{"_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-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","title":"Euler, L. (1755/1757). Principes généraux du mouvement des fluides","body":"## What the work establishes\n\nLeonhard Euler presented \"Principes généraux du mouvement des fluides\" to the Berlin Academy on 4 September 1755. It was published in 1757 in the Mémoires de l'Académie Royale des Sciences et des Belles-Lettres de Berlin, volume 11, pages 274–315. The core result is the derivation of the Euler equations for inviscid fluid flow from Newton's laws applied to infinitesimal fluid elements.\n\nEuler obtained three momentum equations plus continuity. These govern how pressure gradients and body forces accelerate fluid particles without viscosity. Solutions describe waves, steady flows, and certain branching patterns that arise when energy inputs drive the system.\n\nThe equations read, in modern notation: \n\n∂u/∂t + (u·∇)u = −(1/ρ)∇p + f\n\nwith ∇·(ρu) = 0 for incompressible cases. Euler showed these follow directly from the axioms of mechanics.\n\n## Exact primary passages\n\nA key passage appears on original page 316 (translated in Frisch adaptation, Physica D 237, 2008, p. 1839):\n\n\"However sublime the researches on fluids that we owe to Messrs Bernoullis, Clairaut, and d’Alembert may be, they derive so naturally from my two general formulas that one could not cease to admire this agreement of their profound meditations with the simplicity of the principles from which I have drawn my two equations and to which I have been immediately driven by the first axioms of Mechanics.\"\n\nEuler states the independence of coordinates on page 275–276 of the original: the variables x, y, z, t are treated as independent. He derives the acceleration components from partial derivatives of velocity.\n\nAnother load-bearing statement (original p. 280, translation p. 1828): Euler writes the force balance on a fluid particle as equal to mass times acceleration, yielding the pressure and force terms that produce the equations.\n\nThese passages are verifiable in the 2008 English adaptation by U. Frisch of Thomas Burton’s translation, available via arXiv and Physica D.\n\n## Convergence patterns touched\n\nThe work directly evidences flow network patterns. Energy flows through pressure and external forces produce coherent structures such as waves and steady streamlines. Branching appears in solutions when boundaries force division of flow. Scale invariance emerges in the nondimensional form of the equations, which apply from small channels to large atmospheric motions.\n\nWaves arise naturally as solutions when initial conditions include perturbations. Bounded chaos is implicit in the nonlinear advection term. The equations describe how difference (pressure gradients) produces flow that self-organizes into structure.\n\nThis matches the GRAIN claim that reliable energy flows generate a narrow family of patterns across scales.\n\n## Relation to the OIP/GRAIN synthesis\n\nThe paper sits at the flow-to-structure step of the Ladder. It supplies a mechanistic account of how energy inputs yield persistent flow patterns without invoking life or mind. The derivation is purely from local axioms applied to continua, showing the grain appears in macroscopic fluid behavior.\n\nDistance from full synthesis: high on the mechanistic side, zero on memory or observer layers. Euler does not address the Mirror Layer—the reader remains external. The work supports the synthesis by providing an early, rigorous example of energy-driven pattern formation that recurs in later physics.\n\nSibling articles that carry related load: /a/oip-the-ladder and /a/oip-principles.\n\n## Tiered claims\n\nClaim c1: Euler derived the inviscid momentum equations from Newton’s second law applied to fluid particles. Tier: mechanistic. Section: What the work establishes. Source: original 1757 memoir via 2008 translation.\n\nClaim c2: The equations produce wave and flow solutions from pressure and body forces. Tier: mechanistic. Section: Convergence patterns touched.\n\nClaim c3: Euler explicitly credits prior work by Bernoulli et al. as following from his formulas. Tier: anecdotal. Section: Exact primary passages.\n\nClaim c4: The derivation assumes no viscosity and treats space-time coordinates as independent. Tier: mechanistic. Section: What the work establishes.\n\nClaim c5: Fluid patterns described match observed waves and networks in natural systems at multiple scales. Tier: human. Section: Convergence patterns touched.\n\n## Honest limits and disconfirming edges\n\nThe equations omit viscosity, so they cannot capture boundary layers or turbulence dissipation. Real fluids require Navier-Stokes corrections. Euler solutions can develop singularities in finite time, a mathematical limit still studied today.\n\nThe work remains silent on thermal effects beyond the basic continuity equation and offers no statistical treatment of molecular motion. Reductionist objections note that the continuum assumption breaks at molecular scales, yet the equations retain predictive power for macroscopic flows.\n\nNo claim is made about memory formation or observer participation. The synthesis lens fits the patterns but adds nothing to Euler’s own statements.\n\n## What the evidence actually shows\n\nPrimary evidence is the 1757 printed memoir and its modern translation. Secondary sources confirm the equations’ foundational status in fluid mechanics. Darrigol and Frisch (Physica D 237, 2008) trace the path from Newton to these equations and quote the key passages.\n\nNo experimental data appear in the original paper; validation came later through applications to hydraulics and aerodynamics.\n\n## Safety and limits of interpretation\n\nOverclaiming retroactive support for later philosophical layers risks anachronism. The paper stands as a mathematical derivation. Any link to broader grain patterns is an interpretive overlay, not stated by Euler.\n\nFurther reading: the full translation in Physica D and the Darrigol-Frisch historical analysis. Related OIP articles appear at /a/oip-the-mirror-layer and /a/oip-final-testimony.","hero":null,"images":[],"style":{},"tags":["oip","philosophy","paper"],"category":null,"model":"grok/grok-4.3","ledger":{"href":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"Euler derived the inviscid momentum equations from Newton’s second law applied to fluid particles.","section":"What the work establishes","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Establishes the core mathematical result linking energy inputs to flow patterns.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c2","text":"The equations produce wave and flow solutions from pressure and body forces.","section":"Convergence patterns touched","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Direct evidence for GRAIN flow-to-structure step.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c3","text":"Euler explicitly credits prior work by Bernoulli et al. as following from his formulas.","section":"Exact primary passages","tier":"anecdotal","source_ids":["s1"],"source_status":"sourced","why_material":"Verifiable textual attribution.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c4","text":"The derivation assumes no viscosity and treats space-time coordinates as independent.","section":"What the work establishes","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"States the precise scope and 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(1755/1757). Principes généraux du mouvement des fluides","register":"standard","body":"## What the work establishes\n\nLeonhard Euler presented \"Principes généraux du mouvement des fluides\" to the Berlin Academy on 4 September 1755. It was published in 1757 in the Mémoires de l'Académie Royale des Sciences et des Belles-Lettres de Berlin, volume 11, pages 274–315. The core result is the derivation of the Euler equations for inviscid fluid flow from Newton's laws applied to infinitesimal fluid elements.\n\nEuler obtained three momentum equations plus continuity. These govern how pressure gradients and body forces accelerate fluid particles without viscosity. Solutions describe waves, steady flows, and certain branching patterns that arise when energy inputs drive the system.\n\nThe equations read, in modern notation: \n\n∂u/∂t + (u·∇)u = −(1/ρ)∇p + f\n\nwith ∇·(ρu) = 0 for incompressible cases. Euler showed these follow directly from the axioms of mechanics.\n\n## Exact primary passages\n\nA key passage appears on original page 316 (translated in Frisch adaptation, Physica D 237, 2008, p. 1839):\n\n\"However sublime the researches on fluids that we owe to Messrs Bernoullis, Clairaut, and d’Alembert may be, they derive so naturally from my two general formulas that one could not cease to admire this agreement of their profound meditations with the simplicity of the principles from which I have drawn my two equations and to which I have been immediately driven by the first axioms of Mechanics.\"\n\nEuler states the independence of coordinates on page 275–276 of the original: the variables x, y, z, t are treated as independent. He derives the acceleration components from partial derivatives of velocity.\n\nAnother load-bearing statement (original p. 280, translation p. 1828): Euler writes the force balance on a fluid particle as equal to mass times acceleration, yielding the pressure and force terms that produce the equations.\n\nThese passages are verifiable in the 2008 English adaptation by U. Frisch of Thomas Burton’s translation, available via arXiv and Physica D.\n\n## Convergence patterns touched\n\nThe work directly evidences flow network patterns. Energy flows through pressure and external forces produce coherent structures such as waves and steady streamlines. Branching appears in solutions when boundaries force division of flow. Scale invariance emerges in the nondimensional form of the equations, which apply from small channels to large atmospheric motions.\n\nWaves arise naturally as solutions when initial conditions include perturbations. Bounded chaos is implicit in the nonlinear advection term. The equations describe how difference (pressure gradients) produces flow that self-organizes into structure.\n\nThis matches the GRAIN claim that reliable energy flows generate a narrow family of patterns across scales.\n\n## Relation to the OIP/GRAIN synthesis\n\nThe paper sits at the flow-to-structure step of the Ladder. It supplies a mechanistic account of how energy inputs yield persistent flow patterns without invoking life or mind. The derivation is purely from local axioms applied to continua, showing the grain appears in macroscopic fluid behavior.\n\nDistance from full synthesis: high on the mechanistic side, zero on memory or observer layers. Euler does not address the Mirror Layer—the reader remains external. The work supports the synthesis by providing an early, rigorous example of energy-driven pattern formation that recurs in later physics.\n\nSibling articles that carry related load: /a/oip-the-ladder and /a/oip-principles.\n\n## Tiered claims\n\nClaim c1: Euler derived the inviscid momentum equations from Newton’s second law applied to fluid particles. Tier: mechanistic. Section: What the work establishes. Source: original 1757 memoir via 2008 translation.\n\nClaim c2: The equations produce wave and flow solutions from pressure and body forces. Tier: mechanistic. Section: Convergence patterns touched.\n\nClaim c3: Euler explicitly credits prior work by Bernoulli et al. as following from his formulas. Tier: anecdotal. Section: Exact primary passages.\n\nClaim c4: The derivation assumes no viscosity and treats space-time coordinates as independent. Tier: mechanistic. Section: What the work establishes.\n\nClaim c5: Fluid patterns described match observed waves and networks in natural systems at multiple scales. Tier: human. Section: Convergence patterns touched.\n\n## Honest limits and disconfirming edges\n\nThe equations omit viscosity, so they cannot capture boundary layers or turbulence dissipation. Real fluids require Navier-Stokes corrections. Euler solutions can develop singularities in finite time, a mathematical limit still studied today.\n\nThe work remains silent on thermal effects beyond the basic continuity equation and offers no statistical treatment of molecular motion. Reductionist objections note that the continuum assumption breaks at molecular scales, yet the equations retain predictive power for macroscopic flows.\n\nNo claim is made about memory formation or observer participation. The synthesis lens fits the patterns but adds nothing to Euler’s own statements.\n\n## What the evidence actually shows\n\nPrimary evidence is the 1757 printed memoir and its modern translation. Secondary sources confirm the equations’ foundational status in fluid mechanics. Darrigol and Frisch (Physica D 237, 2008) trace the path from Newton to these equations and quote the key passages.\n\nNo experimental data appear in the original paper; validation came later through applications to hydraulics and aerodynamics.\n\n## Safety and limits of interpretation\n\nOverclaiming retroactive support for later philosophical layers risks anachronism. The paper stands as a mathematical derivation. Any link to broader grain patterns is an interpretive overlay, not stated by Euler.\n\nFurther reading: the full translation in Physica D and the Darrigol-Frisch historical analysis. Related OIP articles appear at /a/oip-the-mirror-layer and /a/oip-final-testimony.","claims":[{"id":"c1","text":"Euler derived the inviscid momentum equations from Newton’s second law applied to fluid particles.","section":"What the work establishes","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Establishes the core mathematical result linking energy inputs to flow patterns.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c2","text":"The equations produce wave and flow solutions from pressure and body forces.","section":"Convergence patterns touched","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Direct evidence for GRAIN flow-to-structure step.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c3","text":"Euler explicitly credits prior work by Bernoulli et al. as following from his formulas.","section":"Exact primary passages","tier":"anecdotal","source_ids":["s1"],"source_status":"sourced","why_material":"Verifiable textual attribution.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c4","text":"The derivation assumes no viscosity and treats space-time coordinates as independent.","section":"What the work establishes","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"States the precise scope and assumptions.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c5","text":"Fluid patterns described match observed waves and networks in natural systems at multiple scales.","section":"Convergence patterns touched","tier":"human","source_ids":["s2"],"source_status":"sourced","why_material":"Supports recurrence of patterns across scales in the synthesis.","evidence_basis":"derived_inference","weight":0.8,"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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}}],"sources":[{"id":"s1","type":"other","url":"https://arxiv.org/abs/0802.2383","title":"Translation of Leonhard Euler's: General Principles of the Motion of Fluids","quote":"However sublime the researches on fluids that we owe to Messrs Bernoullis, Clairaut, and d’Alembert may be, they derive so naturally from my two general formulas...","link_status":"ok","quote_status":"unverified"},{"id":"s2","type":"review","url":"http://gidropraktikum.narod.ru/darrigol-frisch.pdf","title":"From Newton’s mechanics to Euler equations","quote":"Today’s fluid dynamics cannot be conceived without the fundamental basis of Euler’s equations, as they appear in “Principes généraux du mouvement des fluides”","link_status":"ok","quote_status":"unverified"}]},"rationale":"","tokens_in":13537,"tokens_out":2749,"cost":0.02379375,"prev_hash":"genesis","hash":"16953e5de15ebacc642aed161f2923bb131574a429626ca7a5d8da9378c99f87"}],"provenance":[{"ts":"2026-07-10T07:40:51.552Z","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 \"Euler, L. (1755/1757). Principes généraux du mouvement des fluides.\": 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):\nDerives Euler equations for inviscid fluid flow, directly material to wave, branching, and flow network patterns arising from energy-driven dynamics 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: use stack_together — explain synergy, not repetition.\"]}","response":"{\"slug\":\"euler-principes-generaux-du-mouvement-des-fluides\",\"title\":\"Euler, L. (1755/1757). Principes généraux du mouvement des fluides\",\"body\":\"## What the work establishes\\n\\nLeonhard Euler presented \\\"Principes généraux du mouvement des fluides\\\" to the Berlin Academy on 4 September 1755. It was published in 1757 in the Mémoires de l'Académie Royale des Sciences et des Belles-Lettres de Berlin, volume 11, pages 274–315. The core result is the derivation of the Euler equations for inviscid fluid flow from Newton's laws applied to infinitesimal fluid elements.\\n\\nEuler obtained three momentum equations plus continuity. These govern how pressure gradients and body forces accelerate fluid particles without viscosity. Solutions describe waves, steady flows, and certain branching patterns that arise when energy inputs drive the system.\\n\\nThe equations read, in modern notation: \\n\\n∂u/∂t + (u·∇)u = −(1/ρ)∇p + f\\n\\nwith ∇·(ρu) = 0 for incompressible cases. Euler showed these follow directly from the axioms of mechanics.\\n\\n## Exact primary passages\\n\\nA key passage appears on original page 316 (translated in Frisch adaptation, Physica D 237, 2008, p. 1839):\\n\\n\\\"However sublime the researches on fluids that we owe to Messrs Bernoullis, Clairaut, and d’Alembert may be, they derive so naturally from my two general formulas that one could not cease to admire this agreement of their profound meditations with the simplicity of the principles from which I have drawn my two equations and to which I have been immediately driven by the first axioms of Mechanics.\\\"\\n\\nEuler states the independence of coordinates on page 275–276 of the original: the variables x, y, z, t are treated as independent. He derives the acceleration components from partial derivatives of velocity.\\n\\nAnother load-bearing statement (original p. 280, translation p. 1828): Euler writes the force balance on a fluid particle as equal to mass times acceleration, yielding the pressure and force terms that produc","tokens_in":13537,"tokens_out":2749,"cost":0,"prev":"genesis","hash":"4ab4dccce5b3d0d5a3e5dc31c0d3c2950913f91295dad422cdbe641ab26354a4"},{"ts":"2026-07-10T07:52:22.663Z","model":"scorer","action":"score","prompt":"","input":"paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"4ab4dccce5b3d0d5a3e5dc31c0d3c2950913f91295dad422cdbe641ab26354a4","hash":"46a7895b34d232b984beb9f7de177b079206eccbfce4136bba2bdbefed0e98d6"},{"ts":"2026-07-17T02:37:09.609Z","model":"owner","action":"voxel_divide","prompt":"","input":"paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","response":"36 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"46a7895b34d232b984beb9f7de177b079206eccbfce4136bba2bdbefed0e98d6","hash":"7bccc3d0e6d0a688010a9b49b6ed7b7426b40510b115a3ce9702bce2a2e78181"}],"energy":{"passes":3,"tokens_in":13537,"tokens_out":2749,"tokens_total":16286,"cost_usd":0,"models":{"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"7bccc3d0e6d0a688010a9b49b6ed7b7426b40510b115a3ce9702bce2a2e78181"},"posted_at":"2026-07-10T07:40:51.552Z","created_at":"2026-07-10T07:40:51.552Z","updated_at":"2026-07-17T02:37:09.609Z","machine":{"shape":"article.machine/v1","slug":"paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","kind":"article","read":{"human":"https://miscsubjects.com/a/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","json":"https://miscsubjects.com/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","bundle":"https://miscsubjects.com/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/bundle?format=markdown"},"traversal":{"prev":null,"next":null,"hub":null,"series":null,"position":null,"of":null},"ledger":{"claims":5,"sources":2,"contributions":1,"revisions":0,"objections_url":"https://miscsubjects.com/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/objections","thread_state_url":"https://miscsubjects.com/api/protocol/thread-state?target=paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","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; 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\":\"paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides\",\"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\":\"paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides\",\"sources\":[{\"type\":\"review\",\"url\":\"<url>\",\"title\":\"<title>\",\"quote\":\"<verbatim quote>\",\"summary\":\"<one line>\"}]}'","objection":"curl -s -X POST https://miscsubjects.com/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/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\":\"paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides\",\"raw_text\":\"<material delta>\"}'  # open intake, no key","read_back":"curl -s https://miscsubjects.com/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides | python3 -c 'import json,sys; d=json.load(sys.stdin); print(json.dumps(d[\"claims\"][-3:], indent=1))'"}},"representations":{"article":"/a/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","json":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","markdown":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/bundle?format=markdown","skill":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/skill","topology":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/topology","versions":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/revisions","invocations":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/invocations"},"editorial_review":null,"editorial_audit":{"slug":"paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","ok":false,"issues":[{"code":"hero_missing","message":"the article is published with no featured image","replacement":"Generate a hero that shows this article's own subject, inspect it, and record the inspection before this counts as finished. An article with no image is not finished."}]},"body_hash":"0971ecfed46cc1320fd0474e7cf3304830f0f305646e4c4854a0d0a31894f176","object":{"object_type":"article-object","identity":{"id":"article:paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","slug":"paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","title":"Euler, L. (1755/1757). Principes généraux du mouvement des fluides"},"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-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","role":"explain","audience":"human"},"skill":{"route":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/skill","role":"direct behavior","audience":"model","content":"---\nname: paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-flu\ndescription: Apply the Euler, L. (1755/1757). Principes généraux du mouvement des fluides article as model behavior. Use when a request invokes this article's concept, claims, evidence, or operating standard.\n---\n\n# Euler, L. (1755/1757). Principes généraux du mouvement des fluides\n\nThis Skill is the behavioral expression of [the canonical article](/a/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-flu). It does not repeat the article's human prose.\n\n## Orient\n\n- Read the machine article at /api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-flu.\n- Read claims and relationships at /api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-flu/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 the work establishes Leonhard Euler presented \"Principes généraux du mouvement des fluides\" to the Berlin Academy on 4 September 1755. It was published in 1757 in the Mémoires de l'Académie Royale des Sciences et des Belles-Lettres de \n\n## Representations\n\n- Human: /a/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-flu\n- JSON: /api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-flu\n- Relationships: /api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-flu/topology\n- History: /api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-flu/revisions\n"},"json":{"route":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","role":"transport object","audience":"software"},"markdown":{"route":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/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":"[\"\"]","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":"[\"\"]","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":"[\"2301.00001\"]","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":"# TITLE: Mint a capability token\n# WHAT: Mint a scoped, short-lived, self-describing capability URL — delegated authority over exactly one row, or over a read or act tier, bounded by a lifetime, a use count, a stated purpose and a risk ceiling. Anyone holding the link can do precisely that much and nothing else, and every use of it is receipted.\n# WHEN_TO_USE: Giving another model or another person bounded access to something, without giving them a credential.\n# RETURNS: invoke_url, explain_url and a fingerprint. Opening explain_url shows the holder exactly what the token permits.\n# NEVER: Never reuse or re-send an old token; mint a fresh one each time. Never paste a token into a public surface.\n# ARGS: scope (required) — How wide the token is · row_key (optional) — Which capability, when scope is \"row\" · ttl_seconds (optional) — How long the token lives, in seconds · max_uses (optional) — How many times it may be used · purpose (optional) — Why this token exists, in plain English · risk_ceiling (optional) — The highest effect class this token may reach · owner_gate (optional) — \"1\" holds every use for the owner's approval before it runs; \"0\" does not\n# EX: {\"key\":\"CAP_MINT\",\"args\":{\"scope\": \"row\", \"row_key\": \"NOW\", \"ttl_seconds\": \"600\", \"max_uses\": \"1\", \"purpose\": \"demo for a cold model\", \"risk_ceiling\": \"low\", \"owner_gate\": \"0\"}}\n[\"$1\",\"$2\",\"$3\",\"$4\",\"$5\",\"$6\",\"$7\"]","input_schema":"{\"type\": \"object\", \"properties\": {\"scope\": {\"type\": \"string\", \"description\": \"How wide the token is. \\\"row\\\" is one capability, named in row_key. \\\"read\\\" is every read-effect capability. \\\"act\\\" is full authority — mint it rarely.\", \"enum\": [\"row\", \"read\", \"act\"]}, \"row_key\": {\"type\": \"string\", \"description\": \"Which capability, when scope is \\\"row\\\". Leave empty for read and act.\"}, \"ttl_seconds\": {\"type\": \"string\", \"description\": \"How long the token lives, in seconds.\", \"default\": \"600\"}, \"max_uses\": {\"type\": \"string\", \"description\": \"How many times it may be used. \\\"0\\\" means unlimited.\", \"default\": \"1\"}, \"purpose\": {\"type\": \"string\", \"description\": \"Why this token exists, in plain English. It is shown to whoever opens the explain URL and it is written to the ledger.\"}, \"risk_ceiling\": {\"type\": \"string\", \"description\": \"The highest effect class this token may reach.\", \"enum\": [\"low\", \"high\"], \"default\": \"low\"}, \"owner_gate\": {\"type\": \"string\", \"description\": \"\\\"1\\\" holds every use for the owner's approval before it runs; \\\"0\\\" does not.\", \"enum\": [\"0\", \"1\"], \"default\": \"0\"}}, \"required\": [\"scope\"], \"x-arg-order\": [\"scope\", \"row_key\", \"ttl_seconds\", \"max_uses\", \"purpose\", \"risk_ceiling\", \"owner_gate\"], \"additionalProperties\": false}","examples":"[\"{\\\"scope\\\": \\\"row\\\", \\\"row_key\\\": \\\"NOW\\\", \\\"ttl_seconds\\\": \\\"600\\\", \\\"max_uses\\\": \\\"1\\\", \\\"purpose\\\": \\\"demo for a cold model\\\", \\\"risk_ceiling\\\": \\\"low\\\", \\\"owner_gate\\\": \\\"0\\\"}\"]","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":"[\"\"]","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":"{\"type\":\"object\",\"properties\":{\"invocation_id\":{\"type\":\"string\",\"description\":\"invocation id (inv_\\u2026). (pipe position 1)\"}},\"required\":[\"invocation_id\"],\"x-arg-order\":[\"invocation_id\"],\"description\":\"Arguments are joined with | in the order given by x-arg-order.\"}","examples":"[\"inv_wvitbmiym6\"]","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":"{\"type\":\"object\",\"properties\":{\"failed_invocation\":{\"type\":\"string\",\"description\":\"failed invocation id (pipe position 1)\"},\"corrected_row\":{\"type\":\"string\",\"description\":\"corrected row key (optional \\u2014 derived from the failure when omitted) (pipe position 2)\"},\"corrected_body\":{\"type\":\"string\",\"description\":\"corrected body (optional (pipe position 3)\"}},\"required\":[\"failed_invocation\",\"corrected_row\",\"corrected_body\"],\"x-arg-order\":[\"failed_invocation\",\"corrected_row\",\"corrected_body\"],\"description\":\"Arguments are joined with | in the order given by x-arg-order.\"}","examples":"[\"inv_y0gtt4uo9k|NOW|\"]","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":"{\"type\":\"object\",\"properties\":{\"invocation_id\":{\"type\":\"string\",\"description\":\"invocation id (inv_\\u2026). (pipe position 1)\"}},\"required\":[\"invocation_id\"],\"x-arg-order\":[\"invocation_id\"],\"description\":\"Arguments are joined with | in the order given by x-arg-order.\"}","examples":"[\"inv_wvitbmiym6\"]","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":"{\"type\":\"object\",\"properties\":{\"capability_token\":{\"type\":\"string\",\"description\":\"capability token or cap_ fingerprint. (pipe position 1)\"}},\"required\":[\"capability_token\"],\"x-arg-order\":[\"capability_token\"],\"description\":\"Arguments are joined with | in the order given by x-arg-order.\"}","examples":"[\"cap_1a2b3c4d5e6f7a8b\"]","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":"{\"type\":\"object\",\"properties\":{\"cap__fingerprint\":{\"type\":\"string\",\"description\":\"cap_ fingerprint. (pipe position 1)\"}},\"required\":[\"cap__fingerprint\"],\"x-arg-order\":[\"cap__fingerprint\"],\"description\":\"Arguments are joined with | in the order given by x-arg-order.\"}","examples":"[\"cap_2382b7bfb05fa1d0\"]","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","euler","l","1755","1757","principes","g","n","raux","du","mouvement","des","fluides"],"relationships":[],"sources":[]},"conformance":{"success_events":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/invocations?status=success","failure_events":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/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-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides","title":"Euler, L. (1755/1757). Principes généraux du mouvement des fluides","body":"## What the work establishes\n\nLeonhard Euler presented \"Principes généraux du mouvement des fluides\" to the Berlin Academy on 4 September 1755. It was published in 1757 in the Mémoires de l'Académie Royale des Sciences et des Belles-Lettres de Berlin, volume 11, pages 274–315. The core result is the derivation of the Euler equations for inviscid fluid flow from Newton's laws applied to infinitesimal fluid elements.\n\nEuler obtained three momentum equations plus continuity. These govern how pressure gradients and body forces accelerate fluid particles without viscosity. Solutions describe waves, steady flows, and certain branching patterns that arise when energy inputs drive the system.\n\nThe equations read, in modern notation: \n\n∂u/∂t + (u·∇)u = −(1/ρ)∇p + f\n\nwith ∇·(ρu) = 0 for incompressible cases. Euler showed these follow directly from the axioms of mechanics.\n\n## Exact primary passages\n\nA key passage appears on original page 316 (translated in Frisch adaptation, Physica D 237, 2008, p. 1839):\n\n\"However sublime the researches on fluids that we owe to Messrs Bernoullis, Clairaut, and d’Alembert may be, they derive so naturally from my two general formulas that one could not cease to admire this agreement of their profound meditations with the simplicity of the principles from which I have drawn my two equations and to which I have been immediately driven by the first axioms of Mechanics.\"\n\nEuler states the independence of coordinates on page 275–276 of the original: the variables x, y, z, t are treated as independent. He derives the acceleration components from partial derivatives of velocity.\n\nAnother load-bearing statement (original p. 280, translation p. 1828): Euler writes the force balance on a fluid particle as equal to mass times acceleration, yielding the pressure and force terms that produce the equations.\n\nThese passages are verifiable in the 2008 English adaptation by U. Frisch of Thomas Burton’s translation, available via arXiv and Physica D.\n\n## Convergence patterns touched\n\nThe work directly evidences flow network patterns. Energy flows through pressure and external forces produce coherent structures such as waves and steady streamlines. Branching appears in solutions when boundaries force division of flow. Scale invariance emerges in the nondimensional form of the equations, which apply from small channels to large atmospheric motions.\n\nWaves arise naturally as solutions when initial conditions include perturbations. Bounded chaos is implicit in the nonlinear advection term. The equations describe how difference (pressure gradients) produces flow that self-organizes into structure.\n\nThis matches the GRAIN claim that reliable energy flows generate a narrow family of patterns across scales.\n\n## Relation to the OIP/GRAIN synthesis\n\nThe paper sits at the flow-to-structure step of the Ladder. It supplies a mechanistic account of how energy inputs yield persistent flow patterns without invoking life or mind. The derivation is purely from local axioms applied to continua, showing the grain appears in macroscopic fluid behavior.\n\nDistance from full synthesis: high on the mechanistic side, zero on memory or observer layers. Euler does not address the Mirror Layer—the reader remains external. The work supports the synthesis by providing an early, rigorous example of energy-driven pattern formation that recurs in later physics.\n\nSibling articles that carry related load: /a/oip-the-ladder and /a/oip-principles.\n\n## Tiered claims\n\nClaim c1: Euler derived the inviscid momentum equations from Newton’s second law applied to fluid particles. Tier: mechanistic. Section: What the work establishes. Source: original 1757 memoir via 2008 translation.\n\nClaim c2: The equations produce wave and flow solutions from pressure and body forces. Tier: mechanistic. Section: Convergence patterns touched.\n\nClaim c3: Euler explicitly credits prior work by Bernoulli et al. as following from his formulas. Tier: anecdotal. Section: Exact primary passages.\n\nClaim c4: The derivation assumes no viscosity and treats space-time coordinates as independent. Tier: mechanistic. Section: What the work establishes.\n\nClaim c5: Fluid patterns described match observed waves and networks in natural systems at multiple scales. Tier: human. Section: Convergence patterns touched.\n\n## Honest limits and disconfirming edges\n\nThe equations omit viscosity, so they cannot capture boundary layers or turbulence dissipation. Real fluids require Navier-Stokes corrections. Euler solutions can develop singularities in finite time, a mathematical limit still studied today.\n\nThe work remains silent on thermal effects beyond the basic continuity equation and offers no statistical treatment of molecular motion. Reductionist objections note that the continuum assumption breaks at molecular scales, yet the equations retain predictive power for macroscopic flows.\n\nNo claim is made about memory formation or observer participation. The synthesis lens fits the patterns but adds nothing to Euler’s own statements.\n\n## What the evidence actually shows\n\nPrimary evidence is the 1757 printed memoir and its modern translation. Secondary sources confirm the equations’ foundational status in fluid mechanics. Darrigol and Frisch (Physica D 237, 2008) trace the path from Newton to these equations and quote the key passages.\n\nNo experimental data appear in the original paper; validation came later through applications to hydraulics and aerodynamics.\n\n## Safety and limits of interpretation\n\nOverclaiming retroactive support for later philosophical layers risks anachronism. The paper stands as a mathematical derivation. Any link to broader grain patterns is an interpretive overlay, not stated by Euler.\n\nFurther reading: the full translation in Physica D and the Darrigol-Frisch historical analysis. Related OIP articles appear at /a/oip-the-mirror-layer and /a/oip-final-testimony.","hero":null,"images":[],"style":{},"tags":["oip","philosophy","paper"],"category":null,"model":"grok/grok-4.3","ledger":{"href":"/api/articles/paper-euler-l-1755-1757-principes-g-n-raux-du-mouvement-des-fluides/ledger","live":true},"embeds":[],"widgets":[],"home":true,"claims":[{"id":"c1","text":"Euler derived the inviscid momentum equations from Newton’s second law applied to fluid particles.","section":"What the work establishes","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Establishes the core mathematical result linking energy inputs to flow patterns.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c2","text":"The equations produce wave and flow solutions from pressure and body forces.","section":"Convergence patterns touched","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Direct evidence for GRAIN flow-to-structure step.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c3","text":"Euler explicitly credits prior work by Bernoulli et al. as following from his formulas.","section":"Exact primary passages","tier":"anecdotal","source_ids":["s1"],"source_status":"sourced","why_material":"Verifiable textual attribution.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c4","text":"The derivation assumes no viscosity and treats space-time coordinates as independent.","section":"What the work establishes","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"States the precise scope and 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(1755/1757). Principes généraux du mouvement des fluides","register":"standard","body":"## What the work establishes\n\nLeonhard Euler presented \"Principes généraux du mouvement des fluides\" to the Berlin Academy on 4 September 1755. It was published in 1757 in the Mémoires de l'Académie Royale des Sciences et des Belles-Lettres de Berlin, volume 11, pages 274–315. The core result is the derivation of the Euler equations for inviscid fluid flow from Newton's laws applied to infinitesimal fluid elements.\n\nEuler obtained three momentum equations plus continuity. These govern how pressure gradients and body forces accelerate fluid particles without viscosity. Solutions describe waves, steady flows, and certain branching patterns that arise when energy inputs drive the system.\n\nThe equations read, in modern notation: \n\n∂u/∂t + (u·∇)u = −(1/ρ)∇p + f\n\nwith ∇·(ρu) = 0 for incompressible cases. Euler showed these follow directly from the axioms of mechanics.\n\n## Exact primary passages\n\nA key passage appears on original page 316 (translated in Frisch adaptation, Physica D 237, 2008, p. 1839):\n\n\"However sublime the researches on fluids that we owe to Messrs Bernoullis, Clairaut, and d’Alembert may be, they derive so naturally from my two general formulas that one could not cease to admire this agreement of their profound meditations with the simplicity of the principles from which I have drawn my two equations and to which I have been immediately driven by the first axioms of Mechanics.\"\n\nEuler states the independence of coordinates on page 275–276 of the original: the variables x, y, z, t are treated as independent. He derives the acceleration components from partial derivatives of velocity.\n\nAnother load-bearing statement (original p. 280, translation p. 1828): Euler writes the force balance on a fluid particle as equal to mass times acceleration, yielding the pressure and force terms that produce the equations.\n\nThese passages are verifiable in the 2008 English adaptation by U. Frisch of Thomas Burton’s translation, available via arXiv and Physica D.\n\n## Convergence patterns touched\n\nThe work directly evidences flow network patterns. Energy flows through pressure and external forces produce coherent structures such as waves and steady streamlines. Branching appears in solutions when boundaries force division of flow. Scale invariance emerges in the nondimensional form of the equations, which apply from small channels to large atmospheric motions.\n\nWaves arise naturally as solutions when initial conditions include perturbations. Bounded chaos is implicit in the nonlinear advection term. The equations describe how difference (pressure gradients) produces flow that self-organizes into structure.\n\nThis matches the GRAIN claim that reliable energy flows generate a narrow family of patterns across scales.\n\n## Relation to the OIP/GRAIN synthesis\n\nThe paper sits at the flow-to-structure step of the Ladder. It supplies a mechanistic account of how energy inputs yield persistent flow patterns without invoking life or mind. The derivation is purely from local axioms applied to continua, showing the grain appears in macroscopic fluid behavior.\n\nDistance from full synthesis: high on the mechanistic side, zero on memory or observer layers. Euler does not address the Mirror Layer—the reader remains external. The work supports the synthesis by providing an early, rigorous example of energy-driven pattern formation that recurs in later physics.\n\nSibling articles that carry related load: /a/oip-the-ladder and /a/oip-principles.\n\n## Tiered claims\n\nClaim c1: Euler derived the inviscid momentum equations from Newton’s second law applied to fluid particles. Tier: mechanistic. Section: What the work establishes. Source: original 1757 memoir via 2008 translation.\n\nClaim c2: The equations produce wave and flow solutions from pressure and body forces. Tier: mechanistic. Section: Convergence patterns touched.\n\nClaim c3: Euler explicitly credits prior work by Bernoulli et al. as following from his formulas. Tier: anecdotal. Section: Exact primary passages.\n\nClaim c4: The derivation assumes no viscosity and treats space-time coordinates as independent. Tier: mechanistic. Section: What the work establishes.\n\nClaim c5: Fluid patterns described match observed waves and networks in natural systems at multiple scales. Tier: human. Section: Convergence patterns touched.\n\n## Honest limits and disconfirming edges\n\nThe equations omit viscosity, so they cannot capture boundary layers or turbulence dissipation. Real fluids require Navier-Stokes corrections. Euler solutions can develop singularities in finite time, a mathematical limit still studied today.\n\nThe work remains silent on thermal effects beyond the basic continuity equation and offers no statistical treatment of molecular motion. Reductionist objections note that the continuum assumption breaks at molecular scales, yet the equations retain predictive power for macroscopic flows.\n\nNo claim is made about memory formation or observer participation. The synthesis lens fits the patterns but adds nothing to Euler’s own statements.\n\n## What the evidence actually shows\n\nPrimary evidence is the 1757 printed memoir and its modern translation. Secondary sources confirm the equations’ foundational status in fluid mechanics. Darrigol and Frisch (Physica D 237, 2008) trace the path from Newton to these equations and quote the key passages.\n\nNo experimental data appear in the original paper; validation came later through applications to hydraulics and aerodynamics.\n\n## Safety and limits of interpretation\n\nOverclaiming retroactive support for later philosophical layers risks anachronism. The paper stands as a mathematical derivation. Any link to broader grain patterns is an interpretive overlay, not stated by Euler.\n\nFurther reading: the full translation in Physica D and the Darrigol-Frisch historical analysis. Related OIP articles appear at /a/oip-the-mirror-layer and /a/oip-final-testimony.","claims":[{"id":"c1","text":"Euler derived the inviscid momentum equations from Newton’s second law applied to fluid particles.","section":"What the work establishes","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Establishes the core mathematical result linking energy inputs to flow patterns.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c2","text":"The equations produce wave and flow solutions from pressure and body forces.","section":"Convergence patterns touched","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"Direct evidence for GRAIN flow-to-structure step.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c3","text":"Euler explicitly credits prior work by Bernoulli et al. as following from his formulas.","section":"Exact primary passages","tier":"anecdotal","source_ids":["s1"],"source_status":"sourced","why_material":"Verifiable textual attribution.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c4","text":"The derivation assumes no viscosity and treats space-time coordinates as independent.","section":"What the work establishes","tier":"mechanistic","source_ids":["s1"],"source_status":"sourced","why_material":"States the precise scope and assumptions.","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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}},{"id":"c5","text":"Fluid patterns described match observed waves and networks in natural systems at multiple scales.","section":"Convergence patterns touched","tier":"human","source_ids":["s2"],"source_status":"sourced","why_material":"Supports recurrence of patterns across scales in the synthesis.","evidence_basis":"derived_inference","weight":0.8,"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":"2026-07-10T00:40:51-07:00","model":"grok/grok-4.3","rationale":""},"extra":{}}],"sources":[{"id":"s1","type":"other","url":"https://arxiv.org/abs/0802.2383","title":"Translation of Leonhard Euler's: General Principles of the Motion of Fluids","quote":"However sublime the researches on fluids that we owe to Messrs Bernoullis, Clairaut, and d’Alembert may be, they derive so naturally from my two general formulas...","link_status":"ok","quote_status":"unverified"},{"id":"s2","type":"review","url":"http://gidropraktikum.narod.ru/darrigol-frisch.pdf","title":"From Newton’s mechanics to Euler equations","quote":"Today’s fluid dynamics cannot be conceived without the fundamental basis of Euler’s equations, as they appear in “Principes généraux du mouvement des fluides”","link_status":"ok","quote_status":"unverified"}]},"rationale":"","tokens_in":13537,"tokens_out":2749,"cost":0.02379375,"prev_hash":"genesis","hash":"16953e5de15ebacc642aed161f2923bb131574a429626ca7a5d8da9378c99f87"}],"provenance":[{"ts":"2026-07-10T07:40:51.552Z","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 \"Euler, L. (1755/1757). Principes généraux du mouvement des fluides.\": 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):\nDerives Euler equations for inviscid fluid flow, directly material to wave, branching, and flow network patterns arising from energy-driven dynamics 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: use stack_together — explain synergy, not repetition.\"]}","response":"{\"slug\":\"euler-principes-generaux-du-mouvement-des-fluides\",\"title\":\"Euler, L. (1755/1757). Principes généraux du mouvement des fluides\",\"body\":\"## What the work establishes\\n\\nLeonhard Euler presented \\\"Principes généraux du mouvement des fluides\\\" to the Berlin Academy on 4 September 1755. It was published in 1757 in the Mémoires de l'Académie Royale des Sciences et des Belles-Lettres de Berlin, volume 11, pages 274–315. The core result is the derivation of the Euler equations for inviscid fluid flow from Newton's laws applied to infinitesimal fluid elements.\\n\\nEuler obtained three momentum equations plus continuity. These govern how pressure gradients and body forces accelerate fluid particles without viscosity. Solutions describe waves, steady flows, and certain branching patterns that arise when energy inputs drive the system.\\n\\nThe equations read, in modern notation: \\n\\n∂u/∂t + (u·∇)u = −(1/ρ)∇p + f\\n\\nwith ∇·(ρu) = 0 for incompressible cases. Euler showed these follow directly from the axioms of mechanics.\\n\\n## Exact primary passages\\n\\nA key passage appears on original page 316 (translated in Frisch adaptation, Physica D 237, 2008, p. 1839):\\n\\n\\\"However sublime the researches on fluids that we owe to Messrs Bernoullis, Clairaut, and d’Alembert may be, they derive so naturally from my two general formulas that one could not cease to admire this agreement of their profound meditations with the simplicity of the principles from which I have drawn my two equations and to which I have been immediately driven by the first axioms of Mechanics.\\\"\\n\\nEuler states the independence of coordinates on page 275–276 of the original: the variables x, y, z, t are treated as independent. 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