{"id": "c1133", "title": "C1133 — Form the joint SP age constraints", "filename": "C1133.md", "role": "Research action", "step": 1133, "sha256": "a4fbbd07efa054e30c00d8d7593b5f0524686afb658985b5c916df4c740b8392", "bytes": 1297, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1133"], "download": "/sources/a4fbbd07efa054e30c00d8d7593b5f0524686afb658985b5c916df4c740b8392.md", "format": "md", "derived": true, "tags": [], "excerpt": "How many free age coordinates remain after the explicit source relations and inherited cap equations?", "content": "# C1133 — Form the joint SP age constraints\n\n## Question\n\nHow many free age coordinates remain after the explicit source relations and inherited cap equations?\n\n## Inputs\n\n```json\n{\n  \"variables\": [\n    \"Adam\",\n    \"Seth\",\n    \"Enosh\",\n    \"Kenan\",\n    \"Mahalalel\",\n    \"Jared\",\n    \"Enoch\",\n    \"Methuselah\",\n    \"Lamech\"\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"C1132\",\n  \"File18 §3.1\",\n  \"File51a §8.3\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:57:51.938865+00:00\n\n## Results\n\n```json\n{\n  \"age_constraints\": {\n    \"path\": \"model/SP_age_constraints.json\",\n    \"sha256\": \"a424c44212d21411e61116d36dad64234cf5602e9c4578c3989ac79f8ab308fd\",\n    \"bytes\": 1226\n  },\n  \"rank\": 6,\n  \"free_coordinates\": 3\n}\n```\n\n## Finding\n\nThe six retained relations have rank6 on nine ages, leaving three free coordinates. They reduce the local input model without uniquely recovering the whole age sequence.\n\n## Reassessment\n\nDescribe the three remaining freedoms explicitly to see which source values are still needed.\n\n## Checks\n\n```json\n{\n  \"all_source_equations\": true,\n  \"rank6\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:57:51.941254+00:00\n\n## Record provenance\n\nExact record hash: `8864da50f84957f28dd0b217d4758a05a60155c6269126a2de444e9ec7d449dd`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-a424c44212d21411", "title": "model/SP_age_constraints.json"}, {"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}]}