{"id": "c844", "title": "C844 — Derive the equal-marginal constraint", "filename": "C844.md", "role": "Research action", "step": 844, "sha256": "fda42712d37a65aec74bbc69b40532ec8845e29f05cfadeb6186be97a655e34c", "bytes": 1109, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C844"], "download": "/sources/fda42712d37a65aec74bbc69b40532ec8845e29f05cfadeb6186be97a655e34c.md", "format": "md", "derived": true, "tags": [], "excerpt": "What exactly must be true for purity and sex totals to coincide?", "content": "# C844 — Derive the equal-marginal constraint\n\n## Question\n\nWhat exactly must be true for purity and sex totals to coincide?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C843\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:33:26.480421+00:00\n\n## Results\n\n```json\n{\n  \"clean_minus_female\": 0,\n  \"unclean_minus_male\": 0,\n  \"fixed_margin_family\": \"[[490−t,t],[t,60−t]], 0≤t≤60\",\n  \"source_t\": 50,\n  \"constraint_count\": 1,\n  \"independence_determinant\": 1900\n}\n```\n\n## Finding\n\nThe double490/60 display imposes one cross-category balance, b=c. Given those margins, one cell parameter remains; the source selects50. Distinct category definitions and equal marginals do not establish statistical independence.\n\n## Reassessment\n\nRecover the exact rank of the nine-row measurement map.\n\n## Checks\n\n```json\n{\n  \"equal_marginals\": true,\n  \"source_family\": true,\n  \"not_product_table\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:33:26.480756+00:00\n\n## Record provenance\n\nExact record hash: `344cf2ae2e5dc74547b9ec04e7fd7fa744e0dcbed85e398976fb9811b1e47a1e`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json"}