{"id": "c1049", "title": "C1049 — Minimal clutch observation basis", "filename": "C1049.md", "role": "Research action", "step": 1049, "sha256": "78bb5bb402b0865ad1fa3b72e67e84c42d27a772ae74f8a82d63c88655e4460c", "bytes": 1099, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1049"], "download": "/sources/78bb5bb402b0865ad1fa3b72e67e84c42d27a772ae74f8a82d63c88655e4460c.md", "format": "md", "derived": true, "tags": ["Cumulative", "Covenant"], "excerpt": "Which observed coordinates recover the unrestricted array?", "content": "# C1049 — Minimal clutch observation basis\n\n## Question\n\nWhich observed coordinates recover the unrestricted array?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1048\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:06:10.774293+00:00\n\n## Results\n\n```json\n{\n  \"basis_indices\": [\n    0,\n    1,\n    2,\n    3,\n    4,\n    5,\n    6,\n    21,\n    7\n  ],\n  \"basis_determinant\": -1,\n  \"incomplete_observation_ranks\": {\n    \"no_Aaron\": 8,\n    \"no_shift\": 8,\n    \"one_row_absent\": 8\n  }\n}\n```\n\n## Finding\n\nSeven unshifted Nisan coordinates, one unshifted Aaron coordinate and one half-clutch coordinate form an integer observation basis. Losing a whole phase, all shifts, or an entire source row leaves one parameter undetermined.\n\n## Reassessment\n\nImpose exact source phase and repeated-lifespan equalities separately.\n\n## Checks\n\n```json\n{\n  \"unimodular\": true,\n  \"all_rank_eight\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:06:10.780793+00:00\n\n## Record provenance\n\nExact record hash: `c8a828e2e93ef2bb227323d1d70b4352e1272e6a17404399769678784e033813`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}