{"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"],"model":null,"ledger":null,"embeds":[],"widgets":[],"home":true,"claims":[],"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}},"register":"oip_protocol","status":"published","revisions":3,"contributions":[],"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"}],"energy":{"passes":2,"tokens_in":0,"tokens_out":0,"tokens_total":0,"cost_usd":0,"models":{"claude-fable-5":2},"head":"324b6ad824422420050d74a3a6010e66d6cc58516807ea7aa20b117b8dcc75eb"},"posted_at":"2026-07-04T02:40:25.610Z","created_at":"2026-07-04T02:40:25.610Z","updated_at":"2026-07-04T05:01:52.872Z","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":0,"sources":0,"contributions":0,"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))'"}}}