{"id": "c713", "title": "C713 — Derive whole-total effects from a retained partition", "filename": "C713.md", "role": "Research action", "step": 713, "sha256": "8d77ef6896494907fb8699ab5480662c53ae20e25d93ce00eafc84184a6d6151", "bytes": 1219, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C713"], "download": "/sources/8d77ef6896494907fb8699ab5480662c53ae20e25d93ce00eafc84184a6d6151.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "Why does partialP produce the364/360 ratio in the new macro family?", "content": "# C713 — Derive whole-total effects from a retained partition\n\n## Question\n\nWhy does partialP produce the364/360 ratio in the new macro family?\n\n## Inputs\n\n```json\n{\n  \"upper\": 9660,\n  \"lower\": 2940,\n  \"total\": 12600\n}\n```\n\n## Sources\n\n```json\n[\n  \"C690; Supplement A §10.3\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:21:39.291265+00:00\n\n## Results\n\n```json\n{\n  \"converted_fraction\": \"23/30\",\n  \"retained_fraction\": \"7/30\",\n  \"effective_total_ratios\": [\n    \"91/90\",\n    \"16/15\"\n  ],\n  \"calendar_ratios\": [\n    \"91/90\",\n    \"16/15\"\n  ]\n}\n```\n\n## Finding\n\nThe converted upper arm is23/30 of12600. Therefore partialP has total ratio1+(P−1)23/30=91/90, and partialE has ratio16/15. These are consequences of this retained partition, explaining its calendar-body outputs without adding universal Keys.\n\n## Reassessment\n\nCompare the new partial-conversion mechanism with the earlier one-sixth and one-twenty-sixth bridges.\n\n## Checks\n\n```json\n{\n  \"fractions\": true,\n  \"effects\": true,\n  \"outputs\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:21:39.291945+00:00\n\n## Record provenance\n\nExact record hash: `4ade86b4f2907d8fc48a9379ec009003bfd126e453b701d6f273a2e02778ab15`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}