{"id": "c875", "title": "C875 — Explain the existing completions by domain membership", "filename": "C875.md", "role": "Research action", "step": 875, "sha256": "6ba32f684df54aa52bb5334cc0b20a368a519e765d54ab5a3254a2e5fa57f26e", "bytes": 2008, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C875"], "download": "/sources/6ba32f684df54aa52bb5334cc0b20a368a519e765d54ab5a3254a2e5fa57f26e.md", "format": "md", "derived": true, "tags": [], "excerpt": "Do established source scalars have different compatibility profiles?", "content": "# C875 — Explain the existing completions by domain membership\n\n## Question\n\nDo established source scalars have different compatibility profiles?\n\n## Inputs\n\n```json\n{\n  \"source_scalars\": [\n    460,\n    690,\n    483,\n    12558\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File46\",\n  \"File63\",\n  \"C831 inherited examples\",\n  \"C874\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:47:05.936749+00:00\n\n## Results\n\n```json\n{\n  \"profiles\": [\n    {\n      \"input\": 460,\n      \"images\": {\n        \"E\": 500,\n        \"P\": \"1400/3\",\n        \"J\": \"6000/13\"\n      },\n      \"integer_keys\": [\n        \"E\"\n      ],\n      \"input_on5Z\": true\n    },\n    {\n      \"input\": 690,\n      \"images\": {\n        \"E\": 750,\n        \"P\": 700,\n        \"J\": \"9000/13\"\n      },\n      \"integer_keys\": [\n        \"E\",\n        \"P\"\n      ],\n      \"input_on5Z\": true\n    },\n    {\n      \"input\": 483,\n      \"images\": {\n        \"E\": 525,\n        \"P\": 490,\n        \"J\": \"6300/13\"\n      },\n      \"integer_keys\": [\n        \"E\",\n        \"P\"\n      ],\n      \"input_on5Z\": false\n    },\n    {\n      \"input\": 12558,\n      \"images\": {\n        \"E\": 13650,\n        \"P\": 12740,\n        \"J\": 12600\n      },\n      \"integer_keys\": [\n        \"E\",\n        \"P\",\n        \"J\"\n      ],\n      \"input_on5Z\": false\n    }\n  ],\n  \"artifact\": {\n    \"path\": \"model/existing_key_profiles.json\",\n    \"sha256\": \"f60bf0b288ce5e0edc4f6928749c64bacca0016149bfab9f40dbe827cccc2b6f\",\n    \"bytes\": 716\n  }\n}\n```\n\n## Finding\n\nThe familiar460,690,483 and12558 completions occupy different exact domains. Their compatibility follows from denominator divisibility; the new explanation is the shared criterion, not the old scalar outputs.\n\n## Reassessment\n\nEvaluate every row of the quarter-carrier family under the three Keys.\n\n## Checks\n\n```json\n{\n  \"profiles\": true,\n  \"all_three\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:47:05.937316+00:00\n\n## Record provenance\n\nExact record hash: `eee6ede40cae40b2fa558ffecbf7ab870d84fac7ebb4883076f16d78147e0dd8`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-f60bf0b288ce5e0e", "title": "model/existing_key_profiles.json"}, {"id": "d-180803601a2db301", "title": "File 63"}, {"id": "d-18e8c54ff1663fb1", "title": "File 46"}]}