{"id": "c978", "title": "C978 — Rounding the cap counts", "filename": "C978.md", "role": "Research action", "step": 978, "sha256": "f5cc9b4df554045b85c96bec4024a34087f974d49f13c2d2114df85694719302", "bytes": 1189, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C978"], "download": "/sources/f5cc9b4df554045b85c96bec4024a34087f974d49f13c2d2114df85694719302.md", "format": "md", "derived": true, "tags": ["Rounded"], "excerpt": "Does nearest-five rounding commute with the source minimum?", "content": "# C978 — Rounding the cap counts\n\n## Question\n\nDoes nearest-five rounding commute with the source minimum?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C953\",\n  \"C955\",\n  \"C956\",\n  \"File51a nearest-five policy\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:50:40.100297+00:00\n\n## Results\n\n```json\n{\n  \"field\": {\n    \"path\": \"model/sp_cap_rounded_counts.json\",\n    \"sha256\": \"ec28f7907b254a793adc02ef6124384b9be3e2f6bf7b3ce347bd2708b35ae779\",\n    \"bytes\": 332\n  },\n  \"rounded_lives\": [\n    930,\n    910,\n    905,\n    910,\n    895,\n    845,\n    365,\n    720,\n    655\n  ],\n  \"proof\": \"A monotone map on a total order preserves binary minima.\"\n}\n```\n\n## Finding\n\nCount rounding commutes with the cap across all nine rows because the rounding map is monotone. This does not yet define Rounded date labels.\n\n## Reassessment\n\nCheck whether this source field keeps the same strict active support.\n\n## Checks\n\n```json\n{\n  \"commutes_all_rows\": true,\n  \"expected_counts\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:50:40.100762+00:00\n\n## Record provenance\n\nExact record hash: `fc8fb73429f76d6d11bad550902e0a5f1f589f89f4f4e0e7a1fabc19ea6591ff`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-ec28f7907b254a79", "title": "model/sp_cap_rounded_counts.json"}, {"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}]}