{"id": "c880", "title": "C880 — Derive the prefix-denominator theorem", "filename": "C880.md", "role": "Research action", "step": 880, "sha256": "d2959a3c5e3b07f9686a3864cbb358b3827642e4a8726e56ef7fab0faef08f53", "bytes": 1044, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C880"], "download": "/sources/d2959a3c5e3b07f9686a3864cbb358b3827642e4a8726e56ef7fab0faef08f53.md", "format": "md", "derived": true, "tags": [], "excerpt": "What must hold for every stage of a finite Key word to preserve a grid?", "content": "# C880 — Derive the prefix-denominator theorem\n\n## Question\n\nWhat must hold for every stage of a finite Key word to preserve a grid?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C873\",\n  \"Strategy partial actions\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:48:14.996601+00:00\n\n## Results\n\n```json\n{\n  \"theorem\": {\n    \"path\": \"model/key_word_domain_theorem.json\",\n    \"sha256\": \"9e8fc429be24813a422a5cbe2e49b519cb624e2b33a35d21147754afe10f1623\",\n    \"bytes\": 369\n  }\n}\n```\n\n## Finding\n\nThe exact all-stage domain is h times the least common multiple of reduced prefix denominators. Final integrality is a weaker condition whenever cancellation occurs only later.\n\n## Reassessment\n\nEvaluate the complete fixed inventory of nine two-Key words.\n\n## Checks\n\n```json\n{\n  \"criterion\": true,\n  \"authorization_retained\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:48:14.996937+00:00\n\n## Record provenance\n\nExact record hash: `3e927bc16221395b1cafd26aad913a64efb1c770c298ee662f946b03a6b7eebe`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-9e8fc429be24813a", "title": "model/key_word_domain_theorem.json"}]}