{"slug":"paper-kosmann-schwarzbach-y-2011-the-noether-theorems-invariance-and-conservation-laws","verification":{"valid":true,"entries":2,"head":"a074bf0a3a35a3a31eab0d9407294316e31fd96164c7f97d347a81bb1ca3c996"},"energy":{"passes":2,"tokens_in":21938,"tokens_out":2829,"tokens_total":24767,"cost_usd":0,"models":{"grok/grok-4.3":1,"scorer":1},"head":"a074bf0a3a35a3a31eab0d9407294316e31fd96164c7f97d347a81bb1ca3c996"},"provenance":[{"ts":"2026-07-10T06:59:45.783Z","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 \"Kosmann-Schwarzbach, Y. (2011). The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century\": 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):\nScholarly monograph on Noether's 1918 theorems, their historical context in relativity and physics, and extensions to conservation principles central to dissipative structures and symmetry/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 — explai","response":"{\n  \"slug\": \"kosmann-schwarzbach-noether-theorems-2011\",\n  \"title\": \"Kosmann-Schwarzbach (2011) on the Noether Theorems\",\n  \"body\": \"## What the Work Establishes\\n\\nYvette Kosmann-Schwarzbach's 2011 monograph provides a scholarly history of Emmy Noether's 1918 paper \\\"Invariante Variationsprobleme.\\\" It supplies the first complete English translation of that paper and traces the theorems' development, reception, and extensions through the twentieth century. The book situates Noether's results in the context of early general relativity debates on energy conservation and the calculus of variations.\\n\\nThe core claim is that continuous symmetries of variational problems imply corresponding conservation laws. Noether proved two main theorems. The first links finite or infinite continuous groups of symmetries to conserved quantities when the action is invariant. The second addresses cases where the invariance holds only up to a divergence term, yielding identities rather than new conservation laws.\\n\\n## Exact Primary Works and Passages\\n\\nThe monograph centers on Emmy Noether, \\\"Invariante Variationsprobleme,\\\" Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse (1918): 235–257. Kosmann-Schwarzbach reproduces and translates this text in full. A verifiable passage from the original (as rendered in the book) states: \\\"We shall deal with variational problems that admit a continuous group (in the Lie sense); the results that this yields for the associated differential equations are the subject of the present work.\\\" Another key statement reads: \\\"If the integral I is invariant with respect to a group... then there exist relations between the Lagrange expressions... which become identities when the Euler-Lagrange equations are satisfied.\\\"\\n\\nKosmann-Schwarzbach also references Noether's correspondence with Felix Klein and David Hilbert in Göttingen around 1915–1918. The book analyzes precursors including Lagrange, Jaco","tokens_in":21938,"tokens_out":2829,"cost":0,"prev":"genesis","hash":"5696d0d01dbbf36b8ea49d82acf801c934659f60c04ab23f6c340d4bffff15a0"},{"ts":"2026-07-10T07:28:23.083Z","model":"scorer","action":"score","prompt":"","input":"paper-kosmann-schwarzbach-y-2011-the-noether-theorems-invariance-and-conservation-laws","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"5696d0d01dbbf36b8ea49d82acf801c934659f60c04ab23f6c340d4bffff15a0","hash":"a074bf0a3a35a3a31eab0d9407294316e31fd96164c7f97d347a81bb1ca3c996"}]}