{"id": "c690", "title": "C690 — Reconstruct the three cumulative completion paths", "filename": "C690.md", "role": "Research action", "step": 690, "sha256": "eda25635f918a6b7f8c31b0fef809e65c2e8d134cfbfaaaf924cc96f035e3d87", "bytes": 1566, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C690"], "download": "/sources/eda25635f918a6b7f8c31b0fef809e65c2e8d134cfbfaaaf924cc96f035e3d87.md", "format": "md", "derived": true, "tags": ["Cumulative", "Rounded", "Calendar Keys"], "excerpt": "Can one retained2940 component generate the12600/12740/13440 family?", "content": "# C690 — Reconstruct the three cumulative completion paths\n\n## Question\n\nCan one retained2940 component generate the12600/12740/13440 family?\n\n## Inputs\n\n```json\n{\n  \"source_head\": 14006,\n  \"hinge\": 4346,\n  \"tail\": 1406,\n  \"upper\": 9660,\n  \"retained_lower\": 2940\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §10.2; inherited source family\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:14:17.581267+00:00\n\n## Results\n\n```json\n{\n  \"paths\": [\n    {\n      \"upper\": 9660,\n      \"lower\": 2940,\n      \"total\": 12600,\n      \"head\": 14006\n    },\n    {\n      \"upper\": 9800,\n      \"lower\": 2940,\n      \"total\": 12740,\n      \"head\": 14146\n    },\n    {\n      \"upper\": 10500,\n      \"lower\": 2940,\n      \"total\": 13440,\n      \"head\": 14846\n    }\n  ],\n  \"calendar_bodies\": [\n    12600,\n    12740,\n    13440\n  ],\n  \"upper_gain\": [\n    0,\n    140,\n    840\n  ]\n}\n```\n\n## Finding\n\nHolding4346→1406 fixed while converting only the9660 upper arm generates all three source totals12600/12740/13440. The generated heads14006/14146/14846 retain their existing status. This realizes the micro register family through retained macro components, not one whole-span conversion.\n\n## Reassessment\n\nConsolidate the micro-to-Rounded bridge and decide which anchored routes best explain its placement.\n\n## Checks\n\n```json\n{\n  \"source_paths\": true,\n  \"heads\": true,\n  \"gains\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:14:17.581549+00:00\n\n## Record provenance\n\nExact record hash: `095d04922354663bba3291939fc2ccf9d76a4e0bc263e88c8a8d95761eacc34c`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}