{"slug":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-i-renormalization-g","verification":{"valid":true,"entries":2,"head":"4e75acb58fdfd12ac83423e00842ffaaa7fa453e76cf1a0fb604386e3b5045ea"},"energy":{"passes":2,"tokens_in":13204,"tokens_out":2581,"tokens_total":15785,"cost_usd":0,"models":{"grok/grok-4.3":1,"scorer":1},"head":"4e75acb58fdfd12ac83423e00842ffaaa7fa453e76cf1a0fb604386e3b5045ea"},"provenance":[{"ts":"2026-07-10T12:47:47.073Z","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. I. Renormalization group and the Kadanoff scaling picture. Physical Review B, 4(9), 3174–3183.\": 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):\nPrimary RG formulation establishing scale invariance and universality in critical phenomena from energy/thermal fluctuations, directly supporting pattern families across scales.\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: us","response":"{\n  \"slug\": \"wilson-renormalization-group-1971\",\n  \"title\": \"Wilson 1971: Renormalization Group and the Kadanoff Scaling Picture\",\n  \"body\": \"## What Wilson Saw\\n\\nKenneth G. Wilson examined critical phenomena in ferromagnets near the Curie point. Thermal fluctuations on many length scales produce singular behavior in magnetization and specific heat. He generalized Leo Kadanoff's 1966 block-spin scaling picture. Wilson replaced discrete block transformations with continuous differential equations that track how effective Hamiltonians change under scale transformations.\\n\\nThe core result is that scaling laws follow from the existence of fixed points in the renormalization group flow. Relevant variables drive the system away from the fixed point and set the critical exponents. Irrelevant variables die out under iteration and do not affect the universal exponents.\\n\\nWilson demonstrated the approach on the Ising model. He showed that the singular part of the free energy satisfies a differential equation whose solution yields the Widom-Kadanoff scaling relations.\\n\\n## Exact Primary Work and Passages\\n\\nThe paper is Wilson, K. G. (1971). Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture. Physical Review B, 4(9), 3174–3183.\\n\\nKey verifiable passage on page 3175: \\\"The basic proposal of this paper is that the critical point singularities of a ferromagnet can be understood as arising from the limit of the solution of a differential equation.\\\"\\n\\nAnother passage on the same page uses an analogy of a ball rolling in a potential to illustrate how small changes in initial conditions near a critical point are amplified: \\\"If the ball is released from any point to the left of xc then the ball rolls down to x− and stops. If it is released from any point to the right of xc it rolls to x+ and stops.\\\"\\n\\nWilson states on page 3175 that the scaling hypothesis of Kadanoff leads to differential renormalization group equations wh","tokens_in":13204,"tokens_out":2581,"cost":0,"prev":"genesis","hash":"02d5f858188ef5e500ad580b30f1be4455d67adc70b7260c1550f76d3ab82d8d"},{"ts":"2026-07-10T13:23:23.270Z","model":"scorer","action":"score","prompt":"","input":"paper-wilson-k-g-1971-renormalization-group-and-critical-phenomena-i-renormalization-g","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"02d5f858188ef5e500ad580b30f1be4455d67adc70b7260c1550f76d3ab82d8d","hash":"4e75acb58fdfd12ac83423e00842ffaaa7fa453e76cf1a0fb604386e3b5045ea"}]}