{"slug":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-ii-phase-space-cell","verification":{"valid":true,"entries":2,"head":"9f02c30b1abb3602c3c9d9e1057d86245ab0007d920eb82cd6fd5ee246192f51"},"energy":{"passes":2,"tokens_in":11448,"tokens_out":2292,"tokens_total":13740,"cost_usd":0,"models":{"grok/grok-4.3":1,"scorer":1},"head":"9f02c30b1abb3602c3c9d9e1057d86245ab0007d920eb82cd6fd5ee246192f51"},"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"}]}