{"id": "c994", "title": "C994 — An equal total can hide internal change", "filename": "C994.md", "role": "Research action", "step": 994, "sha256": "1d0b781df8a973ad761c64424dc497a9ceb87fddcc1809a5369bca379763a074", "bytes": 1255, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C994"], "download": "/sources/1d0b781df8a973ad761c64424dc497a9ceb87fddcc1809a5369bca379763a074.md", "format": "md", "derived": true, "tags": [], "excerpt": "What is the vector defect when partial and uniform transformations share one total?", "content": "# C994 — An equal total can hide internal change\n\n## Question\n\nWhat is the vector defect when partial and uniform transformations share one total?\n\n## Inputs\n\n```json\n{\n  \"S\": 483,\n  \"selected_fraction\": \"1/6\",\n  \"selected_factor\": \"25/23\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"C993\",\n  \"File63 §1.3\",\n  \"C609 inherited example\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:54:03.786038+00:00\n\n## Results\n\n```json\n{\n  \"source_parts\": [\n    \"805/2\",\n    \"161/2\"\n  ],\n  \"partial\": [\n    \"805/2\",\n    \"175/2\"\n  ],\n  \"uniform\": [\n    \"1225/3\",\n    \"245/3\"\n  ],\n  \"defect\": [\n    \"-35/6\",\n    \"35/6\"\n  ],\n  \"general_selected_first_defect\": \"(k−1)f(1−f)S·(1,−1)\"\n}\n```\n\n## Finding\n\nThe inherited490 equality loses an internal displacement of35/6 in opposite directions. The general zero-sum defect explains why equal totals do not identify the same path.\n\n## Reassessment\n\nFind a complete nonredundant measurement basis for retained-part families.\n\n## Checks\n\n```json\n{\n  \"same_total\": true,\n  \"nonzero_shape\": true,\n  \"criterion_fails\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:54:03.786371+00:00\n\n## Record provenance\n\nExact record hash: `15cc695fa2dd8c10163b7a33c74a3ac607d7e682b0642e224d4d4e586b7d65d0`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json", "evidenceLinks": [{"id": "d-180803601a2db301", "title": "File 63"}]}