{"slug":"oip-node-c02-least-action-variational-principles","verification":{"valid":true,"entries":5,"head":"8ac119b9e3d00b6e1d1706c81c75bc1c05ac09f4e1d7fe2304936067bea61599"},"energy":{"passes":5,"tokens_in":3367,"tokens_out":1744,"tokens_total":5111,"cost_usd":0,"models":{"claude-fable-5":2,"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"8ac119b9e3d00b6e1d1706c81c75bc1c05ac09f4e1d7fe2304936067bea61599"},"provenance":[{"ts":"2026-07-04T04:33:58.427Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"ab70cd72337133e3d0914ac2938bdfb6b126b78cdd6d45f13954b202d82f7f8b"},{"ts":"2026-07-04T05:01:55.963Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"ab70cd72337133e3d0914ac2938bdfb6b126b78cdd6d45f13954b202d82f7f8b","hash":"bd869d1e71c8987d81c8b519d4ac30b966e51e31b65765a451f190a924d15701"},{"ts":"2026-07-07T08:02:49.918Z","model":"grok/grok-4.3","action":"atomize","prompt":"You are the claim atomizer for the miscsubjects.com philosophy and OIP corpus. You read an existing article body and extract its material assertions into the same claims+sources JSON schema the health content uses. The body is read-only input.\n\nALWAYS:\n- Extract every material assertion as one atomic claim, tied to the ## section it came from.\n- Tier honestly: human = empirically established; mechanistic = formally proven or mathematical; anecdotal = historical or textual attribution; speculative = metaphysical or interpretive.\n- Attach real sources (primary works, papers, books) with exact quotes only where you can verify them; otherwise mark the claim unsourced.\n- Prefer fewer, harder claims over many soft ones.\n\nNEVER:\n- Never rewrite, summarize, or output the body.\n- Never invent a URL, quote, or publication.\n- Never duplicate an existing claim text.","input":"atomize oip-node-c02-least-action-variational-principles","response":"{\n  \"claims\": [\n    {\n      \"id\": \"c1\",\n      \"text\": \"Nature extremizes a quantity (action, entropy, energy) across all fundamental domains; the actual path is the stationary path.\",\n      \"section\": \"## Node C02: Least Action / Variational Principles\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Core assertion defining the least action principle across domains.\"\n    },\n    {\n      \"id\": \"c2\",\n      \"text\": \"The Euler-Lagrange equations derive from demanding that the integral of the Lagrangian (kinetic minus potential energy) be stationary.\",\n      \"section\": \"## Node C02: Least Action / Variational Principles\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Describes the mathematical derivation mechanism.\"\n    },\n    {\n      \"id\": \"c3\",\n      \"text\": \"Feynman showed this emerges from constructive interference of amplitudes in the path integral formulation.\",\n      \"section\": \"## Node C02: Least Action / Variational Principles\",\n      \"tier\": \"anecdotal\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Links the principle to quantum path integral.\"\n    },\n    {\n      \"id\": \"c4\",\n      \"text\": \"The independence of the principle is extremely high, arising from unrelated starting points in optics, mechanics, and quantum mechanics across three centuries.\",\n      \"section\": \"## Node C02: Least Action / Variational Principles\",\n      \"tier\": \"anecdotal\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Supports robustness via historical independence check.\"\n    }\n  ],\n  \"sources\": []\n}","tokens_in":3367,"tokens_out":1744,"cost":0,"prev":"bd869d1e71c8987d81c8b519d4ac30b966e51e31b65765a451f190a924d15701","hash":"65aff31d34170b91dd84268999bbdf560fa61c3cfe9a0190fb983ab4aa4007d4"},{"ts":"2026-07-07T08:02:50.233Z","model":"scorer","action":"score","prompt":"","input":"oip-node-c02-least-action-variational-principles","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"65aff31d34170b91dd84268999bbdf560fa61c3cfe9a0190fb983ab4aa4007d4","hash":"fff199961001e1ac148c9cd91d59406fc71963d8d9ae0f6141fd440b4a3ac70b"},{"ts":"2026-07-17T02:36:18.814Z","model":"owner","action":"voxel_divide","prompt":"","input":"oip-node-c02-least-action-variational-principles","response":"5 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"fff199961001e1ac148c9cd91d59406fc71963d8d9ae0f6141fd440b4a3ac70b","hash":"8ac119b9e3d00b6e1d1706c81c75bc1c05ac09f4e1d7fe2304936067bea61599"}]}