{"id": "c641", "title": "C641 — Identify the calendar compatibility period", "filename": "C641.md", "role": "Research action", "step": 641, "sha256": "288cd1bad3ebe5fd872df65166d4ca13283422385375c632a776ecd2450aa582", "bytes": 1282, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C641"], "download": "/sources/288cd1bad3ebe5fd872df65166d4ca13283422385375c632a776ecd2450aa582.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "Why is the full congruence period32760, and how does it meet the earlier common-volume family?", "content": "# C641 — Identify the calendar compatibility period\n\n## Question\n\nWhy is the full congruence period32760, and how does it meet the earlier common-volume family?\n\n## Inputs\n\n```json\n{\n  \"half_calendars\": [\n    168,\n    180,\n    182\n  ],\n  \"full_calendars\": [\n    336,\n    360,\n    364\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"C640; File12 calendar definitions; C575\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:58:58.617439+00:00\n\n## Results\n\n```json\n{\n  \"half_calendar_lcm\": 32760,\n  \"full_calendar_lcm\": 65520,\n  \"previous_volume_coefficient\": 327600,\n  \"ratios\": [\n    2,\n    10\n  ]\n}\n```\n\n## Finding\n\nThe period32760 is the least common multiple of the three half-calendars. Doubling gives65520 for full calendars; the earlier327600 common-volume coefficient is ten half-periods. The numerical link comes from the same calendar denominators, with units retained.\n\n## Reassessment\n\nExecute the no-Cainan rail companion and locate which calendar divisibilities it preserves.\n\n## Checks\n\n```json\n{\n  \"period\": true,\n  \"previous_volume\": true,\n  \"counts_increment\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:58:58.617609+00:00\n\n## Record provenance\n\nExact record hash: `aca507fc8cb4d8a7ff368876b5cf8e91a3c68205120bedafce3f964c098b542e`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json", "evidenceLinks": [{"id": "d-9a1eff41920cd0f8", "title": "File 12"}]}