{"id": "c785", "title": "C785 — Distinguish zero row residual from zero coordinate residual", "filename": "C785.md", "role": "Research action", "step": 785, "sha256": "df0aa21207ed23417c663600b11ee0bb530be48cafd7bd3499079a4165ee99f9", "bytes": 1126, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C785"], "download": "/sources/df0aa21207ed23417c663600b11ee0bb530be48cafd7bd3499079a4165ee99f9.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative", "Rounded"], "excerpt": "What residual does the inserted MT Cainan boundary inherit?", "content": "# C785 — Distinguish zero row residual from zero coordinate residual\n\n## Question\n\nWhat residual does the inserted MT Cainan boundary inherit?\n\n## Inputs\n\n```json\n{\n  \"regular_Shelah\": [\n    2421,\n    2421\n  ],\n  \"cumulative_Shelah\": [\n    4393,\n    4396\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File51a paired rows; File18 Cainan130/460\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:02:48.677719+00:00\n\n## Results\n\n```json\n{\n  \"regular_Cainan\": [\n    2551,\n    2551\n  ],\n  \"cumulative_Cainan\": [\n    4853,\n    4856\n  ],\n  \"residuals\": [\n    0,\n    3\n  ]\n}\n```\n\n## Finding\n\nThe inserted local durations are already round, but the cumulative Cainan coordinate inherits Shelah’s+3 residual:4853→4856. Local exactness and coordinate exactness are different properties.\n\n## Reassessment\n\nCheck Terah triangle compatibility with both rounding selectors.\n\n## Checks\n\n```json\n{\n  \"regular\": true,\n  \"cumulative\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:02:48.677947+00:00\n\n## Record provenance\n\nExact record hash: `76684580621cf081e99ba1ffd4554760a41ffeca85473f02b1256844bad31b59`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}]}