{"id": "c714", "title": "C714 — Unify the partial-conversion bridges", "filename": "C714.md", "role": "Research action", "step": 714, "sha256": "44fa5397f5603d8e227b66727c5d99aacb445947a07248d81dbb3982e99d6736", "bytes": 1744, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C714"], "download": "/sources/44fa5397f5603d8e227b66727c5d99aacb445947a07248d81dbb3982e99d6736.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "Can one retained-fraction equation describe the old and new interfaces?", "content": "# C714 — Unify the partial-conversion bridges\n\n## Question\n\nCan one retained-fraction equation describe the old and new interfaces?\n\n## Inputs\n\n```json\n{\n  \"rule\": \"effective(k,f)=1+(k−1)f\",\n  \"cases\": [\n    [\n      \"E\",\n      \"1/6\",\n      \"P\"\n    ],\n    [\n      \"E\",\n      \"1/26\",\n      \"J\"\n    ],\n    [\n      \"P\",\n      \"23/30\",\n      \"91/90\"\n    ],\n    [\n      \"E\",\n      \"23/30\",\n      \"16/15\"\n    ]\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"C631 partial-expansion results; C713\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:21:54.528322+00:00\n\n## Results\n\n```json\n{\n  \"cases\": [\n    {\n      \"key\": \"25/23\",\n      \"converted_fraction\": \"1/6\",\n      \"effective\": \"70/69\",\n      \"target\": \"70/69\"\n    },\n    {\n      \"key\": \"25/23\",\n      \"converted_fraction\": \"1/26\",\n      \"effective\": \"300/299\",\n      \"target\": \"300/299\"\n    },\n    {\n      \"key\": \"70/69\",\n      \"converted_fraction\": \"23/30\",\n      \"effective\": \"91/90\",\n      \"target\": \"91/90\"\n    },\n    {\n      \"key\": \"25/23\",\n      \"converted_fraction\": \"23/30\",\n      \"effective\": \"16/15\",\n      \"target\": \"16/15\"\n    }\n  ]\n}\n```\n\n## Finding\n\nOne retained-fraction law explains four interfaces: partialE can equal wholeP or wholeJ, and the newly supplied23/30 upper component generates the two macro calendar ratios. The source partition remains the premise that licenses each chronological use.\n\n## Reassessment\n\nSeparate this duration law from the extra anchor condition needed for endpoint agreement.\n\n## Checks\n\n```json\n{\n  \"all_four\": true,\n  \"fractions_valid\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:21:54.528635+00:00\n\n## Record provenance\n\nExact record hash: `b25c9fcae07ef36f494c6880ff7e5f2823e4470e576ecd04fbc444a8fa3df804`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}