{"id": "c883", "title": "C883 — Explain the authorized File51a Key chains", "filename": "C883.md", "role": "Research action", "step": 883, "sha256": "7a5b89f888791c825b566a4bc92b1424b69bcdf1566cdc893c5bfe1e0c06e9aa", "bytes": 1483, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C883"], "download": "/sources/7a5b89f888791c825b566a4bc92b1424b69bcdf1566cdc893c5bfe1e0c06e9aa.md", "format": "md", "derived": true, "tags": ["Rounded", "Mirror / 529"], "excerpt": "Do the exact civil inputs satisfy the full stagewise domains?", "content": "# C883 — Explain the authorized File51a Key chains\n\n## Question\n\nDo the exact civil inputs satisfy the full stagewise domains?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"File51a author clarification lines26–66\",\n  \"C880–881\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:49:00.773966+00:00\n\n## Results\n\n```json\n{\n  \"chains\": [\n    {\n      \"civil_input\": 10051,\n      \"EE_chain\": [\n        10051,\n        10925,\n        11875\n      ],\n      \"multiple529\": 19\n    },\n    {\n      \"civil_input\": 55016,\n      \"EE_chain\": [\n        55016,\n        59800,\n        65000\n      ],\n      \"multiple529\": 104,\n      \"EJ_chain\": [\n        55016,\n        59800,\n        60000\n      ],\n      \"multiple6877\": 8\n    }\n  ],\n  \"artifact\": {\n    \"path\": \"model/File51a_authorized_key_chains.json\",\n    \"sha256\": \"164285d8a6e23e20bbf840fa4de7a8c12dd5f5467fd650e8021a0ede0778a34c\",\n    \"bytes\": 330\n  }\n}\n```\n\n## Finding\n\nBoth source E² chains satisfy the529 domain; the55016→59800→60000 E→J chain satisfies6877. The general criterion explains their intermediate integrality while preserving their civil-count input roles.\n\n## Reassessment\n\nTest why the neighboring Rounded widths cannot replace those civil counts.\n\n## Checks\n\n```json\n{\n  \"all_EE\": true,\n  \"EJ\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:49:00.774613+00:00\n\n## Record provenance\n\nExact record hash: `491c2725d66ca43170b69db7da36d6bb67121cb67c028da3d7732b7d31145dfb`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-164285d8a6e23e20", "title": "model/File51a_authorized_key_chains.json"}, {"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}]}