{"id": "c586", "title": "C586 — Unify calendar and paired-endpoint equalities", "filename": "C586.md", "role": "Research action", "step": 586, "sha256": "e24cd983a44d0f1574a20e3bf186d60d3728cee61368569ae7abe0614f9f7c17", "bytes": 1253, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C586"], "download": "/sources/e24cd983a44d0f1574a20e3bf186d60d3728cee61368569ae7abe0614f9f7c17.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "What single normalized comparison underlies the calendar Keys and earlier common endpoints?", "content": "# C586 — Unify calendar and paired-endpoint equalities\n\n## Question\n\nWhat single normalized comparison underlies the calendar Keys and earlier common endpoints?\n\n## Inputs\n\n```json\n{\n  \"calendars\": [\n    336,\n    360,\n    364\n  ],\n  \"Keys\": [\n    \"25/23\",\n    \"70/69\",\n    \"300/299\"\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File12 §§2,6.3; C535; C568–C575\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:20:35.611996+00:00\n\n## Results\n\n```json\n{\n  \"calibration_constant\": [\n    \"8400/23\",\n    \"8400/23\",\n    \"8400/23\"\n  ],\n  \"Key_ratios\": [\n    \"15/14\",\n    \"13/12\",\n    \"91/90\"\n  ],\n  \"calendar_decomposition\": [\n    336,\n    364,\n    360\n  ]\n}\n```\n\n## Finding\n\nAll Keys satisfy d×K_d=8400/23, hence K_d(s)=(8400/23)(s/d). Equal normalized durations explain the calendar-volume agreements and the earlier1566/2926 paired endpoints when anchor and direction also agree.\n\n## Reassessment\n\nTest the Enochic source family for a similarly compact parameter rule.\n\n## Checks\n\n```json\n{\n  \"constant\": true,\n  \"ratios\": true,\n  \"calendars\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:20:35.612360+00:00\n\n## Record provenance\n\nExact record hash: `512b300884f11f09a386de89339f2159011ff73fce2f80bb436d553548622961`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-9a1eff41920cd0f8", "title": "File 12"}]}