{"id": "c964", "title": "C964 — Late begetting constraint rank", "filename": "C964.md", "role": "Research action", "step": 964, "sha256": "09b15d5268c8992a4548c059b40a700d8841a5cf4de9a2fa34fe09cae38a4367", "bytes": 1190, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C964"], "download": "/sources/09b15d5268c8992a4548c059b40a700d8841a5cf4de9a2fa34fe09cae38a4367.md", "format": "md", "derived": true, "tags": ["Regular"], "excerpt": "What do the three capped lives determine about four late begetting intervals?", "content": "# C964 — Late begetting constraint rank\n\n## Question\n\nWhat do the three capped lives determine about four late begetting intervals?\n\n## Inputs\n\n```json\n{\n  \"matrix\": [\n    [\n      1,\n      1,\n      1,\n      1\n    ],\n    [\n      0,\n      0,\n      1,\n      1\n    ],\n    [\n      0,\n      0,\n      0,\n      1\n    ]\n  ],\n  \"rhs\": [\n    246,\n    119,\n    52\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"C961\",\n  \"File18 §3.1\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:47:51.282317+00:00\n\n## Results\n\n```json\n{\n  \"rank\": 3,\n  \"kernel\": [\n    1,\n    -1,\n    0,\n    0\n  ],\n  \"recoverable\": {\n    \"Lamech_completed\": 52,\n    \"Methuselah\": 67,\n    \"Jared_plus_Enoch\": 127\n  }\n}\n```\n\n## Finding\n\nThe cap equations recover Lamech52, Methuselah67, and Jared+Enoch127; they do not separate Jared from Enoch.\n\n## Reassessment\n\nAdd the independently retained Enoch65 row and test the complete late reconstruction.\n\n## Checks\n\n```json\n{\n  \"kernel\": true,\n  \"rank_three\": true,\n  \"recovered\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:47:51.282519+00:00\n\n## Record provenance\n\nExact record hash: `e0fefcf74ffb218e7dac9b3ae1c816bf6c7b3a534f297da3fc5d97eba4206073`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}]}