{"id": "c556", "title": "C556 — Generate all collateral Joseph intervals", "filename": "C556.md", "role": "Research action", "step": 556, "sha256": "99e962e5b49e7200607faaf7202d05f0ff74bd76a2260a9289569201a04cae32", "bytes": 1432, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C556"], "download": "/sources/99e962e5b49e7200607faaf7202d05f0ff74bd76a2260a9289569201a04cae32.md", "format": "md", "derived": true, "tags": ["Cumulative", "Covenant", "Mirror / 529"], "excerpt": "Do two fixed-offset constructions account for every source Joseph rail?", "content": "# C556 — Generate all collateral Joseph intervals\n\n## Question\n\nDo two fixed-offset constructions account for every source Joseph rail?\n\n## Inputs\n\n```json\n{\n  \"Levi\": 1933,\n  \"Kohath\": 1796,\n  \"Joseph_life\": 110\n}\n```\n\n## Sources\n\n```json\n[\n  \"File61 §§11.2–11.3A; File62 §5.2\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:13:20.705602+00:00\n\n## Results\n\n```json\n{\n  \"intervals\": [\n    [\n      1933,\n      1823\n    ],\n    [\n      1906,\n      1796\n    ],\n    [\n      1926,\n      1816\n    ],\n    [\n      1899,\n      1789\n    ],\n    [\n      1919,\n      1809\n    ],\n    [\n      1892,\n      1782\n    ],\n    [\n      \"3873/2\",\n      \"3653/2\"\n    ],\n    [\n      \"3819/2\",\n      \"3599/2\"\n    ],\n    [\n      \"3859/2\",\n      \"3639/2\"\n    ],\n    [\n      \"3805/2\",\n      \"3585/2\"\n    ],\n    [\n      \"3845/2\",\n      \"3625/2\"\n    ],\n    [\n      \"3791/2\",\n      \"3571/2\"\n    ]\n  ],\n  \"matches\": 12\n}\n```\n\n## Finding\n\nTwo collateral constructors, (L,L−110) and (K+110,K), generate all12 exact-phase Joseph intervals. Joseph remains a collateral interval, not an added trunk generation.\n\n## Reassessment\n\nDerive the invariant geometry shared by these interval pairs.\n\n## Checks\n\n```json\n{\n  \"count\": true,\n  \"lifespans\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:13:20.706343+00:00\n\n## Record provenance\n\nExact record hash: `aa8061f481db035298b9c58aa226626ddcc53eb100ff7e64f2530e48549e1456`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-be42daca1d82dac9", "title": "File 62"}, {"id": "d-d580afd48d6e12d6", "title": "File 61"}]}