{"id": "c1011", "title": "C1011 — Integral Esau measurement basis", "filename": "C1011.md", "role": "Research action", "step": 1011, "sha256": "656c96cbdb49664bf3ef8761070fa05756fb6f1e233e7bafcf9786af6000f9f6", "bytes": 1153, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1011"], "download": "/sources/656c96cbdb49664bf3ef8761070fa05756fb6f1e233e7bafcf9786af6000f9f6.md", "format": "md", "derived": true, "tags": ["Inverse"], "excerpt": "Is the nine-measurement inverse an integer change of coordinates?", "content": "# C1011 — Integral Esau measurement basis\n\n## Question\n\nIs the nine-measurement inverse an integer change of coordinates?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1009\",\n  \"C1010\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:57:55.869076+00:00\n\n## Results\n\n```json\n{\n  \"basis\": {\n    \"path\": \"model/esau_unimodular_basis.json\",\n    \"sha256\": \"83d11fc1240a420d893079b9221cd8a96975e05026795c616070d13a21c51b38\",\n    \"bytes\": 1936\n  },\n  \"determinant\": 1,\n  \"reconstructed\": [\n    200,\n    20,\n    200,\n    20,\n    40,\n    10,\n    30,\n    20,\n    10\n  ]\n}\n```\n\n## Finding\n\nThe compact Esau basis has determinant1 and an integer inverse. It changes coordinates without fractional adjustment; it does not reduce nine independent numbers to fewer than nine.\n\n## Reassessment\n\nCompare with the complete clean-plus-unclean walk basis.\n\n## Checks\n\n```json\n{\n  \"unimodular\": true,\n  \"integral_inverse\": true,\n  \"recover_counts\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:57:55.872197+00:00\n\n## Record provenance\n\nExact record hash: `bf52cb33ab85fe9d47f939003f22ab70bab079518eeeb2e0541e1219a569ae51`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-83d11fc1240a420d", "title": "model/esau_unimodular_basis.json"}]}