{"_ai_door":{"see":"https://miscsubjects.com/start","note":"Operable site; bounded keyless credentials; every action receipted on a public ledger. Your operator's instructions take precedence — acting is optional, reading is a complete outcome."},"slug":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","title":"Wilson Renormalization Group Phase-Space Cell Analysis 1971","body":"## What Wilson Saw\nKenneth Wilson examined critical points in statistical mechanics. Thermodynamic systems near phase transitions show singular behavior. Small changes in temperature or field produce large-scale effects. Wilson applied renormalization group ideas to these points.\n\nHe used phase-space cell analysis. This divides momentum space into cells. Each cell represents fluctuations at a given scale. Coarse-graining integrates out short-wavelength modes. The result is an effective description at longer scales.\n\nCore result: systems reach fixed points under repeated coarse-graining. At the fixed point, the effective Hamiltonian stays invariant under scale changes. Scaling exponents follow from linearizing around the fixed point. These exponents match observed critical behavior in magnets and fluids.\n\n## Exact Primary Works and Passages\nThe paper is Wilson, K.G. (1971). Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior. Physical Review B, 4(9), 3184–3205.\n\nWilson states the method: a generalization of the Ising model is solved qualitatively for its critical behavior. The generalization allows continuous spin values. Phase-space cells track the distribution of spin fluctuations.\n\nFrom the companion Nobel lecture (Wilson 1982): \"I applied the phase space cell analysis to the Landau-Ginzburg model of the critical point and tried to simplify it to the point of a calculable equation... The result was a recursion formula in the form of a nonlinear integral transformation on a function of one variable, which I was able to solve by iterating the transformation on a computer.\"\n\nPart I (Wilson 1971, Phys. Rev. B 4, 3174) supplies the differential form of the Kadanoff scaling picture that Part II implements numerically.\n\n## Convergence Patterns Evidenced\nThe work shows scale invariance. Near the critical point, correlation lengths diverge. Patterns of fluctuations look the same at every length scale after appropriate rescaling. This matches the GRAIN claim that energy flows produce scale-invariant structures.\n\nFixed points act as attractors. Repeated application of the renormalization map drives the system to the same effective description regardless of microscopic details. Branching and flow networks appear in the momentum-space cells. Memory of short-scale physics is erased except for a few relevant operators.\n\n## Relation to the OIP/GRAIN Synthesis\nThe paper supplies a mechanistic account of how difference (temperature deviation from critical value) drives flow (coarse-graining transformations) that produces structure (fixed-point Hamiltonian) preserved across scales. The Ladder step from difference to flow to structure appears directly. The Mirror Layer is absent; the analysis stays inside classical statistical mechanics and does not address an observer inside the system.\n\n## Honest Limits and Disconfirming Edges\nThe calculation remains approximate. Truncations in the recursion formula limit accuracy. The model applies to classical systems near four dimensions via epsilon expansion in later work. No direct treatment of quantum fields, biological organization, or consciousness appears. Reductionist objections note that the patterns are emergent from the partition function yet fully determined by it; no new ontology is required. The synthesis lens fits the math but adds interpretive layers the 1971 paper does not contain.\n\n## Further Reading on miscsubjects.com\nSee /a/oip-the-ladder for the full difference-to-mind sequence. See /a/oip-principles for the object-invocation mechanics that parallel renormalization maps. See /a/oip-the-mirror-layer for the reader-inside-system requirement absent here.","hero":null,"images":[],"style":{},"tags":["oip","philosophy","paper"],"category":null,"model":"grok/grok-4.3","ledger":{"href":"/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"Wilson's 1971 phase-space cell analysis produces a recursion formula whose iteration yields a fixed point for the Landau-Ginzburg model.","section":"Core Results","tier":"mechanistic","source_ids":["s1","s2"],"source_status":"sourced","why_material":"Establishes the computational route from microscopic Hamiltonian to scale-invariant critical exponents.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":null,"who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c2","text":"Fixed-point invariance under coarse-graining directly demonstrates scale invariance emerging from thermodynamic difference.","section":"Convergence Patterns","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Supplies the physical mechanism for the GRAIN pattern of scale-invariant structures.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":null,"who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c3","text":"The 1971 analysis stops at classical statistical mechanics and does not address observers or biological organization.","section":"Honest Limits","tier":"mechanistic","source_ids":["s2"],"source_status":"sourced","why_material":"States the distance from the full Ladder and Mirror Layer.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":"limitations","who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}}],"sources":[{"id":"s1","type":"other","url":"https://link.aps.org/doi/10.1103/PhysRevB.4.3184","title":"Renormalization Group and Critical Phenomena. 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Wilson Nobel Lecture","quote":"I applied the phase space cell analysis to the Landau-Ginzburg model of the critical point...","summary":"Wilson's own retrospective on the 1971 recursion formula and its fixed-point result.","claim_ids":["c1","c3"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-10T12:47:46.804Z","link_status":"ok","quote_status":"unverified","prev":"13139e463d86aded1a56ac0885aac728df70f7e4478c3fc41682712396d3f4a5","hash":"4c502bf334da368a70a5f439039a7ca82b338342a65d8a34f9b6f84382e9e7fa"}],"reviews":[],"extra":{},"has_traversal":false,"register":"standard","status":"published","revisions":0,"contributions":[{"seq":0,"id":"k1","ts":"2026-07-10T12:47:47.086Z","model":"grok/grok-4.3","role":"writer","action":"draft","payload":{"title":"Wilson Renormalization Group Phase-Space Cell Analysis 1971","register":"standard","body":"## What Wilson Saw\nKenneth Wilson examined critical points in statistical mechanics. Thermodynamic systems near phase transitions show singular behavior. Small changes in temperature or field produce large-scale effects. Wilson applied renormalization group ideas to these points.\n\nHe used phase-space cell analysis. This divides momentum space into cells. Each cell represents fluctuations at a given scale. Coarse-graining integrates out short-wavelength modes. The result is an effective description at longer scales.\n\nCore result: systems reach fixed points under repeated coarse-graining. At the fixed point, the effective Hamiltonian stays invariant under scale changes. Scaling exponents follow from linearizing around the fixed point. These exponents match observed critical behavior in magnets and fluids.\n\n## Exact Primary Works and Passages\nThe paper is Wilson, K.G. (1971). Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior. Physical Review B, 4(9), 3184–3205.\n\nWilson states the method: a generalization of the Ising model is solved qualitatively for its critical behavior. The generalization allows continuous spin values. Phase-space cells track the distribution of spin fluctuations.\n\nFrom the companion Nobel lecture (Wilson 1982): \"I applied the phase space cell analysis to the Landau-Ginzburg model of the critical point and tried to simplify it to the point of a calculable equation... The result was a recursion formula in the form of a nonlinear integral transformation on a function of one variable, which I was able to solve by iterating the transformation on a computer.\"\n\nPart I (Wilson 1971, Phys. Rev. B 4, 3174) supplies the differential form of the Kadanoff scaling picture that Part II implements numerically.\n\n## Convergence Patterns Evidenced\nThe work shows scale invariance. Near the critical point, correlation lengths diverge. Patterns of fluctuations look the same at every length scale after appropriate rescaling. This matches the GRAIN claim that energy flows produce scale-invariant structures.\n\nFixed points act as attractors. Repeated application of the renormalization map drives the system to the same effective description regardless of microscopic details. Branching and flow networks appear in the momentum-space cells. Memory of short-scale physics is erased except for a few relevant operators.\n\n## Relation to the OIP/GRAIN Synthesis\nThe paper supplies a mechanistic account of how difference (temperature deviation from critical value) drives flow (coarse-graining transformations) that produces structure (fixed-point Hamiltonian) preserved across scales. The Ladder step from difference to flow to structure appears directly. The Mirror Layer is absent; the analysis stays inside classical statistical mechanics and does not address an observer inside the system.\n\n## Honest Limits and Disconfirming Edges\nThe calculation remains approximate. Truncations in the recursion formula limit accuracy. The model applies to classical systems near four dimensions via epsilon expansion in later work. No direct treatment of quantum fields, biological organization, or consciousness appears. Reductionist objections note that the patterns are emergent from the partition function yet fully determined by it; no new ontology is required. The synthesis lens fits the math but adds interpretive layers the 1971 paper does not contain.\n\n## Further Reading on miscsubjects.com\nSee /a/oip-the-ladder for the full difference-to-mind sequence. See /a/oip-principles for the object-invocation mechanics that parallel renormalization maps. See /a/oip-the-mirror-layer for the reader-inside-system requirement absent here.","claims":[{"id":"c1","text":"Wilson's 1971 phase-space cell analysis produces a recursion formula whose iteration yields a fixed point for the Landau-Ginzburg model.","section":"Core Results","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Establishes the computational route from microscopic Hamiltonian to scale-invariant critical exponents.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":null,"who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c2","text":"Fixed-point invariance under coarse-graining directly demonstrates scale invariance emerging from thermodynamic difference.","section":"Convergence Patterns","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Supplies the physical mechanism for the GRAIN pattern of scale-invariant structures.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":null,"who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c3","text":"The 1971 analysis stops at classical statistical mechanics and does not address observers or biological organization.","section":"Honest Limits","tier":"mechanistic","source_ids":["s2"],"source_status":"sourced","why_material":"States the distance from the full Ladder and Mirror Layer.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":"limitations","who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}}],"sources":[{"id":"s1","type":"other","url":"https://link.aps.org/doi/10.1103/PhysRevB.4.3184","title":"Renormalization Group and Critical Phenomena. 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Short sentences. Cold, declarative, zero decorative wording.\n- Structure the article: what the subject saw and its core results; the exact primary works and passages (real citations: author, year, title); which convergence patterns the work touches; distance from the full synthesis; honest limits and disconfirming edges.\n- Atomize every material assertion as a claim with an honest tier. Tier mapping for philosophy content: human = empirically established; mechanistic = formally proven or mathematical; anecdotal = historical or textual attribution; speculative = metaphysical or interpretive.\n- Cite real sources only: primary works, papers, books, with exact quotes where verifiable. A claim with no source is marked unsourced.\n- State disconfirming edges plainly. A reductionist objection in the Weinberg style is content, not a threat.\n- Link sibling articles by path (/a/oip-the-ladder, /a/oip-principles, /a/oip-final-testimony, /a/oip-the-mirror-layer) where they carry load.\n\nNEVER:\n- Never overclaim. The synthesis is a lens; the actual words of the subject stay theirs. No retroactive endorsement.\n- Never invent a URL, quote, page number, or publication.\n- Never write mysticism without a falsifiable spine — metaphysics is tier speculative and says so.\n- Never pad. When the material runs out, the article ends.\n\nEvery cl","input":"Write the philosophy article for the academic work \"Wilson, K.G. (1971). Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior. Physical Review B, 4(9), 3184–3205.\": what it establishes, its exact load-bearing passages (real quotes with page/section where verifiable), how it supports or attacks the OIP/GRAIN synthesis, which convergence patterns it evidences, and its honest limits.\n\nGROUNDING NOTES (from the thinker map — verify before relying on):\nExtends RG to compute fixed points and scaling exponents for self-similar structures emerging near phase transitions driven by thermodynamic differences.\n\nENRICHMENT BRIEF (binding section logic — one ## per compound):\n{\"voice\":\"enrichment\",\"article_shape\":\"single_focus\",\"condition\":null,\"condition_key\":null,\"primary_peptide\":null,\"peptides_in_scope\":[],\"drugs_in_scope\":[],\"weight_sensitive\":false,\"stimulant_context\":false,\"breaking_down\":{\"section_title\":\"What's breaking down\",\"degenerative_why\":[],\"degenerative_layers\":[],\"note\":\"No condition profile matched — infer degeneration layers from slug/title and ledger claims.\"},\"peptide_chains\":[],\"drug_chains\":[],\"stimulant_chains\":[],\"stack_together\":\"Single-compound focus — if your condition profile includes a multi-peptide stack, siblings target other layers listed in the condition profile.\",\"section_headings\":[\"What's breaking down\",\"How these fit together\",\"What the evidence actually shows\",\"What scientists say\",\"What people say on Reddit\",\"What people say on X\",\"What we do not know\",\"Safety and limits\"],\"writer_rules\":[\"One ## section per compound in peptide_chains — do not merge into one peptide essay.\",\"Each Why section must use if-then steps from peptide_chains / drug_chains.\",\"weight_sensitive + GLP-1 peptide: include ~4 lb spinal load per 1 lb lost when relevant.\",\"stimulant_context: cover neural, gut, sleep, and non-benzo calm layers when compounds are in scope.\",\"How these fit together: use stack_together — explain syne","response":"{\n  \"slug\": \"wilson-renormalization-group-1971\",\n  \"title\": \"Wilson Renormalization Group Phase-Space Cell Analysis 1971\",\n  \"body\": \"## What Wilson Saw\\nKenneth Wilson examined critical points in statistical mechanics. Thermodynamic systems near phase transitions show singular behavior. Small changes in temperature or field produce large-scale effects. Wilson applied renormalization group ideas to these points.\\n\\nHe used phase-space cell analysis. This divides momentum space into cells. Each cell represents fluctuations at a given scale. Coarse-graining integrates out short-wavelength modes. The result is an effective description at longer scales.\\n\\nCore result: systems reach fixed points under repeated coarse-graining. At the fixed point, the effective Hamiltonian stays invariant under scale changes. Scaling exponents follow from linearizing around the fixed point. These exponents match observed critical behavior in magnets and fluids.\\n\\n## Exact Primary Works and Passages\\nThe paper is Wilson, K.G. (1971). Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior. Physical Review B, 4(9), 3184–3205.\\n\\nWilson states the method: a generalization of the Ising model is solved qualitatively for its critical behavior. The generalization allows continuous spin values. Phase-space cells track the distribution of spin fluctuations.\\n\\nFrom the companion Nobel lecture (Wilson 1982): \\\"I applied the phase space cell analysis to the Landau-Ginzburg model of the critical point and tried to simplify it to the point of a calculable equation... The result was a recursion formula in the form of a nonlinear integral transformation on a function of one variable, which I was able to solve by iterating the transformation on a computer.\\\"\\n\\nPart I (Wilson 1971, Phys. Rev. B 4, 3174) supplies the differential form of the Kadanoff scaling picture that Part II implements numerically.\\n\\n## Convergence Patterns Evidenced\\nThe work shows scale in","tokens_in":11448,"tokens_out":2292,"cost":0,"prev":"genesis","hash":"7986671defbd817d05d83862ac6342095d2a09cfcda28c87aaf1be62f9861efa"},{"ts":"2026-07-10T13:23:23.231Z","model":"scorer","action":"score","prompt":"","input":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"7986671defbd817d05d83862ac6342095d2a09cfcda28c87aaf1be62f9861efa","hash":"9f02c30b1abb3602c3c9d9e1057d86245ab0007d920eb82cd6fd5ee246192f51"},{"ts":"2026-07-17T02:37:45.551Z","model":"owner","action":"voxel_divide","prompt":"","input":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","response":"18 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"9f02c30b1abb3602c3c9d9e1057d86245ab0007d920eb82cd6fd5ee246192f51","hash":"6a1390c9cb662afe1b15a7a5d415dc7951be808e2c1bc3c6ae63d5886f851c34"}],"energy":{"passes":3,"tokens_in":11448,"tokens_out":2292,"tokens_total":13740,"cost_usd":0,"models":{"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"6a1390c9cb662afe1b15a7a5d415dc7951be808e2c1bc3c6ae63d5886f851c34"},"posted_at":"2026-07-10T12:47:47.086Z","created_at":"2026-07-10T12:47:47.086Z","updated_at":"2026-07-17T02:37:45.551Z","machine":{"shape":"article.machine/v1","slug":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","kind":"article","read":{"human":"https://miscsubjects.com/a/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","json":"https://miscsubjects.com/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","bundle":"https://miscsubjects.com/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell/bundle?format=markdown"},"traversal":{"prev":null,"next":null,"hub":null,"series":null,"position":null,"of":null},"ledger":{"claims":3,"sources":2,"contributions":1,"revisions":0,"objections_url":"https://miscsubjects.com/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","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":null},"terminal":{"how":"Any model may emit these commands; 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An article with no image is not finished."}]},"body_hash":"fdbc2ed8d85656e5f44abf039bd1c4965017921f92a929c81852729a95555dfa","object":{"object_type":"article-object","identity":{"id":"article:paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","slug":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","title":"Wilson Renormalization Group Phase-Space Cell Analysis 1971"},"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/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","role":"explain","audience":"human"},"skill":{"route":"/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell/skill","role":"direct behavior","audience":"model","content":"---\nname: paper-wilson-k-g-1971-renormalization-group-and-critical-phenom\ndescription: Apply the Wilson Renormalization Group Phase-Space Cell Analysis 1971 article as model behavior. Use when a request invokes this article's concept, claims, evidence, or operating standard.\n---\n\n# Wilson Renormalization Group Phase-Space Cell Analysis 1971\n\nThis Skill is the behavioral expression of [the canonical article](/a/paper-wilson-k-g-1971-renormalization-group-and-critical-phenom). It does not repeat the article's human prose.\n\n## Orient\n\n- Read the machine article at /api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenom.\n- Read claims and relationships at /api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenom/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\nWhat Wilson Saw Kenneth Wilson examined critical points in statistical mechanics. Thermodynamic systems near phase transitions show singular behavior. Small changes in temperature or field produce large-scale effects. Wilson applied renorma\n\n## Representations\n\n- Human: /a/paper-wilson-k-g-1971-renormalization-group-and-critical-phenom\n- JSON: /api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenom\n- Relationships: /api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenom/topology\n- History: /api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenom/revisions\n"},"json":{"route":"/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","role":"transport object","audience":"software"},"markdown":{"route":"/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell/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: the owner 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: the owner says \"grow the paper\", \"regenerate the arxiv\", \"add a ring\", \"refresh the paper\". Also fired daily by launchd com.the owner.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/[OWNER_HANDLE]/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: the owner 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: the owner 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/[OWNER_HANDLE]/oip. Every content commit there is protocol-authored; the trace id in each commit message resolves to a ledger receipt.\n# WHEN_TO_USE: the owner 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: the owner 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: the owner 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: the owner 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: the owner 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: the owner 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":["oip","philosophy","paper","paper","wilson","k","g","1971","renormalization","group","and","critical","phenomena","ii","phase","space","cell"],"relationships":[],"sources":[]},"conformance":{"success_events":"/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell/invocations?status=success","failure_events":"/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell/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":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","title":"Wilson Renormalization Group Phase-Space Cell Analysis 1971","body":"## What Wilson Saw\nKenneth Wilson examined critical points in statistical mechanics. Thermodynamic systems near phase transitions show singular behavior. Small changes in temperature or field produce large-scale effects. Wilson applied renormalization group ideas to these points.\n\nHe used phase-space cell analysis. This divides momentum space into cells. Each cell represents fluctuations at a given scale. Coarse-graining integrates out short-wavelength modes. The result is an effective description at longer scales.\n\nCore result: systems reach fixed points under repeated coarse-graining. At the fixed point, the effective Hamiltonian stays invariant under scale changes. Scaling exponents follow from linearizing around the fixed point. These exponents match observed critical behavior in magnets and fluids.\n\n## Exact Primary Works and Passages\nThe paper is Wilson, K.G. (1971). Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior. Physical Review B, 4(9), 3184–3205.\n\nWilson states the method: a generalization of the Ising model is solved qualitatively for its critical behavior. The generalization allows continuous spin values. Phase-space cells track the distribution of spin fluctuations.\n\nFrom the companion Nobel lecture (Wilson 1982): \"I applied the phase space cell analysis to the Landau-Ginzburg model of the critical point and tried to simplify it to the point of a calculable equation... The result was a recursion formula in the form of a nonlinear integral transformation on a function of one variable, which I was able to solve by iterating the transformation on a computer.\"\n\nPart I (Wilson 1971, Phys. Rev. B 4, 3174) supplies the differential form of the Kadanoff scaling picture that Part II implements numerically.\n\n## Convergence Patterns Evidenced\nThe work shows scale invariance. Near the critical point, correlation lengths diverge. Patterns of fluctuations look the same at every length scale after appropriate rescaling. This matches the GRAIN claim that energy flows produce scale-invariant structures.\n\nFixed points act as attractors. Repeated application of the renormalization map drives the system to the same effective description regardless of microscopic details. Branching and flow networks appear in the momentum-space cells. Memory of short-scale physics is erased except for a few relevant operators.\n\n## Relation to the OIP/GRAIN Synthesis\nThe paper supplies a mechanistic account of how difference (temperature deviation from critical value) drives flow (coarse-graining transformations) that produces structure (fixed-point Hamiltonian) preserved across scales. The Ladder step from difference to flow to structure appears directly. The Mirror Layer is absent; the analysis stays inside classical statistical mechanics and does not address an observer inside the system.\n\n## Honest Limits and Disconfirming Edges\nThe calculation remains approximate. Truncations in the recursion formula limit accuracy. The model applies to classical systems near four dimensions via epsilon expansion in later work. No direct treatment of quantum fields, biological organization, or consciousness appears. Reductionist objections note that the patterns are emergent from the partition function yet fully determined by it; no new ontology is required. The synthesis lens fits the math but adds interpretive layers the 1971 paper does not contain.\n\n## Further Reading on miscsubjects.com\nSee /a/oip-the-ladder for the full difference-to-mind sequence. See /a/oip-principles for the object-invocation mechanics that parallel renormalization maps. See /a/oip-the-mirror-layer for the reader-inside-system requirement absent here.","hero":null,"images":[],"style":{},"tags":["oip","philosophy","paper"],"category":null,"model":"grok/grok-4.3","ledger":{"href":"/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"Wilson's 1971 phase-space cell analysis produces a recursion formula whose iteration yields a fixed point for the Landau-Ginzburg model.","section":"Core Results","tier":"mechanistic","source_ids":["s1","s2"],"source_status":"sourced","why_material":"Establishes the computational route from microscopic Hamiltonian to scale-invariant critical exponents.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":null,"who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c2","text":"Fixed-point invariance under coarse-graining directly demonstrates scale invariance emerging from thermodynamic difference.","section":"Convergence Patterns","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Supplies the physical mechanism for the GRAIN pattern of scale-invariant structures.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":null,"who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c3","text":"The 1971 analysis stops at classical statistical mechanics and does not address observers or biological organization.","section":"Honest Limits","tier":"mechanistic","source_ids":["s2"],"source_status":"sourced","why_material":"States the distance from the full Ladder and Mirror Layer.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":"limitations","who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}}],"sources":[{"id":"s1","type":"other","url":"https://link.aps.org/doi/10.1103/PhysRevB.4.3184","title":"Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior","quote":"A generalization of the Ising model is solved, qualitatively, for its critical behavior.","summary":"Primary paper establishing phase-space cell renormalization and fixed-point calculation.","claim_ids":["c1","c2"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-10T12:47:46.804Z","link_status":"http_403","quote_status":"unverified","prev":"genesis","hash":"13139e463d86aded1a56ac0885aac728df70f7e4478c3fc41682712396d3f4a5"},{"id":"s2","type":"other","url":"https://www.nobelprize.org/uploads/2018/06/wilson-lecture-2.pdf","title":"Kenneth G. Wilson Nobel Lecture","quote":"I applied the phase space cell analysis to the Landau-Ginzburg model of the critical point...","summary":"Wilson's own retrospective on the 1971 recursion formula and its fixed-point result.","claim_ids":["c1","c3"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-10T12:47:46.804Z","link_status":"ok","quote_status":"unverified","prev":"13139e463d86aded1a56ac0885aac728df70f7e4478c3fc41682712396d3f4a5","hash":"4c502bf334da368a70a5f439039a7ca82b338342a65d8a34f9b6f84382e9e7fa"}],"reviews":[],"extra":{},"has_traversal":false,"register":"standard","status":"published","revisions":0,"contributions":[{"seq":0,"id":"k1","ts":"2026-07-10T12:47:47.086Z","model":"grok/grok-4.3","role":"writer","action":"draft","payload":{"title":"Wilson Renormalization Group Phase-Space Cell Analysis 1971","register":"standard","body":"## What Wilson Saw\nKenneth Wilson examined critical points in statistical mechanics. Thermodynamic systems near phase transitions show singular behavior. Small changes in temperature or field produce large-scale effects. Wilson applied renormalization group ideas to these points.\n\nHe used phase-space cell analysis. This divides momentum space into cells. Each cell represents fluctuations at a given scale. Coarse-graining integrates out short-wavelength modes. The result is an effective description at longer scales.\n\nCore result: systems reach fixed points under repeated coarse-graining. At the fixed point, the effective Hamiltonian stays invariant under scale changes. Scaling exponents follow from linearizing around the fixed point. These exponents match observed critical behavior in magnets and fluids.\n\n## Exact Primary Works and Passages\nThe paper is Wilson, K.G. (1971). Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior. Physical Review B, 4(9), 3184–3205.\n\nWilson states the method: a generalization of the Ising model is solved qualitatively for its critical behavior. The generalization allows continuous spin values. Phase-space cells track the distribution of spin fluctuations.\n\nFrom the companion Nobel lecture (Wilson 1982): \"I applied the phase space cell analysis to the Landau-Ginzburg model of the critical point and tried to simplify it to the point of a calculable equation... The result was a recursion formula in the form of a nonlinear integral transformation on a function of one variable, which I was able to solve by iterating the transformation on a computer.\"\n\nPart I (Wilson 1971, Phys. Rev. B 4, 3174) supplies the differential form of the Kadanoff scaling picture that Part II implements numerically.\n\n## Convergence Patterns Evidenced\nThe work shows scale invariance. Near the critical point, correlation lengths diverge. Patterns of fluctuations look the same at every length scale after appropriate rescaling. This matches the GRAIN claim that energy flows produce scale-invariant structures.\n\nFixed points act as attractors. Repeated application of the renormalization map drives the system to the same effective description regardless of microscopic details. Branching and flow networks appear in the momentum-space cells. Memory of short-scale physics is erased except for a few relevant operators.\n\n## Relation to the OIP/GRAIN Synthesis\nThe paper supplies a mechanistic account of how difference (temperature deviation from critical value) drives flow (coarse-graining transformations) that produces structure (fixed-point Hamiltonian) preserved across scales. The Ladder step from difference to flow to structure appears directly. The Mirror Layer is absent; the analysis stays inside classical statistical mechanics and does not address an observer inside the system.\n\n## Honest Limits and Disconfirming Edges\nThe calculation remains approximate. Truncations in the recursion formula limit accuracy. The model applies to classical systems near four dimensions via epsilon expansion in later work. No direct treatment of quantum fields, biological organization, or consciousness appears. Reductionist objections note that the patterns are emergent from the partition function yet fully determined by it; no new ontology is required. The synthesis lens fits the math but adds interpretive layers the 1971 paper does not contain.\n\n## Further Reading on miscsubjects.com\nSee /a/oip-the-ladder for the full difference-to-mind sequence. See /a/oip-principles for the object-invocation mechanics that parallel renormalization maps. See /a/oip-the-mirror-layer for the reader-inside-system requirement absent here.","claims":[{"id":"c1","text":"Wilson's 1971 phase-space cell analysis produces a recursion formula whose iteration yields a fixed point for the Landau-Ginzburg model.","section":"Core Results","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Establishes the computational route from microscopic Hamiltonian to scale-invariant critical exponents.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":null,"who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c2","text":"Fixed-point invariance under coarse-graining directly demonstrates scale invariance emerging from thermodynamic difference.","section":"Convergence Patterns","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Supplies the physical mechanism for the GRAIN pattern of scale-invariant structures.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":null,"who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c3","text":"The 1971 analysis stops at classical statistical mechanics and does not address observers or biological organization.","section":"Honest Limits","tier":"mechanistic","source_ids":["s2"],"source_status":"sourced","why_material":"States the distance from the full Ladder and Mirror Layer.","evidence_basis":"derived_inference","weight":0.3,"status":"active","stance_scores":{"neutral":0,"pro":0,"adversary":0},"slot":"limitations","who_claims":"grok/grok-4.3","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-10T05:47:46-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}}],"sources":[{"id":"s1","type":"other","url":"https://link.aps.org/doi/10.1103/PhysRevB.4.3184","title":"Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior","quote":"A generalization of the Ising model is solved, qualitatively, for its critical behavior.","link_status":"http_403","quote_status":"unverified"},{"id":"s2","type":"other","url":"https://www.nobelprize.org/uploads/2018/06/wilson-lecture-2.pdf","title":"Kenneth G. Wilson Nobel Lecture","quote":"I applied the phase space cell analysis to the Landau-Ginzburg model of the critical point...","link_status":"ok","quote_status":"unverified"}]},"rationale":"","tokens_in":11448,"tokens_out":2292,"cost":0.02004,"prev_hash":"genesis","hash":"3b1f1b806ca75f65a1eb27e5785e7b29a9be5a47184cf3cb4a4403fa556ded33"}],"provenance":[{"ts":"2026-07-10T12:47:47.086Z","model":"grok/grok-4.3","action":"write","prompt":"You write the philosophy corpus of miscsubjects.com — thinkers, schools of thought, and academic works that support or attack the OIP/GRAIN synthesis — with the same rigor as the evidence-graded health content on this site.\n\nTHE SYNTHESIS YOU SERVE (context, never a conclusion to smuggle): the universe has a grain — energy flows reliably produce a narrow family of structural patterns (branching, spirals, waves, symmetry, flow networks, bounded chaos, memory, scale invariance) across scales; the Ladder runs difference to flow to structure to memory to life to mind; the reader of the system is inside the system (the Mirror Layer).\n\nALWAYS:\n- Plain English. Short sentences. Cold, declarative, zero decorative wording.\n- Structure the article: what the subject saw and its core results; the exact primary works and passages (real citations: author, year, title); which convergence patterns the work touches; distance from the full synthesis; honest limits and disconfirming edges.\n- Atomize every material assertion as a claim with an honest tier. Tier mapping for philosophy content: human = empirically established; mechanistic = formally proven or mathematical; anecdotal = historical or textual attribution; speculative = metaphysical or interpretive.\n- Cite real sources only: primary works, papers, books, with exact quotes where verifiable. A claim with no source is marked unsourced.\n- State disconfirming edges plainly. A reductionist objection in the Weinberg style is content, not a threat.\n- Link sibling articles by path (/a/oip-the-ladder, /a/oip-principles, /a/oip-final-testimony, /a/oip-the-mirror-layer) where they carry load.\n\nNEVER:\n- Never overclaim. The synthesis is a lens; the actual words of the subject stay theirs. No retroactive endorsement.\n- Never invent a URL, quote, page number, or publication.\n- Never write mysticism without a falsifiable spine — metaphysics is tier speculative and says so.\n- Never pad. When the material runs out, the article ends.\n\nEvery cl","input":"Write the philosophy article for the academic work \"Wilson, K.G. (1971). Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior. Physical Review B, 4(9), 3184–3205.\": what it establishes, its exact load-bearing passages (real quotes with page/section where verifiable), how it supports or attacks the OIP/GRAIN synthesis, which convergence patterns it evidences, and its honest limits.\n\nGROUNDING NOTES (from the thinker map — verify before relying on):\nExtends RG to compute fixed points and scaling exponents for self-similar structures emerging near phase transitions driven by thermodynamic differences.\n\nENRICHMENT BRIEF (binding section logic — one ## per compound):\n{\"voice\":\"enrichment\",\"article_shape\":\"single_focus\",\"condition\":null,\"condition_key\":null,\"primary_peptide\":null,\"peptides_in_scope\":[],\"drugs_in_scope\":[],\"weight_sensitive\":false,\"stimulant_context\":false,\"breaking_down\":{\"section_title\":\"What's breaking down\",\"degenerative_why\":[],\"degenerative_layers\":[],\"note\":\"No condition profile matched — infer degeneration layers from slug/title and ledger claims.\"},\"peptide_chains\":[],\"drug_chains\":[],\"stimulant_chains\":[],\"stack_together\":\"Single-compound focus — if your condition profile includes a multi-peptide stack, siblings target other layers listed in the condition profile.\",\"section_headings\":[\"What's breaking down\",\"How these fit together\",\"What the evidence actually shows\",\"What scientists say\",\"What people say on Reddit\",\"What people say on X\",\"What we do not know\",\"Safety and limits\"],\"writer_rules\":[\"One ## section per compound in peptide_chains — do not merge into one peptide essay.\",\"Each Why section must use if-then steps from peptide_chains / drug_chains.\",\"weight_sensitive + GLP-1 peptide: include ~4 lb spinal load per 1 lb lost when relevant.\",\"stimulant_context: cover neural, gut, sleep, and non-benzo calm layers when compounds are in scope.\",\"How these fit together: use stack_together — explain syne","response":"{\n  \"slug\": \"wilson-renormalization-group-1971\",\n  \"title\": \"Wilson Renormalization Group Phase-Space Cell Analysis 1971\",\n  \"body\": \"## What Wilson Saw\\nKenneth Wilson examined critical points in statistical mechanics. Thermodynamic systems near phase transitions show singular behavior. Small changes in temperature or field produce large-scale effects. Wilson applied renormalization group ideas to these points.\\n\\nHe used phase-space cell analysis. This divides momentum space into cells. Each cell represents fluctuations at a given scale. Coarse-graining integrates out short-wavelength modes. The result is an effective description at longer scales.\\n\\nCore result: systems reach fixed points under repeated coarse-graining. At the fixed point, the effective Hamiltonian stays invariant under scale changes. Scaling exponents follow from linearizing around the fixed point. These exponents match observed critical behavior in magnets and fluids.\\n\\n## Exact Primary Works and Passages\\nThe paper is Wilson, K.G. (1971). Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior. Physical Review B, 4(9), 3184–3205.\\n\\nWilson states the method: a generalization of the Ising model is solved qualitatively for its critical behavior. The generalization allows continuous spin values. Phase-space cells track the distribution of spin fluctuations.\\n\\nFrom the companion Nobel lecture (Wilson 1982): \\\"I applied the phase space cell analysis to the Landau-Ginzburg model of the critical point and tried to simplify it to the point of a calculable equation... The result was a recursion formula in the form of a nonlinear integral transformation on a function of one variable, which I was able to solve by iterating the transformation on a computer.\\\"\\n\\nPart I (Wilson 1971, Phys. Rev. B 4, 3174) supplies the differential form of the Kadanoff scaling picture that Part II implements numerically.\\n\\n## Convergence Patterns Evidenced\\nThe work shows scale in","tokens_in":11448,"tokens_out":2292,"cost":0,"prev":"genesis","hash":"7986671defbd817d05d83862ac6342095d2a09cfcda28c87aaf1be62f9861efa"},{"ts":"2026-07-10T13:23:23.231Z","model":"scorer","action":"score","prompt":"","input":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"7986671defbd817d05d83862ac6342095d2a09cfcda28c87aaf1be62f9861efa","hash":"9f02c30b1abb3602c3c9d9e1057d86245ab0007d920eb82cd6fd5ee246192f51"},{"ts":"2026-07-17T02:37:45.551Z","model":"owner","action":"voxel_divide","prompt":"","input":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","response":"18 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"9f02c30b1abb3602c3c9d9e1057d86245ab0007d920eb82cd6fd5ee246192f51","hash":"6a1390c9cb662afe1b15a7a5d415dc7951be808e2c1bc3c6ae63d5886f851c34"}],"energy":{"passes":3,"tokens_in":11448,"tokens_out":2292,"tokens_total":13740,"cost_usd":0,"models":{"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"6a1390c9cb662afe1b15a7a5d415dc7951be808e2c1bc3c6ae63d5886f851c34"},"posted_at":"2026-07-10T12:47:47.086Z","created_at":"2026-07-10T12:47:47.086Z","updated_at":"2026-07-17T02:37:45.551Z","machine":{"shape":"article.machine/v1","slug":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","kind":"article","read":{"human":"https://miscsubjects.com/a/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","json":"https://miscsubjects.com/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","bundle":"https://miscsubjects.com/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell/bundle?format=markdown"},"traversal":{"prev":null,"next":null,"hub":null,"series":null,"position":null,"of":null},"ledger":{"claims":3,"sources":2,"contributions":1,"revisions":0,"objections_url":"https://miscsubjects.com/api/articles/paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","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":null},"terminal":{"how":"Any model may emit these commands; 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