{"id": "c1208", "title": "C1208 — Explain the change from exact to rounded cap reduction", "filename": "C1208.md", "role": "Research action", "step": 1208, "sha256": "a99052314ef89d050c3b5d2f26d0099591be75f12e1f02adf37b618341331aba", "bytes": 1141, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1208"], "download": "/sources/a99052314ef89d050c3b5d2f26d0099591be75f12e1f02adf37b618341331aba.md", "format": "md", "derived": true, "tags": ["Rounded"], "excerpt": "Why does total488 become485 under row rounding?", "content": "# C1208 — Explain the change from exact to rounded cap reduction\n\n## Question\n\nWhy does total488 become485 under row rounding?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1204\",\n  \"C1143\",\n  \"C1131 inherited cap-round result\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:27:09.166462+00:00\n\n## Results\n\n```json\n{\n  \"loss_identity\": {\n    \"path\": \"model/cap_round_loss_identity.json\",\n    \"sha256\": \"238adb4d7804f3f7873b3ee15c3ac61e23e8c1f7b8bf0615c2b7b462b5c3cb14\",\n    \"bytes\": 1794\n  },\n  \"exact_total\": 488,\n  \"rounded_total\": 485\n}\n```\n\n## Finding\n\nRounded reduction equals exact removed life plus the difference of the two rounding errors. The three SP cap losses115/249/124 become115/250/120, explaining488→485 without a second cap rule.\n\n## Reassessment\n\nCheck what commutes when both the cap and its input are rounded consistently.\n\n## Checks\n\n```json\n{\n  \"identity_all\": true,\n  \"totals\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:27:09.167822+00:00\n\n## Record provenance\n\nExact record hash: `1244961a0b50d087dce02dadbe3282140ad91c9f13efd6c1ebc5df68703fb63c`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-238adb4d7804f3f7", "title": "model/cap_round_loss_identity.json"}]}