{"id": "c866", "title": "C866 — Classify the complete finite E return family", "filename": "C866.md", "role": "Research action", "step": 866, "sha256": "0ee7c9bf6004a61b990e74c211fc2985e963b6d8525ec6bb33624828058c8667", "bytes": 1748, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C866"], "download": "/sources/0ee7c9bf6004a61b990e74c211fc2985e963b6d8525ec6bb33624828058c8667.md", "format": "md", "derived": true, "tags": [], "excerpt": "Which positive display indices return to display indices under E?", "content": "# C866 — Classify the complete finite E return family\n\n## Question\n\nWhich positive display indices return to display indices under E?\n\n## Inputs\n\n```json\n{\n  \"domain\": \"r=0,...,76\",\n  \"E\": \"25/23\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"File43 complete display\",\n  \"File54 Enoch fork\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:44:22.442355+00:00\n\n## Results\n\n```json\n{\n  \"returns\": [\n    {\n      \"r\": 0,\n      \"image_r\": 0,\n      \"source\": \"Jesus\",\n      \"image\": \"Jesus\",\n      \"source_BC\": 6,\n      \"image_BC\": 6\n    },\n    {\n      \"r\": 23,\n      \"image_r\": 25,\n      \"source\": \"Melki\",\n      \"image\": \"Cosam\",\n      \"source_BC\": 1616,\n      \"image_BC\": 1756\n    },\n    {\n      \"r\": 46,\n      \"image_r\": 50,\n      \"source\": \"Salmon\",\n      \"image\": \"Hezron\",\n      \"source_BC\": 3226,\n      \"image_BC\": 3506\n    },\n    {\n      \"r\": 69,\n      \"image_r\": 75,\n      \"source\": \"Enoch\",\n      \"image\": \"Creation of Adam\",\n      \"source_BC\": 4836,\n      \"image_BC\": 5256\n    }\n  ],\n  \"artifact\": {\n    \"path\": \"model/NT_E_returns.json\",\n    \"sha256\": \"3fd2848a494b025de9c077ff77f10011cb24bf0a463fc3b1f5a7754b04e029d7\",\n    \"bytes\": 528\n  }\n}\n```\n\n## Finding\n\nCoprimality of25 and23 makes 23-divisibility the complete return rule. The four finite returns, including the fixed hinge, follow from one lattice condition; only the Enoch fork carries the supplied interpretation.\n\n## Reassessment\n\nClassify P on the same fixed domain and compare its intersection with E.\n\n## Checks\n\n```json\n{\n  \"complete\": true,\n  \"bounded\": true,\n  \"Enoch\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:44:22.442971+00:00\n\n## Record provenance\n\nExact record hash: `7a7af985e43def3235d6fa05b9eb770002797be530012a5eb1ba9c126ab729df`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-3fd2848a494b025d", "title": "model/NT_E_returns.json"}, {"id": "d-1ff1914fa180de2a", "title": "File 54"}, {"id": "d-dde4eca7c1f64eae", "title": "File 43"}]}