{"slug":"paper-poincar-h-1890-sur-le-probl-me-des-trois-corps-et-les-quations-de-la-dynamique-a","verification":{"valid":true,"entries":2,"head":"e9f718823aa5535d7b1b3d824d5b2f00b74447c59f8c0606125a4560660007a4"},"energy":{"passes":2,"tokens_in":13798,"tokens_out":2621,"tokens_total":16419,"cost_usd":0,"models":{"grok/grok-4.3":1,"scorer":1},"head":"e9f718823aa5535d7b1b3d824d5b2f00b74447c59f8c0606125a4560660007a4"},"provenance":[{"ts":"2026-07-09T02:13:11.388Z","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 \"Poincaré, H. (1890). Sur le problème des trois corps et les équations de la dynamique. Acta Mathematica, 13, 1-270.\": 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 source establishing sensitive dependence on initial conditions and bounded chaos in nonlinear dynamical systems, foundational for pattern emergence like spirals and flow networks.\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 synergy, ","response":"{\"slug\":\"poincare-1890-three-body-problem\",\"title\":\"Poincaré 1890: Three-Body Problem and Bounded Chaos\",\"body\":\"## What the work establishes\\nHenri Poincaré submitted his memoir to the 1889 King Oscar II prize competition. The revised version appeared in Acta Mathematica volume 13 in 1890. The paper examines the motion of three bodies under Newtonian gravity. It shows that no general analytic integral exists beyond the known energy and momentum integrals. It also demonstrates that certain orbits exhibit sensitive dependence on initial conditions. Small changes in starting positions or velocities produce trajectories that diverge exponentially over time while remaining bounded.\\n\\nThe memoir introduces qualitative methods. Poincaré studies periodic solutions and their stability. He identifies homoclinic orbits where a trajectory returns arbitrarily close to a saddle point after looping away. These tangles generate complex behavior that cannot be captured by convergent series expansions of the classical type.\\n\\n## Exact primary work and verifiable passages\\nThe primary source is Poincaré, H. (1890). Sur le problème des trois corps et les équations de la dynamique. Acta Mathematica, 13, 1-270. No page-specific verbatim excerpts from the original French text appear in publicly indexed secondary sources with verifiable pagination. Secondary accounts confirm the core claims: non-existence of additional analytic integrals and the presence of homoclinic tangles. June Barrow-Green's monograph provides the most detailed historical reconstruction.\\n\\nA later popular formulation of sensitive dependence appears in Poincaré's Science and Hypothesis (1902), not in the 1890 memoir itself. That formulation states: \\\"If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we co","tokens_in":13798,"tokens_out":2621,"cost":0,"prev":"genesis","hash":"33912ae56c2492cc6dd236e7687650d3b1715b6f4d91894d629751967c17da77"},{"ts":"2026-07-09T02:26:34.560Z","model":"scorer","action":"score","prompt":"","input":"paper-poincar-h-1890-sur-le-probl-me-des-trois-corps-et-les-quations-de-la-dynamique-a","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"33912ae56c2492cc6dd236e7687650d3b1715b6f4d91894d629751967c17da77","hash":"e9f718823aa5535d7b1b3d824d5b2f00b74447c59f8c0606125a4560660007a4"}]}