{"id": "c1220", "title": "C1220 — Prove coherence of consecutive rounded-residual translations", "filename": "C1220.md", "role": "Research action", "step": 1220, "sha256": "8fbb6a865e3385fc1cb1cf827c0d71715e8a1e6d8567b0505cf1481d1be679f0", "bytes": 1127, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1220"], "download": "/sources/8fbb6a865e3385fc1cb1cf827c0d71715e8a1e6d8567b0505cf1481d1be679f0.md", "format": "md", "derived": true, "tags": ["Rounded"], "excerpt": "Does the lifted action depend on how an admitted total shift is decomposed?", "content": "# C1220 — Prove coherence of consecutive rounded-residual translations\n\n## Question\n\nDoes the lifted action depend on how an admitted total shift is decomposed?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1218\",\n  \"C1219\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:30:59.326469+00:00\n\n## Results\n\n```json\n{\n  \"composition\": {\n    \"path\": \"model/rounded_translation_composition.json\",\n    \"sha256\": \"75a28f7bb3d4a6f20397c95c1ee5d51b30d61bd6dc6d190fbb0db940da93dba8\",\n    \"bytes\": 384\n  },\n  \"diagnostic_cases\": 25\n}\n```\n\n## Finding\n\nThe lifted translations compose exactly because they retain the full original value. Their coherence is mathematical; source authorization of each intermediate state remains separate.\n\n## Reassessment\n\nDetermine precisely when the residual may be dropped without breaking a universal shift rule.\n\n## Checks\n\n```json\n{\n  \"all_cases\": true,\n  \"25cases\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:30:59.326980+00:00\n\n## Record provenance\n\nExact record hash: `c74d03e7bb0f6fd6dc2f9508f6ca8d8f644702e763748aefb46f89434f09b18d`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-75a28f7bb3d4a6f2", "title": "model/rounded_translation_composition.json"}]}