{"id": "c709", "title": "C709 — Separate Short and Long whole-field translations", "filename": "C709.md", "role": "Research action", "step": 709, "sha256": "a1d9db931d5ce5ac406536220bb3b16fbd3e5349e0e73e1831e1b3b07c837247", "bytes": 1193, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C709"], "download": "/sources/a1d9db931d5ce5ac406536220bb3b16fbd3e5349e0e73e1831e1b3b07c837247.md", "format": "md", "derived": true, "tags": ["Mirror / 529"], "excerpt": "Does a50-shifted center preserve the5842 whole-field closure requirement?", "content": "# C709 — Separate Short and Long whole-field translations\n\n## Question\n\nDoes a50-shifted center preserve the5842 whole-field closure requirement?\n\n## Inputs\n\n```json\n{\n  \"Short_center\": -2921,\n  \"Long_center\": -2871,\n  \"shape\": \"same fixed phase template\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §13.9; C707\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:19:36.381089+00:00\n\n## Results\n\n```json\n{\n  \"self_mirror_lengths\": [\n    5842,\n    5742\n  ],\n  \"length_difference\": 100,\n  \"Long_center_residual_under5842\": 100\n}\n```\n\n## Finding\n\nThe supplied Long center requires5742 for its own mirror closure,100 less than the Short field’s5842. A50 center displacement doubles in the required translation. No adjacent state or remote extension is introduced to erase this distinction.\n\n## Reassessment\n\nCompare the conserved quantities across the now-completed chronological mechanisms.\n\n## Checks\n\n```json\n{\n  \"lengths\": true,\n  \"double_shift\": true,\n  \"fixed5842_fails\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:19:36.381472+00:00\n\n## Record provenance\n\nExact record hash: `f699d548aa4d3dbd3fc8d791a624fc57e81fed7ac6e8617c0c6dbd76278467fc`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}