{"id": "c493", "title": "C493 — Cumulative residuals and completion selection", "filename": "C493.md", "role": "Research action", "step": 493, "sha256": "93fc2023fb566f82eb5d851723e6ca4621bb7989918e0584aeb4f7fce9aa6816", "bytes": 1461, "origins": ["C480–C1634/Research_Cycles/C0482_C0531/journal.json#C493"], "download": "/sources/93fc2023fb566f82eb5d851723e6ca4621bb7989918e0584aeb4f7fce9aa6816.md", "format": "md", "derived": true, "tags": ["Cumulative", "Rounded"], "excerpt": "Does cumulative rounding itself create the −2 change used in C481?", "content": "# C493 — Cumulative residuals and completion selection\n\n## Question\n\nDoes cumulative rounding itself create the −2 change used in C481?\n\n## Inputs\n\n```json\n{\n  \"MT_26_lifespans\": [\n    930,\n    912,\n    905,\n    910,\n    895,\n    962,\n    365,\n    969,\n    777,\n    950,\n    600,\n    438,\n    433,\n    464,\n    239,\n    239,\n    230,\n    148,\n    205,\n    175,\n    180,\n    147,\n    137,\n    133,\n    137,\n    120\n  ],\n  \"terminal_anchor\": 1406,\n  \"actual_completion\": 14004\n}\n```\n\n## Sources\n\n```json\n[\n  \"File51a §§16.1–16.2\",\n  \"File22 §5.1\"\n]\n```\n\n## Opened utc\n\n2026-09-27T22:41:47.928076+00:00\n\n## Results\n\n```json\n{\n  \"actual_sum\": 12600,\n  \"rounded_sum\": 12600,\n  \"positive_rounding\": 12,\n  \"negative_rounding\": -12,\n  \"Moses_line_heads\": [\n    14006,\n    14006\n  ],\n  \"completion_offset\": -2\n}\n```\n\n## Finding\n\nCumulative rounding preserves12600 and the14006 Moses-line head exactly. The−2 is the selected lower completion endpoint14004, not a cumulative rounding error. The bridge uses both row residuals and explicit endpoint selection.\n\n## Reassessment\n\nCombine the two separately explained shifts and test which endpoint alternatives preserve the anchor.\n\n## Checks\n\n```json\n{\n  \"total\": true,\n  \"residuals\": true\n}\n```\n\n## Closed utc\n\n2026-09-27T22:41:47.928329+00:00\n\n## Record provenance\n\nExact record hash: `191fcfd19b8f4216ab56a16ed411f0e8f1405b5a2eb2e1412f960d17370da41e`\n\nSource journal: `Research_Cycles/C0482_C0531/journal.json`", "journalDownload": "/sources/6eaeccad4734eff2f6ac20ba847967877b944f9758c53c712ac8b5be2ddf61eb.json", "evidenceLinks": [{"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}, {"id": "d-1c77fd504afbf59b", "title": "File 22"}]}