{"id": "c1042", "title": "C1042 — Independence changes with held source values", "filename": "C1042.md", "role": "Research action", "step": 1042, "sha256": "9c7895e47d1bb64facc6cee35a778bda5f87f3a35458a7931978b4cb89a0df68", "bytes": 1085, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1042"], "download": "/sources/9c7895e47d1bb64facc6cee35a778bda5f87f3a35458a7931978b4cb89a0df68.md", "format": "md", "derived": true, "tags": ["Cumulative", "Covenant"], "excerpt": "Are the centered and E-completed radius conditions still independent when175/147 are supplied?", "content": "# C1042 — Independence changes with held source values\n\n## Question\n\nAre the centered and E-completed radius conditions still independent when175/147 are supplied?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"File60 §2.6\",\n  \"C1041\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:04:41.562315+00:00\n\n## Results\n\n```json\n{\n  \"identity\": \"25A8−2A7 = 21·Abraham_life−25·Jacob_life\",\n  \"held_rhs\": 0,\n  \"consequence\": \"with175/147 held, the two radius conditions are equivalent\"\n}\n```\n\n## Finding\n\nThe two radius conditions are independent only while the relevant lifespans vary. With source175 and147 held, one condition implies the other. Constraint counts must state their held premises.\n\n## Reassessment\n\nReduce the entire selected Covenant claim list to a precise row basis.\n\n## Checks\n\n```json\n{\n  \"coefficient_identity\": true,\n  \"source_rhs_zero\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:04:41.563266+00:00\n\n## Record provenance\n\nExact record hash: `f8fc7ab12886e6ede3b60312a8d1839116124cd21d82e8850a59feb20969de25`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-12a48221b7fdcdcd", "title": "File 60"}]}