{"id": "c1218", "title": "C1218 — Lift source translations to Rounded values plus residuals", "filename": "C1218.md", "role": "Research action", "step": 1218, "sha256": "011110284de3dfb0d6b488940c09399bba5bb50fa828eb62b31042ba23a84f42", "bytes": 1791, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1218"], "download": "/sources/011110284de3dfb0d6b488940c09399bba5bb50fa828eb62b31042ba23a84f42.md", "format": "md", "derived": true, "tags": ["Cumulative", "Rounded"], "excerpt": "How can a non-grid row change act coherently on the Rounded representation?", "content": "# C1218 — Lift source translations to Rounded values plus residuals\n\n## Question\n\nHow can a non-grid row change act coherently on the Rounded representation?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1213–C1217\",\n  \"prep/round_joint_fibres.md\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:30:55.328517+00:00\n\n## Results\n\n```json\n{\n  \"translation\": {\n    \"path\": \"model/rounded_residual_translation.json\",\n    \"sha256\": \"f9e2b0fdc53f2c54c40d63f1de6d2aaa0aa0eef6eb8f7fe79eb7cde3bd98fdee\",\n    \"bytes\": 936\n  },\n  \"examples\": [\n    {\n      \"x\": 777,\n      \"d\": -24,\n      \"Q_x\": 775,\n      \"rho\": 2,\n      \"rounded_shift\": -20,\n      \"new_rounded\": 755,\n      \"new_residual\": -2\n    },\n    {\n      \"x\": 595,\n      \"d\": -24,\n      \"Q_x\": 595,\n      \"rho\": 0,\n      \"rounded_shift\": -25,\n      \"new_rounded\": 570,\n      \"new_residual\": 1\n    },\n    {\n      \"x\": 438,\n      \"d\": 27,\n      \"Q_x\": 440,\n      \"rho\": -2,\n      \"rounded_shift\": 25,\n      \"new_rounded\": 465,\n      \"new_residual\": 0\n    },\n    {\n      \"x\": 433,\n      \"d\": 27,\n      \"Q_x\": 435,\n      \"rho\": -2,\n      \"rounded_shift\": 25,\n      \"new_rounded\": 460,\n      \"new_residual\": 0\n    }\n  ]\n}\n```\n\n## Finding\n\nThe retained residual determines how an off-grid change crosses rounded cells. This single rule explains why the same−24 change produces−20 in Lamech’s rounded lifespan and−25 in his rounded remainder.\n\n## Reassessment\n\nVerify the lifted rule across every ordinary existing tradition comparison.\n\n## Checks\n\n```json\n{\n  \"all_examples\": true,\n  \"different_shifts\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:30:55.328995+00:00\n\n## Record provenance\n\nExact record hash: `ab653031c1d0b310364ae75a98de6bfb2be19a9338c613c6a4e47707f1f75ba4`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-f9e2b0fdc53f2c54", "title": "model/rounded_residual_translation.json"}]}