{"id": "c684", "title": "C684 — Connect civil brackets with the micro gain", "filename": "C684.md", "role": "Research action", "step": 684, "sha256": "0eaa08b5154ca1b168d486864a0521147c453ea3f25d476858b289d1475e8797", "bytes": 1199, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C684"], "download": "/sources/0eaa08b5154ca1b168d486864a0521147c453ea3f25d476858b289d1475e8797.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "How do the supplied750 brackets and AD27→30 completion arise?", "content": "# C684 — Connect civil brackets with the micro gain\n\n## Question\n\nHow do the supplied750 brackets and AD27→30 completion arise?\n\n## Inputs\n\n```json\n{\n  \"civil_pairs\": [\n    [\n      726,\n      25\n    ],\n    [\n      724,\n      27\n    ]\n  ],\n  \"micro_input\": \"69/2\",\n  \"AD_start\": 27\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §§5.3–5.4\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:13:00.121864+00:00\n\n## Results\n\n```json\n{\n  \"civil_widths\": [\n    750,\n    750\n  ],\n  \"coordinate_translation\": 2,\n  \"E_micro_gain\": 3,\n  \"completed_AD_label\": 30\n}\n```\n\n## Finding\n\nBoth supplied civil pairs have width750 and differ by a uniform two-year forward translation. The separate AD27→30 completion uses the micro E-gain3. Equal durations and later completion are connected operations with separately supplied anchors.\n\n## Reassessment\n\nClose the three-calendar calibration triangle at the micro input34.5.\n\n## Checks\n\n```json\n{\n  \"widths\": true,\n  \"gain\": true,\n  \"completion\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:13:00.122209+00:00\n\n## Record provenance\n\nExact record hash: `16f3165d0ad36e19154aa17131c11fbedf5e7f7ece0ca2f8ed67e20274403d66`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}