{"id": "c845", "title": "C845 — Measure the information retained by the category projections", "filename": "C845.md", "role": "Research action", "step": 845, "sha256": "72b7df1023020dc2facdd2b5a6139fe267bc3ba44dd81dc93782ac35765817fc", "bytes": 1423, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C845"], "download": "/sources/72b7df1023020dc2facdd2b5a6139fe267bc3ba44dd81dc93782ac35765817fc.md", "format": "md", "derived": true, "tags": [], "excerpt": "How many independent totals do the four marginals supply?", "content": "# C845 — Measure the information retained by the category projections\n\n## Question\n\nHow many independent totals do the four marginals supply?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"File58 nine-row ledger; C843–844\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:33:41.804403+00:00\n\n## Results\n\n```json\n{\n  \"incidence_matrix\": [\n    [\n      1,\n      1,\n      1,\n      1,\n      1,\n      1,\n      0,\n      0,\n      0\n    ],\n    [\n      0,\n      0,\n      0,\n      0,\n      0,\n      0,\n      1,\n      1,\n      1\n    ],\n    [\n      1,\n      0,\n      1,\n      0,\n      1,\n      0,\n      1,\n      1,\n      0\n    ],\n    [\n      0,\n      1,\n      0,\n      1,\n      0,\n      1,\n      0,\n      0,\n      1\n    ]\n  ],\n  \"rank\": 3,\n  \"kernel_dimension_on_unrestricted_nine_counts\": 6,\n  \"row_relation\": \"clean+unclean=female+male\"\n}\n```\n\n## Finding\n\nThe four totals contain three independent linear measurements of nine source counts. Six numerical directions are invisible to these marginals; species, order and individual counts remain necessary source data.\n\n## Reassessment\n\nRegenerate the complete source-admitted clean category-order walk.\n\n## Checks\n\n```json\n{\n  \"rank3\": true,\n  \"row_relation\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:33:41.806576+00:00\n\n## Record provenance\n\nExact record hash: `2632e305cdbf2bb4ff5b314986b760a4d0766745390a8e53ba2419cf81c17f79`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-924db415dff003d2", "title": "File 58"}]}