{"id": "c877", "title": "C877 — Derive the quarter-family divisibility law", "filename": "C877.md", "role": "Research action", "step": 877, "sha256": "e505eb92538e5ecc9865e01dfb8aeb2eeeb5ef931cac8160f6559545c6dbbdca", "bytes": 1181, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C877"], "download": "/sources/e505eb92538e5ecc9865e01dfb8aeb2eeeb5ef931cac8160f6559545c6dbbdca.md", "format": "md", "derived": true, "tags": [], "excerpt": "What single condition explains each whole-family grid profile?", "content": "# C877 — Derive the quarter-family divisibility law\n\n## Question\n\nWhat single condition explains each whole-family grid profile?\n\n## Inputs\n\n```json\n{\n  \"seed\": \"161/4\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"C873,876\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:47:39.086772+00:00\n\n## Results\n\n```json\n{\n  \"coefficients\": {\n    \"E\": \"175/4\",\n    \"P\": \"245/6\",\n    \"J\": \"525/13\"\n  },\n  \"quarter_index_divisors\": {\n    \"E\": 1,\n    \"P\": 3,\n    \"J\": 13\n  },\n  \"artifact\": {\n    \"path\": \"model/quarter_multiplier_law.json\",\n    \"sha256\": \"ca5bfffc2493bf2b6fdb41f0f8d6a5c203fc730d0372a1cf7cce21c17ab9afd2\",\n    \"bytes\": 229\n  }\n}\n```\n\n## Finding\n\nFor source161m/4, E gives175m/4, P gives245m/6 and J gives525m/13. Quarter preservation is automatic for E, requires3|m for P and13|m for J. This explains the entire finite ladder.\n\n## Reassessment\n\nApply E to every head in File46 rather than only its outer width.\n\n## Checks\n\n```json\n{\n  \"divisors\": true,\n  \"whole_family\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:47:39.087292+00:00\n\n## Record provenance\n\nExact record hash: `cf65c4496550ec684c3078f89c83c62e8ebcc84d085c61a1d9eda8c0482bdfd5`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-ca5bfffc2493bf2b", "title": "model/quarter_multiplier_law.json"}, {"id": "d-18e8c54ff1663fb1", "title": "File 46"}]}