{"id": "c1174", "title": "C1174 — Test order against the biography domain", "filename": "C1174.md", "role": "Research action", "step": 1174, "sha256": "00b3525f4a6d99e61f3bf5140eab67fa9b2fb04e355d2e47a3d2f3f089a22cf6", "bytes": 1179, "origins": ["C480–C1634/Research_Cycles/C1132_C1431_Recovered/journal.json#C1174"], "download": "/sources/00b3525f4a6d99e61f3bf5140eab67fa9b2fb04e355d2e47a3d2f3f089a22cf6.md", "format": "md", "derived": true, "tags": [], "excerpt": "Can commuting formulas fail to define both source-compatible intermediate paths?", "content": "# C1174 — Test order against the biography domain\n\n## Question\n\nCan commuting formulas fail to define both source-compatible intermediate paths?\n\n## Inputs\n\n```json\n{\n  \"row\": [\n    1,\n    1,\n    2\n  ],\n  \"d\": 2,\n  \"e\": 1\n}\n```\n\n## Sources\n\n```json\n[\n  \"C1173\"\n]\n```\n\n## Opened utc\n\n2026-09-28T05:11:49.125757+00:00\n\n## Results\n\n```json\n{\n  \"order_counterexample\": {\n    \"path\": \"model/row_order_domain_counterexample.json\",\n    \"sha256\": \"b7317aad0bab6daf107563c28761bb167acc40b4845d3452487bdd43095d171f\",\n    \"bytes\": 363\n  }\n}\n```\n\n## Finding\n\nThe formulas commute on unrestricted coordinates, yet R-first produces a negative remainder in this diagnostic while A-first remains valid. A common endpoint therefore does not authorize every intermediate route.\n\n## Reassessment\n\nCheck how the complete source packet uses the domain-qualified operations.\n\n## Checks\n\n```json\n{\n  \"same_endpoint\": true,\n  \"R_invalid\": true,\n  \"A_path_valid\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T05:11:49.126064+00:00\n\n## Record provenance\n\nExact record hash: `a46f365e6e41597ffe79e56d7428e6324239db52b7bc6c9cf5cd7f7031046875`\n\nSource journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`", "journalDownload": "/sources/6adb632ce171623c2bce60d7ed58ae319ccb379cf76b751c0a477c1742fd348c.json", "evidenceLinks": [{"id": "d-b7317aad0bab6daf", "title": "model/row_order_domain_counterexample.json"}]}