{"id": "c697", "title": "C697 — Derive directional convergence from the Key gap", "filename": "C697.md", "role": "Research action", "step": 697, "sha256": "5840f91df86e4798829f989c3ccec0bc0ddc6360aee6f539ee74625e1f4b0a76", "bytes": 1150, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C697"], "download": "/sources/5840f91df86e4798829f989c3ccec0bc0ddc6360aee6f539ee74625e1f4b0a76.md", "format": "md", "derived": true, "tags": [], "excerpt": "What source offset makes the paired anchored outputs equal?", "content": "# C697 — Derive directional convergence from the Key gap\n\n## Question\n\nWhat source offset makes the paired anchored outputs equal?\n\n## Inputs\n\n```json\n{\n  \"span\": 690,\n  \"held_forward\": [\n    3626,\n    3576\n  ],\n  \"held_reverse\": [\n    2216,\n    2166\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"C696; Supplement A §8\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:16:27.059306+00:00\n\n## Results\n\n```json\n{\n  \"Key_output_gap\": 50,\n  \"forward_residual\": 0,\n  \"reverse_residual\": 0,\n  \"individual_gains\": [\n    10,\n    60\n  ]\n}\n```\n\n## Finding\n\nThe50 source offset equals(E−P)×690. With the declared direction and assignment, that one equality forces both convergences. The four outputs are structured consequences of the offset and operators, not four independent confirmations.\n\n## Reassessment\n\nRecover the complete70-wide quartet and its supplied1470 translation.\n\n## Checks\n\n```json\n{\n  \"gap\": true,\n  \"residuals\": true,\n  \"gains\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:16:27.059594+00:00\n\n## Record provenance\n\nExact record hash: `7d177b1e037e0e89f11da8a55776b08a414cbe3f4868ce0427c15c6c02d11037`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}