{"id": "c567", "title": "C567 — Unify full half and quarter Key scales", "filename": "C567.md", "role": "Research action", "step": 567, "sha256": "25aca879aeb2848cff95f9da6cf1cf297d58a98aebbf24f75d8f56b6df959887", "bytes": 1085, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C567"], "download": "/sources/25aca879aeb2848cff95f9da6cf1cf297d58a98aebbf24f75d8f56b6df959887.md", "format": "md", "derived": true, "tags": ["Covenant"], "excerpt": "Do14,7 and3.5 require separate expansion laws?", "content": "# C567 — Unify full half and quarter Key scales\n\n## Question\n\nDo14,7 and3.5 require separate expansion laws?\n\n## Inputs\n\n```json\n{\n  \"scales\": [\n    7,\n    \"7/2\",\n    \"7/4\"\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File62 §8.3; File60 §7\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:15:57.467599+00:00\n\n## Results\n\n```json\n{\n  \"input_output_gain\": [\n    [\n      161,\n      175,\n      14\n    ],\n    [\n      \"161/2\",\n      \"175/2\",\n      7\n    ],\n    [\n      \"161/4\",\n      \"175/4\",\n      \"7/2\"\n    ]\n  ],\n  \"general_rule\": \"23u→25u, gain2u\"\n}\n```\n\n## Finding\n\nThe three gains are scaled evaluations of E, not new Keys. They connect the161/175 Covenant unit to80.5/87.5 and40.25/43.75 duration units without making their event placements interchangeable.\n\n## Reassessment\n\nCompare the two source routes from483 to490.\n\n## Checks\n\n```json\n{\n  \"rule\": true,\n  \"gains\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:15:57.467964+00:00\n\n## Record provenance\n\nExact record hash: `0742ca056f0055f89dbf2ad53ec97c22107efb6313ba309b6f077554fd3c7bb3`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-be42daca1d82dac9", "title": "File 62"}, {"id": "d-12a48221b7fdcdcd", "title": "File 60"}]}