{"id": "c538", "title": "C538 — The14 gain links reconciliation and clutch scales", "filename": "C538.md", "role": "Research action", "step": 538, "sha256": "a6492680c3574fb075916f12b5af243f0b92cf4579f835636ac3433715ebbcc1", "bytes": 1234, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C538"], "download": "/sources/a6492680c3574fb075916f12b5af243f0b92cf4579f835636ac3433715ebbcc1.md", "format": "md", "derived": true, "tags": ["Calendar Keys", "Covenant"], "excerpt": "What common arithmetic underlies147/161/175 and the full/half clutch values?", "content": "# C538 — The14 gain links reconciliation and clutch scales\n\n## Question\n\nWhat common arithmetic underlies147/161/175 and the full/half clutch values?\n\n## Inputs\n\n```json\n{\n  \"source_values\": [\n    147,\n    161,\n    175\n  ],\n  \"calendar_factor\": \"25/23\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"File60 §§2.6,3.3; File62 dependency note\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:00:48.866885+00:00\n\n## Results\n\n```json\n{\n  \"coefficients_over7\": [\n    21,\n    23,\n    25\n  ],\n  \"E_gain\": 14,\n  \"half_relation\": {\n    \"input\": \"161/2\",\n    \"output\": \"175/2\",\n    \"gain\": 7\n  },\n  \"center_identity\": 322\n}\n```\n\n## Finding\n\nThe progression is7×(21,23,25). E raises161 to175 by14; halving gives80.5→87.5 by7. This provides a value-level bridge to T14/H7, while their chronology domains still require the File61/62 source rules.\n\n## Reassessment\n\nReconstruct the ordered147 rails, testing translation of both endpoints rather than isolated widths.\n\n## Checks\n\n```json\n{\n  \"progression\": true,\n  \"half\": true,\n  \"center\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:00:48.867078+00:00\n\n## Record provenance\n\nExact record hash: `a9fd20f178bc310ed114e04f8fd566d51261b678e7b14c344f59fc875e6c7940`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-be42daca1d82dac9", "title": "File 62"}, {"id": "d-d580afd48d6e12d6", "title": "File 61"}, {"id": "d-12a48221b7fdcdcd", "title": "File 60"}]}