{"id": "c742", "title": "C742 — Explain equal births with unequal cumulative boundaries", "filename": "C742.md", "role": "Research action", "step": 742, "sha256": "aff26960637568306d396c6f4492830d5c8f88178ca1b441f990e54d4422c23f", "bytes": 1549, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C742"], "download": "/sources/aff26960637568306d396c6f4492830d5c8f88178ca1b441f990e54d4422c23f.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative"], "excerpt": "Why does the entireLXX/SP birthsuffix coincide while itscumulativeprofilediverges?", "content": "# C742 — Explain equal births with unequal cumulative boundaries\n\n## Question\n\nWhy does the entireLXX/SP birthsuffix coincide while itscumulativeprofilediverges?\n\n## Inputs\n\n```json\n{\n  \"nodes\": [\n    \"Shelah\",\n    \"Eber\",\n    \"Peleg\",\n    \"Reu\",\n    \"Serug\",\n    \"Nahor\",\n    \"Terah\",\n    \"Abraham\"\n  ],\n  \"native_Cainan\": [\n    \"LXXON\",\n    \"SPOFF\"\n  ],\n  \"regular_frame\": \"commonfull430\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"File18 §§3–4,6C–D; C738\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:44:58.868367+00:00\n\n## Results\n\n```json\n{\n  \"regular_differences\": [\n    0,\n    0,\n    0,\n    0,\n    0,\n    0,\n    0,\n    0\n  ],\n  \"cumulative_differences\": [\n    547,\n    520,\n    420,\n    320,\n    220,\n    120,\n    60,\n    0\n  ],\n  \"lifespan_changes\": [\n    27,\n    100,\n    100,\n    100,\n    100,\n    60,\n    60\n  ]\n}\n```\n\n## Finding\n\nAll eightLXX/SP birthpositionsShelah throughAbraham coincide. Their cumulative differences547→520→420→320→220→120→60→0 are exactly generated by the local lifespan changes. This is a complete positive example of shared regular geometry with divergent cumulative realization.\n\n## Reassessment\n\nInsert the single admittedCainan row intoSP and test how far the shared birthsuffix extends.\n\n## Checks\n\n```json\n{\n  \"same_births\": true,\n  \"cumulative_profile\": true,\n  \"local_cause\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:44:58.868769+00:00\n\n## Record provenance\n\nExact record hash: `7d48feefa5ce07e9b29d58a4588ba5dcf022c193c8e691361d07812b220d9d89`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}]}