{"slug":"oip-node-c16-branching-optimal-transport","verification":{"valid":true,"entries":5,"head":"e6a52eb33b457e14a857f1d3eca9f745d0b47064423479ceae4ece09ae21f024"},"energy":{"passes":5,"tokens_in":3478,"tokens_out":1980,"tokens_total":5458,"cost_usd":0,"models":{"claude-fable-5":2,"grok/grok-4.3":1,"scorer":1,"owner":1},"head":"e6a52eb33b457e14a857f1d3eca9f745d0b47064423479ceae4ece09ae21f024"},"provenance":[{"ts":"2026-07-04T04:34:06.031Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"genesis","hash":"4e91442b25c414ab64694c24d04241bb26c0f9a70793fabb133432b9cfb6a719"},{"ts":"2026-07-04T05:02:02.772Z","model":"claude-fable-5","action":"edit","prompt":"","input":"","response":"","tokens_in":0,"tokens_out":0,"cost":0,"prev":"4e91442b25c414ab64694c24d04241bb26c0f9a70793fabb133432b9cfb6a719","hash":"a00c66a7eb798789cc1493105261ab1ded3fc7b1f10315d50d18c5581b0c4108"},{"ts":"2026-07-07T07:55:51.361Z","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-c16-branching-optimal-transport","response":"{\n  \"claims\": [\n    {\n      \"id\": \"c1\",\n      \"text\": \"The solution to connecting one source to many sinks with minimum transport cost converges on hierarchical branching networks.\",\n      \"section\": \"# Node C16: Branching / Optimal Transport\",\n      \"tier\": \"human\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Core assertion linking optimal transport minimization to network structure.\"\n    },\n    {\n      \"id\": \"c2\",\n      \"text\": \"These networks follow scaling laws (Murray's Law, constructal scaling) across 22 orders of magnitude.\",\n      \"section\": \"# Node C16: Branching / Optimal Transport\",\n      \"tier\": \"human\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Quantifies the range and universality of the scaling pattern.\"\n    },\n    {\n      \"id\": \"c3\",\n      \"text\": \"Murray's Law states that for minimum viscous energy dissipation in a bifurcating network, r_0^3 = r_1^3 + r_2^3.\",\n      \"section\": \"# Node C16: Branching / Optimal Transport\",\n      \"tier\": \"mechanistic\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Provides the explicit mathematical mechanism for the branching optimization.\"\n    },\n    {\n      \"id\": \"c4\",\n      \"text\": \"Bejan's constructal law states that flow systems evolve to provide easier access to currents.\",\n      \"section\": \"# Node C16: Branching / Optimal Transport\",\n      \"tier\": \"anecdotal\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Defines the evolutionary mechanism underlying the observed scaling.\"\n    },\n    {\n      \"id\": \"c5\",\n      \"text\": \"Horton's laws state that stream number and length decrease geometrically with stream order.\",\n      \"section\": \"# Node C16: Branching / Optimal Transport\",\n      \"tier\": \"human\",\n      \"source_ids\": [],\n      \"source_status\": \"unsourced\",\n      \"why_material\": \"Empirical geological scaling relation supporting the pattern.\"\n    },\n    {\n      \"id\":","tokens_in":3478,"tokens_out":1980,"cost":0,"prev":"a00c66a7eb798789cc1493105261ab1ded3fc7b1f10315d50d18c5581b0c4108","hash":"9cff85d6ab84799bffff92a67ca340a61bc66ec6b29337eabee9279b2af0567c"},{"ts":"2026-07-07T07:55:51.673Z","model":"scorer","action":"score","prompt":"","input":"oip-node-c16-branching-optimal-transport","response":"[]","tokens_in":0,"tokens_out":0,"cost":0,"prev":"9cff85d6ab84799bffff92a67ca340a61bc66ec6b29337eabee9279b2af0567c","hash":"d91bc573866e94b72d308661211ba506666f78854c1d6717dd7dbe389dbd5b31"},{"ts":"2026-07-17T02:36:21.656Z","model":"owner","action":"voxel_divide","prompt":"","input":"oip-node-c16-branching-optimal-transport","response":"5 DIVs from body (verbatim, roundtrip-checked)","tokens_in":0,"tokens_out":0,"cost":0,"prev":"d91bc573866e94b72d308661211ba506666f78854c1d6717dd7dbe389dbd5b31","hash":"e6a52eb33b457e14a857f1d3eca9f745d0b47064423479ceae4ece09ae21f024"}]}