{"id": "c881", "title": "C881 — Classify all nine two-Key grid domains", "filename": "C881.md", "role": "Research action", "step": 881, "sha256": "8b4d1805e1805279c0be32eee5d6180c8ea4de97c9e3a91e4348f062a0ed0f16", "bytes": 2806, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C881"], "download": "/sources/8b4d1805e1805279c0be32eee5d6180c8ea4de97c9e3a91e4348f062a0ed0f16.md", "format": "md", "derived": true, "tags": ["Mirror / 529"], "excerpt": "Which ordered pairs differ between final and stagewise membership?", "content": "# C881 — Classify all nine two-Key grid domains\n\n## Question\n\nWhich ordered pairs differ between final and stagewise membership?\n\n## Inputs\n\n```json\n{\n  \"inventory\": \"E,P,J each followed by E,P,J\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"C880\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:48:29.014031+00:00\n\n## Results\n\n```json\n{\n  \"matrix\": {\n    \"path\": \"model/two_key_domains.json\",\n    \"sha256\": \"2dc016baa528ed002f1d353d53f91d2e5c971f0e0bb4222bf778e008349f1a58\",\n    \"bytes\": 1578\n  },\n  \"rows\": [\n    {\n      \"execution\": \"E→E\",\n      \"coefficient\": \"625/529\",\n      \"final_integer_domain\": 529,\n      \"all_stage_integer_domain\": 529,\n      \"all_stage_5Z_domain\": 2645\n    },\n    {\n      \"execution\": \"E→P\",\n      \"coefficient\": \"1750/1587\",\n      \"final_integer_domain\": 1587,\n      \"all_stage_integer_domain\": 1587,\n      \"all_stage_5Z_domain\": 7935\n    },\n    {\n      \"execution\": \"E→J\",\n      \"coefficient\": \"7500/6877\",\n      \"final_integer_domain\": 6877,\n      \"all_stage_integer_domain\": 6877,\n      \"all_stage_5Z_domain\": 34385\n    },\n    {\n      \"execution\": \"P→E\",\n      \"coefficient\": \"1750/1587\",\n      \"final_integer_domain\": 1587,\n      \"all_stage_integer_domain\": 1587,\n      \"all_stage_5Z_domain\": 7935\n    },\n    {\n      \"execution\": \"P→P\",\n      \"coefficient\": \"4900/4761\",\n      \"final_integer_domain\": 4761,\n      \"all_stage_integer_domain\": 4761,\n      \"all_stage_5Z_domain\": 23805\n    },\n    {\n      \"execution\": \"P→J\",\n      \"coefficient\": \"7000/6877\",\n      \"final_integer_domain\": 6877,\n      \"all_stage_integer_domain\": 20631,\n      \"all_stage_5Z_domain\": 103155\n    },\n    {\n      \"execution\": \"J→E\",\n      \"coefficient\": \"7500/6877\",\n      \"final_integer_domain\": 6877,\n      \"all_stage_integer_domain\": 6877,\n      \"all_stage_5Z_domain\": 34385\n    },\n    {\n      \"execution\": \"J→P\",\n      \"coefficient\": \"7000/6877\",\n      \"final_integer_domain\": 6877,\n      \"all_stage_integer_domain\": 6877,\n      \"all_stage_5Z_domain\": 34385\n    },\n    {\n      \"execution\": \"J→J\",\n      \"coefficient\": \"90000/89401\",\n      \"final_integer_domain\": 89401,\n      \"all_stage_integer_domain\": 89401,\n      \"all_stage_5Z_domain\": 447005\n    }\n  ]\n}\n```\n\n## Finding\n\nEight of nine ordered pairs have the same final and stagewise integer domain. P→J is the exception: its final domain is6877Z, but its intermediate stage requires20631Z. Scalar products commute while partial integer-grid actions can differ.\n\n## Reassessment\n\nExpose the P/J asymmetry with the denominator-forced minimal example.\n\n## Checks\n\n```json\n{\n  \"complete\": true,\n  \"unique_exception\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:48:29.014485+00:00\n\n## Record provenance\n\nExact record hash: `3233b76aea2010c86d72c2f7d7b9c7c56417bcef7d2297d864c262db6783b029`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-2dc016baa528ed00", "title": "model/two_key_domains.json"}]}