{"id": "c1202", "title": "C1202 — Derive the composite cap-plus-round inverse set", "filename": "C1202.md", "role": "Research action", "step": 1202, "sha256": "c4c71204bc79b6ba9c8fe5dd0a5ede9fa00746a63b1524621d1418fe92daf7a4", "bytes": 1053, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1202"], "download": "/sources/c4c71204bc79b6ba9c8fe5dd0a5ede9fa00746a63b1524621d1418fe92daf7a4.md", "format": "md", "derived": true, "tags": ["Cumulative", "Rounded", "Inverse"], "excerpt": "What original lifespans can produce a fixed rounded capped value when capacity is known?", "content": "# C1202 — Derive the composite cap-plus-round inverse set\n\n## Question\n\nWhat original lifespans can produce a fixed rounded capped value when capacity is known?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1201\",\n  \"C1143\",\n  \"C1131 cap analysis\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:26:09.238998+00:00\n\n## Results\n\n```json\n{\n  \"fibre_law\": {\n    \"path\": \"model/cap_round_fibre_law.json\",\n    \"sha256\": \"4ff7af76d04d05a1559f9918457b5a1ea19a6369cf01f0740073105104291fbf\",\n    \"bytes\": 2166\n  }\n}\n```\n\n## Finding\n\nAt the rounded capacity, a finite rounding cell joins an unbounded cap tail. The rounded capped output can therefore forget even whether clipping occurred.\n\n## Reassessment\n\nApply the threshold formula to the three SP clipped capacities.\n\n## Checks\n\n```json\n{\n  \"thresholds\": true,\n  \"tails\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:26:09.239508+00:00\n\n## Record provenance\n\nExact record hash: `df5e09d75d05022c7bc20ea540505645c79ac555ed0492221773a5d49d1198f6`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-4ff7af76d04d05a1", "title": "model/cap_round_fibre_law.json"}]}