{"id": "c987", "title": "C987 — Four relations contain three constraints", "filename": "C987.md", "role": "Research action", "step": 987, "sha256": "281f4435fa53a2611b87bf9bf25bb8484a344aa6e532c11ce8376886316f8f2f", "bytes": 1270, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C987"], "download": "/sources/281f4435fa53a2611b87bf9bf25bb8484a344aa6e532c11ce8376886316f8f2f.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "What is the exact dependence certificate for calibration and allocation?", "content": "# C987 — Four relations contain three constraints\n\n## Question\n\nWhat is the exact dependence certificate for calibration and allocation?\n\n## Inputs\n\n```json\n{\n  \"matrix\": [\n    [\n      336,\n      -360,\n      0\n    ],\n    [\n      336,\n      0,\n      -364\n    ],\n    [\n      1,\n      -6,\n      0\n    ],\n    [\n      1,\n      0,\n      -26\n    ]\n  ],\n  \"rhs\": [\n    0,\n    0,\n    -5,\n    -25\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"C985\",\n  \"C986\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:53:02.193428+00:00\n\n## Results\n\n```json\n{\n  \"basis\": {\n    \"path\": \"model/key_calibration_basis.json\",\n    \"sha256\": \"0cd31da8f6cd69b1b9a7f33ef4fc1994b80e977c2715a19b08cf9043e76d1155\",\n    \"bytes\": 365\n  },\n  \"rank\": 3,\n  \"augmented_rank\": 3,\n  \"dependency_products\": [\n    0,\n    0,\n    0,\n    0\n  ]\n}\n```\n\n## Finding\n\nThe four equations have rank three, with7A−6B−420C+84D=0 including constants. One relation is dependent.\n\n## Reassessment\n\nIdentify the freedom left by calendar calibration alone.\n\n## Checks\n\n```json\n{\n  \"rank_three\": true,\n  \"certificate\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:53:02.194512+00:00\n\n## Record provenance\n\nExact record hash: `4943fd50616d70bca539f25bdd91ca12d2ce73d480b2b4b55006098679591407`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-0cd31da8f6cd69b1", "title": "model/key_calibration_basis.json"}]}