{"id": "c642", "title": "C642 — Reconstruct the no-Cainan companion", "filename": "C642.md", "role": "Research action", "step": 642, "sha256": "e57a1c83162e81657d357e10686a1ade13fe9ea10a31db7909c78160c2c100ed", "bytes": 1347, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C642"], "download": "/sources/e57a1c83162e81657d357e10686a1ade13fe9ea10a31db7909c78160c2c100ed.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "Which relations survive when the Creation rail alone moves130?", "content": "# C642 — Reconstruct the no-Cainan companion\n\n## Question\n\nWhich relations survive when the Creation rail alone moves130?\n\n## Inputs\n\n```json\n{\n  \"standard_Creation\": [\n    4121,\n    4114,\n    4107\n  ],\n  \"Joseph\": [\n    1885,\n    1878,\n    1871\n  ],\n  \"standard_exposure\": 4108\n}\n```\n\n## Sources\n\n```json\n[\n  \"File70 §§6.1,6.6\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:59:33.175668+00:00\n\n## Results\n\n```json\n{\n  \"span_family\": [\n    2210,\n    2222,\n    2236,\n    2250\n  ],\n  \"corresponding_spans\": [\n    2236,\n    2236,\n    2236\n  ],\n  \"calendar_half_counts\": [\n    \"221/18\",\n    \"1111/84\",\n    \"86/7\"\n  ],\n  \"shift_from_restored\": 130\n}\n```\n\n## Finding\n\nRemoving130 preserves both7+7 rails and all their relative diagonals, giving2236 as the corresponding translation. It changes the calendar counts to nonintegers, so the restored state’s13/14/13 specialization is not automatic from rail shape alone.\n\n## Reassessment\n\nAsk whether the fixed standard state and three-calendar conditions select130 as the least nonnegative correction.\n\n## Checks\n\n```json\n{\n  \"companion\": true,\n  \"shape\": true,\n  \"counts_changed\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:59:33.175833+00:00\n\n## Record provenance\n\nExact record hash: `bfffe3745aa25cf6e552ea3071d48994bddd5bd76620a6756efff51414405fdc`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json", "evidenceLinks": [{"id": "d-0fa80217c94b3951", "title": "File 70"}]}