{"id": "c1200", "title": "C1200 — Separate carry information from exact residual information", "filename": "C1200.md", "role": "Research action", "step": 1200, "sha256": "a261f90f67d335c768d0761ef3629b27a27e8a572fd9faec50289b68e2a12fca", "bytes": 1149, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1200"], "download": "/sources/a261f90f67d335c768d0761ef3629b27a27e8a572fd9faec50289b68e2a12fca.md", "format": "md", "derived": true, "tags": ["Cumulative", "Rounded"], "excerpt": "Can knowing the carry replace knowing the exact lifespan in joint recovery?", "content": "# C1200 — Separate carry information from exact residual information\n\n## Question\n\nCan knowing the carry replace knowing the exact lifespan in joint recovery?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1199\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:25:03.301412+00:00\n\n## Results\n\n```json\n{\n  \"carry_information\": {\n    \"path\": \"model/rounding_carry_information.json\",\n    \"sha256\": \"92e6d16905b18c5ee3305c094f7ef6fc0af0339cb3dc69ba596d574bf7f12d12\",\n    \"bytes\": 365\n  },\n  \"pair_counts\": {\n    \"-5\": 3,\n    \"0\": 19,\n    \"5\": 3\n  }\n}\n```\n\n## Finding\n\nA carry stores only a branch: its three classes contain3,19 and3 residual pairs. Even an extreme carry leaves three possible exact decompositions when exact life is absent.\n\n## Reassessment\n\nCombine this result with the cap, which removes excess lifespan rather than a small rounding residual.\n\n## Checks\n\n```json\n{\n  \"partition25\": true,\n  \"counts\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:25:03.301807+00:00\n\n## Record provenance\n\nExact record hash: `813eaaeffb6b87bd3fd12d69ccad203afa18ebae55aa133985fdb18b4f4b1464`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-92e6d16905b18c5e", "title": "model/rounding_carry_information.json"}]}