{"id": "c678", "title": "C678 — Derive the nested25|35|35|25 field", "filename": "C678.md", "role": "Research action", "step": 678, "sha256": "1a2882f2f73f53bdbf266e8678625aa10296a20ce0493c308ab119b913aeb3b5", "bytes": 1186, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C678"], "download": "/sources/1a2882f2f73f53bdbf266e8678625aa10296a20ce0493c308ab119b913aeb3b5.md", "format": "md", "derived": true, "tags": [], "excerpt": "What follows once the source70 and120 bodies share center2911?", "content": "# C678 — Derive the nested25|35|35|25 field\n\n## Question\n\nWhat follows once the source70 and120 bodies share center2911?\n\n## Inputs\n\n```json\n{\n  \"center\": 2911,\n  \"outer_width\": 120,\n  \"Enoch_width\": 70,\n  \"source_Enoch\": [\n    2946,\n    2876\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §4.5\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:11:43.642567+00:00\n\n## Results\n\n```json\n{\n  \"nodes\": [\n    2971,\n    2946,\n    2911,\n    2876,\n    2851\n  ],\n  \"gaps\": [\n    25,\n    35,\n    35,\n    25\n  ],\n  \"margin\": 25,\n  \"Key_decomposition\": [\n    25,\n    35,\n    35,\n    25\n  ]\n}\n```\n\n## Finding\n\nThe two source widths and their common center force25|35|35|25. Each35 is P(34.5), each25 is E(23), but their sum is a retained-component construction rather than a newly defined whole120 Key image.\n\n## Reassessment\n\nDistinguish the source’s scalar1470 closure from its coordinate1475 envelope.\n\n## Checks\n\n```json\n{\n  \"source_Enoch\": true,\n  \"gaps\": true,\n  \"keys\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:11:43.642795+00:00\n\n## Record provenance\n\nExact record hash: `6a61820ebb7e0772f460ab3438ba227612a57983e352c71197f9ccf96669d696`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}