{"id": "c1039", "title": "C1039 — An explicit Covenant dependency circuit", "filename": "C1039.md", "role": "Research action", "step": 1039, "sha256": "323fa69a6f58bb7c8af6d38952f9babf52059bbce26d1b52567cef42230c5490", "bytes": 1065, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C1039"], "download": "/sources/323fa69a6f58bb7c8af6d38952f9babf52059bbce26d1b52567cef42230c5490.md", "format": "md", "derived": true, "tags": ["Covenant"], "excerpt": "Is the household-middle equality independent of the other source conditions?", "content": "# C1039 — An explicit Covenant dependency circuit\n\n## Question\n\nIs the household-middle equality independent of the other source conditions?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C1035–C1038\"\n]\n```\n\n## Opened utc\n\n2026-09-28T04:04:10.364331+00:00\n\n## Results\n\n```json\n{\n  \"dependency\": \"A9 = −A2 + A3 + A4 + A5\",\n  \"coefficient_residual\": [\n    0,\n    0,\n    0,\n    0,\n    0,\n    0,\n    0,\n    0,\n    0,\n    0,\n    0,\n    0,\n    0\n  ]\n}\n```\n\n## Finding\n\nThe household-middle equality is forced by the second147 rail, equal lives, twin death arms and Joseph’s double span. It adds no separate constraint after those are retained.\n\n## Reassessment\n\nDerive the common-Key landing condition without using its299/276 outputs as inputs.\n\n## Checks\n\n```json\n{\n  \"full_coefficient_identity\": true,\n  \"nontrivial_circuit\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T04:04:10.365715+00:00\n\n## Record provenance\n\nExact record hash: `9077235cff22b1c3611d63caf46ccc7f96c50ef126f428e7733246504b3ce587`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}