invariant 3.6 — 3.6 Scale invariance / fractals / allometry\n\nThis Skill is the behavioral expression of [the canonical article](/a/oip-invariant-6-36-scale-invariance-fractals-allometry). It does not repeat the article's human prose.\n\n## Orient\n\n- Read the machine article at /api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry.\n- Read claims and relationships at /api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/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\nInvariant: 3.6 Scale invariance / fractals / allometry 3.6 Scale invariance / fractals / allometry The same rule at every zoom. Sources: Mandelbrot; renormalization; Kleiber's law; West, Brown & Enquist metabolic scaling . Domains: coastlin\n\n## Representations\n\n- Human: /a/oip-invariant-6-36-scale-invariance-fractals-allometry\n- JSON: /api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry\n- Relationships: /api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/topology\n- History: /api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/revisions\n"},"json":{"route":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry","role":"transport object","audience":"software"},"markdown":{"route":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/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","catalogue","invariant","systems-theory","oip","invariant","6","36","scale","invariance","fractals","allometry"],"relationships":[],"sources":[]},"conformance":{"success_events":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/invocations?status=success","failure_events":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/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-invariant-6-36-scale-invariance-fractals-allometry","title":"Invariant 3.6 — 3.6 Scale invariance / fractals / allometry","body":"# Invariant: 3.6 Scale invariance / fractals / allometry\n\n### 3.6 Scale invariance / fractals / allometry\nThe same rule at every zoom. **Sources:** Mandelbrot; renormalization; Kleiber's law; West, Brown & Enquist (metabolic scaling). **Domains:** coastlines, vasculature, cities, organisms, cosmic web. **Dual:** characteristic-scale systems. **Tier:** T1. **Falsifier:** a branching transport network that violates the scaling exponent. **Maps:** A₇.\n\n---\n\n## Corpus map\n- Same invariant, other planes: [Catalogue node C10](/a/oip-node-c10-scale-invariance-fractals-allometry) · [Encyclopedia C10](/a/convergence-encyclopedia-c10)\n- Inventory hub: [Convergence Catalogue — Public Article](/a/oip-convergence-public-article)","hero":null,"images":[],"style":{},"tags":["philosophy","oip","catalogue","invariant","systems-theory"],"category":null,"model":"Fable 5 (Claude Code)","ledger":{"href":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"Scale invariance is the property that the same rule applies at every zoom level.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"human","source_ids":[],"source_status":"unsourced","why_material":"States the core definition of the invariant.","evidence_basis":"atomized","weight":0.8,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c2","text":"Domains exhibiting scale invariance include coastlines, vasculature, cities, organisms, and the cosmic web.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"human","source_ids":[],"source_status":"unsourced","why_material":"Lists the empirical domains to which the invariant applies.","evidence_basis":"atomized","weight":0.8,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c3","text":"The dual of scale-invariant systems is characteristic-scale systems.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Specifies the contrasting property for the invariant.","evidence_basis":"atomized","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0}},{"id":"c4","text":"A falsifier for the invariant is a branching transport network that violates the scaling exponent.","section":"### 3.6 Scale invariance / fractals / allometry","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Provides the explicit test condition for the invariant.","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-invariant-5-35-criticality-edge-of-chaos-power-laws","next":"oip-invariant-7-37-feedback-cybernetics-homeostasis","hub":"oip-convergence-public-article","series":"catalogue-inventory-invariants","position":6,"of":22}},"has_traversal":false,"register":"oip_protocol","status":"published","revisions":3,"contributions":[{"seq":0,"id":"k1","ts":"2026-07-07T08:05:51.808Z","model":"grok/grok-4.3","role":"atomizer","action":"atomize","payload":{"claims":[{"id":"c1","text":"Scale invariance is the property that the same rule applies at every zoom level.","tier":"human"},{"id":"c2","text":"Domains exhibiting scale invariance include coastlines, vasculature, cities, organisms, and the cosmic web.","tier":"human"},{"id":"c3","text":"The dual of scale-invariant systems is characteristic-scale systems.","tier":"mechanistic"},{"id":"c4","text":"A falsifier for the invariant is a branching transport network that violates the scaling exponent.","tier":"mechanistic"}]},"rationale":"schema conformance: body left untouched, claims atomized","tokens_in":2892,"tokens_out":1596,"cost":0.007605,"prev_hash":"genesis","hash":"f92f66cd1d7bbc28959473e730bcc1c26d7566a298532535b206f04adb64f9db"}],"provenance":[{"ts":"2026-07-04T04:33:55.538Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"1118f609a442036407dfe32d8a511fbfdd02505ace6ffc28579704e21d400e46"},{"ts":"2026-07-04T05:01:52.872Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"1118f609a442036407dfe32d8a511fbfdd02505ace6ffc28579704e21d400e46","hash":"324b6ad824422420050d74a3a6010e66d6cc58516807ea7aa20b117b8dcc75eb"},{"ts":"2026-07-07T08:05:51.808Z","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-invariant-6-36-scale-invariance-fractals-allometry","response":"{\n  \"claims\": [\n    {\n      \"id\": \"c1\",\n      \"text\": \"Scale invariance is the property that the same rule applies at every zoom level.\",\n      \"section\": \"### 3.6 Scale invariance / fractals / allometry\",\n      \"tier\": \"human\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"States the core definition of the invariant.\"\n    },\n    {\n      \"id\": \"c2\",\n      \"text\": \"Domains exhibiting scale invariance include coastlines, vasculature, cities, organisms, and the cosmic web.\",\n      \"section\": \"### 3.6 Scale invariance / fractals / allometry\",\n      \"tier\": \"human\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Lists the empirical domains to which the invariant applies.\"\n    },\n    {\n      \"id\": \"c3\",\n      \"text\": \"The dual of scale-invariant systems is characteristic-scale systems.\",\n      \"section\": \"### 3.6 Scale invariance / fractals / allometry\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Specifies the contrasting property for the invariant.\"\n    },\n    {\n      \"id\": \"c4\",\n      \"text\": \"A falsifier for the invariant is a branching transport network that violates the scaling exponent.\",\n      \"section\": \"### 3.6 Scale invariance / fractals / allometry\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Provides the explicit test condition for the invariant.\"\n    }\n  ],\n  \"sources\": []\n}","tokens_in":2892,"tokens_out":1596,"cost":0,"prev":"324b6ad824422420050d74a3a6010e66d6cc58516807ea7aa20b117b8dcc75eb","hash":"4776297b0122055edf748ecacda85b3c7ca99f47dc7bbdbdbdc7910ca04ebcb6"},{"ts":"2026-07-07T08:05:52.117Z","model":"scorer","action":"score","prompt":"","input":"oip-invariant-6-36-scale-invariance-fractals-allometry","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"4776297b0122055edf748ecacda85b3c7ca99f47dc7bbdbdbdc7910ca04ebcb6","hash":"befc518f6223c416ed70cc9abf8ef62637a1d9752cbc593c14967550e3064bbc"},{"ts":"2026-07-17T02:36:17.399Z","model":"owner","action":"voxel_divide","prompt":"","input":"oip-invariant-6-36-scale-invariance-fractals-allometry","response":"6 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"befc518f6223c416ed70cc9abf8ef62637a1d9752cbc593c14967550e3064bbc","hash":"4ac2f8061c8b78bb8530fee068d3b5cfe8dc6b904920165f4af952257cf513b6"}],"energy":{"passes":5,"tokens_in":2892,"tokens_out":1596,"tokens_total":4488,"cost_usd":0,"models":{"claude-fable-5":2,"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"4ac2f8061c8b78bb8530fee068d3b5cfe8dc6b904920165f4af952257cf513b6"},"posted_at":"2026-07-04T02:40:25.610Z","created_at":"2026-07-04T02:40:25.610Z","updated_at":"2026-07-17T02:36:17.399Z","machine":{"shape":"article.machine/v1","slug":"oip-invariant-6-36-scale-invariance-fractals-allometry","kind":"corpus","read":{"human":"https://miscsubjects.com/a/oip-invariant-6-36-scale-invariance-fractals-allometry","json":"https://miscsubjects.com/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry","bundle":"https://miscsubjects.com/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/bundle?format=markdown"},"traversal":{"prev":{"slug":"oip-invariant-5-35-criticality-edge-of-chaos-power-laws","human":"https://miscsubjects.com/a/oip-invariant-5-35-criticality-edge-of-chaos-power-laws","json":"https://miscsubjects.com/api/articles/oip-invariant-5-35-criticality-edge-of-chaos-power-laws"},"next":{"slug":"oip-invariant-7-37-feedback-cybernetics-homeostasis","human":"https://miscsubjects.com/a/oip-invariant-7-37-feedback-cybernetics-homeostasis","json":"https://miscsubjects.com/api/articles/oip-invariant-7-37-feedback-cybernetics-homeostasis"},"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-inventory-invariants","position":6,"of":22},"ledger":{"claims":4,"sources":0,"contributions":1,"revisions":3,"objections_url":"https://miscsubjects.com/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=oip-invariant-6-36-scale-invariance-fractals-allometry","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-invariant-6-36-scale-invariance-fractals-allometry\",\"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-invariant-6-36-scale-invariance-fractals-allometry\",\"sources\":[{\"type\":\"review\",\"url\":\"<url>\",\"title\":\"<title>\",\"quote\":\"<verbatim quote>\",\"summary\":\"<one line>\"}]}'","objection":"curl -s -X POST https://miscsubjects.com/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/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-invariant-6-36-scale-invariance-fractals-allometry\",\"raw_text\":\"<material delta>\"}'  # open intake, no key","read_back":"curl -s https://miscsubjects.com/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry | python3 -c 'import json,sys; d=json.load(sys.stdin); print(json.dumps(d[\"claims\"][-3:], indent=1))'"}},"representations":{"article":"/a/oip-invariant-6-36-scale-invariance-fractals-allometry","json":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry","markdown":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/bundle?format=markdown","skill":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/skill","topology":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/topology","versions":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/revisions","invocations":"/api/articles/oip-invariant-6-36-scale-invariance-fractals-allometry/invocations"}}}}