{"id": "c705", "title": "C705 — Verify the whole-set affine mirror", "filename": "C705.md", "role": "Research action", "step": 705, "sha256": "e588cbd6d8891494db52b904aaaa53a60b1116fd0d9330f56f7c8e02d910d5cf", "bytes": 1481, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C705"], "download": "/sources/e588cbd6d8891494db52b904aaaa53a60b1116fd0d9330f56f7c8e02d910d5cf.md", "format": "md", "derived": true, "tags": ["Rounded", "Inverse", "Mirror / 529"], "excerpt": "Does the declared5842 translation match the mirror for every fixed node?", "content": "# C705 — Verify the whole-set affine mirror\n\n## Question\n\nDoes the declared5842 translation match the mirror for every fixed node?\n\n## Inputs\n\n```json\n{\n  \"center\": -2921,\n  \"template_coefficients\": [\n    15,\n    2,\n    \"1/4\"\n  ],\n  \"translation\": 5842\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §13.2; C704\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:18:37.278527+00:00\n\n## Results\n\n```json\n{\n  \"transpositions\": [\n    [\n      \"-11753/4\",\n      \"-11615/4\"\n    ],\n    [\n      \"-11751/4\",\n      \"-11617/4\"\n    ],\n    [\n      \"-11745/4\",\n      \"-11623/4\"\n    ],\n    [\n      \"-11743/4\",\n      \"-11625/4\"\n    ],\n    [\n      \"-11737/4\",\n      \"-11631/4\"\n    ],\n    [\n      \"-11735/4\",\n      \"-11633/4\"\n    ]\n  ],\n  \"fixed_points\": 0,\n  \"translated_equals_mirrored\": true\n}\n```\n\n## Finding\n\nThe5842 translation sends the entire fixed field onto its mirror; the associated reflection permutes it in six pairs with no fixed node. This is affine reflection of phase coordinates, distinct from decimal digit reversal and from File52c’s rounded mirror chart.\n\n## Reassessment\n\nCompare all four source-listed cycle totals against the same fixed set.\n\n## Checks\n\n```json\n{\n  \"set_reflection\": true,\n  \"double_reflection\": true,\n  \"translation\": true,\n  \"six_pairs\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:18:37.278975+00:00\n\n## Record provenance\n\nExact record hash: `3ca6c07e4fdfc146cf513c30c5638764db6f6517c8e69613dc0b5d44257409bf`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json", "evidenceLinks": [{"id": "file52c", "title": "File 52c"}]}