{"id": "c533", "title": "C533 — Uniform and mixed calendar branches", "filename": "C533.md", "role": "Research action", "step": 533, "sha256": "5426d3a2a4ea799bb7cdb1aef4fbe8eb00e504bfcdd1c6b9a9210045d6236a49", "bytes": 1160, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C533"], "download": "/sources/5426d3a2a4ea799bb7cdb1aef4fbe8eb00e504bfcdd1c6b9a9210045d6236a49.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "Can the completed299 and161 arms be treated as one uniform expansion?", "content": "# C533 — Uniform and mixed calendar branches\n\n## Question\n\nCan the completed299 and161 arms be treated as one uniform expansion?\n\n## Inputs\n\n```json\n{\n  \"arms\": [\n    299,\n    161\n  ],\n  \"E\": \"25/23\",\n  \"J\": \"300/299\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"File60 §5\",\n  \"C532\"\n]\n```\n\n## Opened utc\n\n2026-09-27T23:59:21.577572+00:00\n\n## Results\n\n```json\n{\n  \"all_E\": [\n    325,\n    175,\n    500\n  ],\n  \"all_J\": [\n    300,\n    \"2100/13\",\n    \"6000/13\"\n  ],\n  \"mixed\": [\n    300,\n    175,\n    475\n  ]\n}\n```\n\n## Finding\n\nUniform E preserves the partition as325+175=500. The mixed J/E completion is300+175=475 and is a different operation. Shared coefficients do not make the Keys interchangeable; source-declared mixed branches must retain their separate labels.\n\n## Reassessment\n\nTest the actual common1566 landing where File60 deliberately uses two different Keys.\n\n## Checks\n\n```json\n{\n  \"E_total\": true,\n  \"mixed\": true,\n  \"distinct\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T23:59:21.577876+00:00\n\n## Record provenance\n\nExact record hash: `ab6e064311e941d5c0963b904abcbee26c793332d130c148bf1a200f9c3900b6`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-12a48221b7fdcdcd", "title": "File 60"}]}