{"id": "c1278", "title": "C1278 — Recover the whole exact Moses field from the Rounded field", "filename": "C1278.md", "role": "Research action", "step": 1278, "sha256": "aa7809e9229ba5dd70e0c2917a1a0a2e98cb640ac3478d9336ab215f6824b35f", "bytes": 1162, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1278"], "download": "/sources/aa7809e9229ba5dd70e0c2917a1a0a2e98cb640ac3478d9336ab215f6824b35f.md", "format": "md", "derived": true, "tags": ["Rounded", "Inverse"], "excerpt": "Do accumulatedrowresiduals retain everyintermediate coordinate?", "content": "# C1278 — Recover the whole exact Moses field from the Rounded field\n\n## Question\n\nDo accumulatedrowresiduals retain everyintermediate coordinate?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1277\",\n  \"C1234\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:59:58.768804+00:00\n\n## Results\n\n```json\n{\n  \"whole_field_recovery\": {\n    \"path\": \"model/Moses_complete_residual_recovery.json\",\n    \"sha256\": \"6e6ac50f823898352efd4b6313348899dfbc8f55e8fda1a51a04c975336db550\",\n    \"bytes\": 4249\n  },\n  \"nodes\": 25,\n  \"head_residual\": 6\n}\n```\n\n## Finding\n\nAll25 exactcoordinates are recovered fromtheir Roundedcoordinates andthelocated residualsums. Thehead residual6 staysun-normalized, preserving thepublished4106 Roundedhead while recoveringstrict4112.\n\n## Reassessment\n\nWrite thegenealogy-to-inverse bridge withitsoperationorder andsource-roleconstraints.\n\n## Checks\n\n```json\n{\n  \"all25\": true,\n  \"all_recovered\": true,\n  \"head6\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:59:58.770216+00:00\n\n## Record provenance\n\nExact record hash: `c3e225ca05688f0f3a1d89f692cf58d9b1809db67ae1ef28979439cc7a1dc30b`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-6e6ac50f82389835", "title": "model/Moses_complete_residual_recovery.json"}]}