{"id": "c1204", "title": "C1204 — Separate the two loss types by the known cap branch", "filename": "C1204.md", "role": "Research action", "step": 1204, "sha256": "7935a34f279eb85e165ec564585ed2de47981721815912f829dfb933fb37d91b", "bytes": 1152, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1204"], "download": "/sources/7935a34f279eb85e165ec564585ed2de47981721815912f829dfb933fb37d91b.md", "format": "md", "derived": true, "tags": ["Rounded"], "excerpt": "Are rounding residual and cap excess independent missing quantities on every row?", "content": "# C1204 — Separate the two loss types by the known cap branch\n\n## Question\n\nAre rounding residual and cap excess independent missing quantities on every row?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1202\",\n  \"C1203\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:26:13.150833+00:00\n\n## Results\n\n```json\n{\n  \"branch_information\": {\n    \"path\": \"model/cap_round_branch_information.json\",\n    \"sha256\": \"496cab05f8d37f8f3f5ac004911fb79736ca2e4435da321932625405a2f45d59\",\n    \"bytes\": 2128\n  }\n}\n```\n\n## Finding\n\nThe two loss registers are not two independent unknowns per row. A known clipped row has y=c, fixing its rounding residual; a known unclipped row has zero excess and needs only its rounding residual.\n\n## Reassessment\n\nVerify reconstruction of all nine baseline lives using the branch-appropriate register.\n\n## Checks\n\n```json\n{\n  \"identity_all\": true,\n  \"three_clipped\": true,\n  \"branch_constraints\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:26:13.151348+00:00\n\n## Record provenance\n\nExact record hash: `582d9b8d493849e89b92c6868c8b2072903e0d9da9fc0d9ed995d316d2ccdcc8`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-496cab05f8d37f8f", "title": "model/cap_round_branch_information.json"}]}