{"id": "c906", "title": "C906 — Derive the retained-subdivision criterion", "filename": "C906.md", "role": "Research action", "step": 906, "sha256": "d6e523ebbd0b498bfcb398b68b061aac9ee83aeb895e30545679845b32d72da9", "bytes": 1368, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C906"], "download": "/sources/d6e523ebbd0b498bfcb398b68b061aac9ee83aeb895e30545679845b32d72da9.md", "format": "md", "derived": true, "tags": [], "excerpt": "When can two constructions share an outer span but disagree at an internal biography?", "content": "# C906 — Derive the retained-subdivision criterion\n\n## Question\n\nWhen can two constructions share an outer span but disagree at an internal biography?\n\n## Inputs\n\n```json\n{\n  \"S\": 144900,\n  \"l\": 147,\n  \"k\": \"70/69\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"C898\",\n  \"C831 complete-path criterion\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:55:38.238978+00:00\n\n## Results\n\n```json\n{\n  \"criterion\": {\n    \"path\": \"model/subdivision_retention_criterion.json\",\n    \"sha256\": \"f99e9c904c85e66da56fa237f9701db460678c4fd4ceb1744d71bd1a91e452fb\",\n    \"bytes\": 325\n  },\n  \"partitions\": {\n    \"uniform\": [\n      \"3377570/23\",\n      \"3430/23\"\n    ],\n    \"retained\": [\n      146853,\n      147\n    ]\n  },\n  \"cut_difference\": \"49/23\"\n}\n```\n\n## Finding\n\nUniform expansion and retained biography have the same outer span but internal cuts differing by(k−1)l. They coincide only for unit scale or zero-length biography. The complete path, rather than its total, distinguishes these constructions.\n\n## Reassessment\n\nCompare the distinct mechanisms behind apparent operation-order effects.\n\n## Checks\n\n```json\n{\n  \"outer_equal\": true,\n  \"cut_delta\": true,\n  \"nontrivial\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:55:38.239426+00:00\n\n## Record provenance\n\nExact record hash: `65893c56d5a9dbd7a122e42927d3ef837f86d3468b95bf5e11dd55fb5a71160b`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-f99e9c904c85e66d", "title": "model/subdivision_retention_criterion.json"}]}