{"slug":"oip-pattern-2-pattern-2-spirals-the-growth-rotation-solution","verification":{"valid":true,"entries":5,"head":"6004f722ec1791b29565cf53928079b4c20d7612775a4bf632753d83552724d8"},"energy":{"passes":5,"tokens_in":3786,"tokens_out":2510,"tokens_total":6296,"cost_usd":0,"models":{"claude-fable-5":2,"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"6004f722ec1791b29565cf53928079b4c20d7612775a4bf632753d83552724d8"},"provenance":[{"ts":"2026-07-04T04:34:13.690Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"ef498bd16f6b226317ddf9e80c9a3731cd68406f559e5a0c62bf11b05de6650a"},{"ts":"2026-07-04T05:02:10.362Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"ef498bd16f6b226317ddf9e80c9a3731cd68406f559e5a0c62bf11b05de6650a","hash":"7def41f302a839649956198fda3d23de4ef92aa44073107c4a77a9580cddd7c7"},{"ts":"2026-07-07T07:49:48.861Z","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-pattern-2-pattern-2-spirals-the-growth-rotation-solution","response":"{\n  \"claims\": [\n    {\"id\":\"c1\",\"text\":\"A spiral is the locus of a point moving outward from a center at a rate proportional to its angular displacement.\",\"section\":\"## Formal definition\",\"tier\":\"mechanistic\",\"source_ids\":[],\"source_status\":\"unsourced\",\"why_material\":\"Core geometric definition of spiral in the pattern.\"},\n    {\"id\":\"c2\",\"text\":\"The spiral solves the problem of packing growing elements into a circular or spherical region without overlap where each new element must be added at the periphery.\",\"section\":\"## Formal definition\",\"tier\":\"mechanistic\",\"source_ids\":[],\"source_status\":\"unsourced\",\"why_material\":\"States functional purpose of the spiral pattern.\"},\n    {\"id\":\"c3\",\"text\":\"The optimal spiral achieves maximum packing density for elements of varying size.\",\"section\":\"## Formal definition\",\"tier\":\"mechanistic\",\"source_ids\":[],\"source_status\":\"unsourced\",\"why_material\":\"Defines optimality criterion for the pattern.\"},\n    {\"id\":\"c4\",\"text\":\"If a growing structure adds new material at a fixed angular interval while expanding radially the result is a logarithmic spiral.\",\"section\":\"## Mechanism\",\"tier\":\"mechanistic\",\"source_ids\":[],\"source_status\":\"unsourced\",\"why_material\":\"Describes the generative mechanism of logarithmic spirals.\"},\n    {\"id\":\"c5\",\"text\":\"The key parameter of spiral growth is the divergence angle the angular separation between successive elements.\",\"section\":\"## Mechanism\",\"tier\":\"mechanistic\",\"source_ids\":[],\"source_status\":\"unsourced\",\"why_material\":\"Identifies the critical control parameter.\"},\n    {\"id\":\"c6\",\"text\":\"The phyllotaxis equation is θₙ = n × φ and rₙ = a√n where φ is the golden angle 137.507764…° derived from the golden ratio (1+√5)/2.\",\"section\":\"## Mathematical load: the Golden Angle and Phyllotaxis\",\"tier\":\"mechanistic\",\"source_ids\":[],\"source_status\":\"unsourced\",\"why_material\":\"Presents the exact mathematical model for phyllotaxis.\"},\n    {\"id\":\"c7\",\"text\":\"The radial scaling rₙ = a√n ensures constant area per elem","tokens_in":3786,"tokens_out":2510,"cost":0,"prev":"7def41f302a839649956198fda3d23de4ef92aa44073107c4a77a9580cddd7c7","hash":"6028ebb86683aa28c80743da5f02d6c44adac14ce0319cbb7070526705c9db66"},{"ts":"2026-07-07T07:49:49.198Z","model":"scorer","action":"score","prompt":"","input":"oip-pattern-2-pattern-2-spirals-the-growth-rotation-solution","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"6028ebb86683aa28c80743da5f02d6c44adac14ce0319cbb7070526705c9db66","hash":"77e5dcc8f242b2c1cb914f9f78c02edac7c3ae2b1297b3649a9950795baab547"},{"ts":"2026-07-17T02:36:24.654Z","model":"owner","action":"voxel_divide","prompt":"","input":"oip-pattern-2-pattern-2-spirals-the-growth-rotation-solution","response":"5 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"77e5dcc8f242b2c1cb914f9f78c02edac7c3ae2b1297b3649a9950795baab547","hash":"6004f722ec1791b29565cf53928079b4c20d7612775a4bf632753d83552724d8"}]}