{"id": "c1199", "title": "C1199 — Derive the row rounding carry from the hidden residual sum", "filename": "C1199.md", "role": "Research action", "step": 1199, "sha256": "7308f22ffef4fdd1a09f05c4eabc16dadc90ee38def3a025e33b7c161a5a141b", "bytes": 1236, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1199"], "download": "/sources/7308f22ffef4fdd1a09f05c4eabc16dadc90ee38def3a025e33b7c161a5a141b.md", "format": "md", "derived": true, "tags": ["Cumulative", "Rounded"], "excerpt": "How does the joint observation control the difference between rounded life and rounded parts?", "content": "# C1199 — Derive the row rounding carry from the hidden residual sum\n\n## Question\n\nHow does the joint observation control the difference between rounded life and rounded parts?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1191\",\n  \"C1192\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:25:01.340720+00:00\n\n## Results\n\n```json\n{\n  \"carry_bridge\": {\n    \"path\": \"model/joint_rounding_carry_bridge.json\",\n    \"sha256\": \"09df548a9ff72ded568e716ef1fca3f0cb17d025f60f6662d99181bdcbd7b46e\",\n    \"bytes\": 4134\n  },\n  \"branches\": {\n    \"-4\": -5,\n    \"-3\": -5,\n    \"-2\": 0,\n    \"-1\": 0,\n    \"0\": 0,\n    \"1\": 0,\n    \"2\": 0,\n    \"3\": 5,\n    \"4\": 5\n  }\n}\n```\n\n## Finding\n\nThe same residual sum that measures joint ambiguity determines the carry between rounded lifespan and rounded parts. Carry is−5 for z≤−3, zero for |z|≤2, and+5 for z≥3.\n\n## Reassessment\n\nCheck whether the carry by itself retains the exact joint recovery information.\n\n## Checks\n\n```json\n{\n  \"all_rows\": true,\n  \"three_branches\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:25:01.341533+00:00\n\n## Record provenance\n\nExact record hash: `6b92f05310cbabfa085134c859ff27941d3690ae2debfe145287ead85194d7fc`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-09df548a9ff72ded", "title": "model/joint_rounding_carry_bridge.json"}]}