{"id": "c1306", "title": "C1306 — Register coherent translation through Rounded residuals", "filename": "C1306.md", "role": "Research action", "step": 1306, "sha256": "cde9b5d9f39b370cb31b866cf8c0190da888a11bfeb7ab1e657a16c9b312a9df", "bytes": 1114, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1306"], "download": "/sources/cde9b5d9f39b370cb31b866cf8c0190da888a11bfeb7ab1e657a16c9b312a9df.md", "format": "md", "derived": true, "tags": ["Rounded"], "excerpt": "How does exactsourcechange remaincompatiblewiththeRoundedrepresentation?", "content": "# C1306 — Register coherent translation through Rounded residuals\n\n## Question\n\nHow does exactsourcechange remaincompatiblewiththeRoundedrepresentation?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1305\",\n  \"C1218–C1221\",\n  \"C1278\"\n]\n```\n\n## Opened utc\n\n2026-09-28T06:10:25.090906+00:00\n\n## Results\n\n```json\n{\n  \"residual_relation\": {\n    \"path\": \"model/relation_rounded_residuals.json\",\n    \"sha256\": \"1c0b4aa4f98bb9e353a968eb99533277ba860ce60b040fe488a24060ad35574e\",\n    \"bytes\": 839\n  }\n}\n```\n\n## Finding\n\nTheRoundedplusresidual representation carries exactsourcechanges coherently, anditsaccumulatedresiduals recovercompletepaths. Itworks byretaininginformation, notby makingroundingadditive.\n\n## Reassessment\n\nRegister uniformKeycompatibility withsums andthelimitforcomponent-specificKeys.\n\n## Checks\n\n```json\n{\n  \"two_applications\": true,\n  \"proof_bound\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T06:10:25.091366+00:00\n\n## Record provenance\n\nExact record hash: `cd8423799fd21e6fc407edabdcdb75d6a5b7bbb127020996a63de30f268b80c9`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-1c0b4aa4f98bb9e3", "title": "model/relation_rounded_residuals.json"}]}