{"id": "c558", "title": "C558 — Generate the fixed-Joseph comparison family", "filename": "C558.md", "role": "Research action", "step": 558, "sha256": "b3204f8e516c8f3683c4ae97a63758f02e12a53625a7d1875e807082114052f3", "bytes": 1461, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C558"], "download": "/sources/b3204f8e516c8f3683c4ae97a63758f02e12a53625a7d1875e807082114052f3.md", "format": "md", "derived": true, "tags": ["Regular", "Covenant"], "excerpt": "Can one flank-transfer formula reproduce all nine comparison states?", "content": "# C558 — Generate the fixed-Joseph comparison family\n\n## Question\n\nCan one flank-transfer formula reproduce all nine comparison states?\n\n## Inputs\n\n```json\n{\n  \"regular_Joseph\": [\n    1915,\n    1805\n  ],\n  \"phases\": [\n    0,\n    3,\n    \"7/2\"\n  ],\n  \"clutch\": [\n    0,\n    7,\n    14\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File62 §§6.1–6.4\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:13:53.938889+00:00\n\n## Results\n\n```json\n{\n  \"partitions\": [\n    [\n      18,\n      9,\n      83\n    ],\n    [\n      11,\n      16,\n      83\n    ],\n    [\n      4,\n      23,\n      83\n    ],\n    [\n      \"43/2\",\n      \"11/2\",\n      83\n    ],\n    [\n      \"29/2\",\n      \"25/2\",\n      83\n    ],\n    [\n      \"15/2\",\n      \"39/2\",\n      83\n    ],\n    [\n      21,\n      6,\n      83\n    ],\n    [\n      14,\n      13,\n      83\n    ],\n    [\n      7,\n      20,\n      83\n    ]\n  ],\n  \"formula\": [\n    \"18+p−d\",\n    \"9−p+d\",\n    \"83\"\n  ]\n}\n```\n\n## Finding\n\nThe clutch transfers duration between two flanks while preserving their27 total and the83 overlap. All nine states follow without moving regular Joseph1915–1805.\n\n## Reassessment\n\nTest whether the reported cyclic symmetry acts on dates or on duration components.\n\n## Checks\n\n```json\n{\n  \"nine\": true,\n  \"totals\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:13:53.939439+00:00\n\n## Record provenance\n\nExact record hash: `b91c3ca9bc4a64f1989f0bd86f9b584dec686a7ba001f9a48b4ae95796aa0f35`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-be42daca1d82dac9", "title": "File 62"}]}