{"id": "c1029", "title": "C1029 — NT equal-block coarsening preserves reflection", "filename": "C1029.md", "role": "Research action", "step": 1029, "sha256": "c72234476ff1efe15d9e290756e654faa268afe14d6da13b0df85106d10cd9ed", "bytes": 1318, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1029"], "download": "/sources/c72234476ff1efe15d9e290756e654faa268afe14d6da13b0df85106d10cd9ed.md", "format": "md", "derived": true, "tags": [], "excerpt": "Does the complete77-edge NT field carry reflection through seven-edge blocks?", "content": "# C1029 — NT equal-block coarsening preserves reflection\n\n## Question\n\nDoes the complete77-edge NT field carry reflection through seven-edge blocks?\n\n## Inputs\n\n```json\n{\n  \"edges\": 77,\n  \"block_size\": 7\n}\n```\n\n## Sources\n\n```json\n[\n  \"File43\",\n  \"File54\",\n  \"C1028\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:01:19.343924+00:00\n\n## Results\n\n```json\n{\n  \"block_map\": [\n    10,\n    9,\n    8,\n    7,\n    6,\n    5,\n    4,\n    3,\n    2,\n    1,\n    0\n  ],\n  \"selected_boundaries\": [\n    0,\n    7,\n    14,\n    21,\n    28,\n    35,\n    42,\n    49,\n    56,\n    63,\n    70,\n    77\n  ],\n  \"reflected_boundaries\": [\n    77,\n    70,\n    63,\n    56,\n    49,\n    42,\n    35,\n    28,\n    21,\n    14,\n    7,\n    0\n  ]\n}\n```\n\n## Finding\n\nReflection permutes all eleven equal seven-edge blocks, so the NT490 coarsening passes the criterion. This explains why one contraction preserves the reflection that the Toledot section quotient loses.\n\n## Reassessment\n\nCompare the three kinds of retained information now exposed.\n\n## Checks\n\n```json\n{\n  \"all_blocks\": true,\n  \"boundary_invariance\": true,\n  \"eleven_blocks\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:01:19.344406+00:00\n\n## Record provenance\n\nExact record hash: `fceec64736d298c84820860ac60bcf8a9becb90c69fa152136e26fc41d36ce65`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-1ff1914fa180de2a", "title": "File 54"}, {"id": "d-dde4eca7c1f64eae", "title": "File 43"}]}