{"id": "c752", "title": "C752 — Derive the finite rounding defect law", "filename": "C752.md", "role": "Research action", "step": 752, "sha256": "25f870fb6195400b4941bd0d89b00955c4301f3036c841adc609f6c78e55bf0d", "bytes": 1239, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C752"], "download": "/sources/25f870fb6195400b4941bd0d89b00955c4301f3036c841adc609f6c78e55bf0d.md", "format": "md", "derived": true, "tags": ["Rounded"], "excerpt": "Can one residue table explain every parts-versus-total defect?", "content": "# C752 — Derive the finite rounding defect law\n\n## Question\n\nCan one residue table explain every parts-versus-total defect?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C749–750; File51a rounding rules\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:53:30.703808+00:00\n\n## Results\n\n```json\n{\n  \"table_b_rows_r_columns\": [\n    [\n      0,\n      0,\n      0,\n      0,\n      0\n    ],\n    [\n      0,\n      0,\n      -5,\n      0,\n      0\n    ],\n    [\n      0,\n      -5,\n      -5,\n      0,\n      0\n    ],\n    [\n      0,\n      0,\n      0,\n      5,\n      5\n    ],\n    [\n      0,\n      0,\n      0,\n      5,\n      0\n    ]\n  ],\n  \"formula\": \"K(b,r)=Q(b)+Q(r)-Q(b+r)\",\n  \"periodicity\": \"Q(x+5k)=Q(x)+5k\"\n}\n```\n\n## Finding\n\nEvery compatible integer row belongs to one of 25 residue classes; defects are only −5,0,+5. Methuselah and Reu share class(2,2).\n\n## Reassessment\n\nCheck whether the three traditions add new defect classes within the admitted domains.\n\n## Checks\n\n```json\n{\n  \"values\": true,\n  \"periodic_exhaustion\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:53:30.706032+00:00\n\n## Record provenance\n\nExact record hash: `5ccd38e85638d691f9012d5c0547fe166baa524b185c348fa0797ba2e05ac2e1`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json", "evidenceLinks": [{"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}]}