{"id": "c1059", "title": "C1059 — All proper E prefixes remain fractional", "filename": "C1059.md", "role": "Research action", "step": 1059, "sha256": "fa8b2de23bede3cb6ba5b17e2af816fce7ea69fc1df64daee01ac15445384867", "bytes": 1278, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1059"], "download": "/sources/fa8b2de23bede3cb6ba5b17e2af816fce7ea69fc1df64daee01ac15445384867.md", "format": "md", "derived": true, "tags": [], "excerpt": "Does an integral outer completion imply integral internal coordinates?", "content": "# C1059 — All proper E prefixes remain fractional\n\n## Question\n\nDoes an integral outer completion imply integral internal coordinates?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1058\",\n  \"File52c §3.4\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:09:17.331603+00:00\n\n## Results\n\n```json\n{\n  \"prefix_field\": {\n    \"path\": \"model/completed_path_prefix_field.json\",\n    \"sha256\": \"c98eb407ba3004a21db63eb3b15047d068852f258f3c057c20f80431d6650339\",\n    \"bytes\": 1594\n  },\n  \"residues_by_path\": [\n    [\n      6,\n      2,\n      0\n    ],\n    [\n      6,\n      4,\n      0\n    ],\n    [\n      6,\n      2,\n      4,\n      0\n    ],\n    [\n      6,\n      9,\n      0\n    ]\n  ]\n}\n```\n\n## Finding\n\nAll four paths complete14720→16000, but every proper E prefix remains fractional with denominator23. Integral outer completion is weaker than integral preservation of all source boundaries.\n\n## Reassessment\n\nIdentify the finest numerical coarsening compatible with integral E block lengths.\n\n## Checks\n\n```json\n{\n  \"whole_duration\": true,\n  \"only_final_integral\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:09:17.332262+00:00\n\n## Record provenance\n\nExact record hash: `00fa9a8467856f507863ed572ae15a8b117434c60c60ee28defc04087c4238ad`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-c98eb407ba3004a2", "title": "model/completed_path_prefix_field.json"}, {"id": "file52c", "title": "File 52c"}]}