{"id": "c559", "title": "C559 — Locate the Joseph cyclic symmetry", "filename": "C559.md", "role": "Research action", "step": 559, "sha256": "73ec40813770942f26b502c702f1cbb6ad723f3d5475e89c9337fc3f9265890e", "bytes": 1137, "origins": ["C480–C1634/Research_Cycles/C0532_C0631/journal.json#C559"], "download": "/sources/73ec40813770942f26b502c702f1cbb6ad723f3d5475e89c9337fc3f9265890e.md", "format": "md", "derived": true, "tags": [], "excerpt": "Does a three-cycle act consistently on the complete component family?", "content": "# C559 — Locate the Joseph cyclic symmetry\n\n## Question\n\nDoes a three-cycle act consistently on the complete component family?\n\n## Inputs\n\n```json\n{\n  \"rotation\": \"(a,b,c)→(b,c,a)\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"File62 §§6.1–6.4; C558\"\n]\n```\n\n## Opened utc\n\n2026-09-28T00:14:08.923110+00:00\n\n## Results\n\n```json\n{\n  \"states\": 9,\n  \"component_displays\": 27,\n  \"example\": [\n    [\n      4,\n      23,\n      83\n    ],\n    [\n      23,\n      83,\n      4\n    ],\n    [\n      83,\n      4,\n      23\n    ]\n  ],\n  \"action_domain\": \"ordered duration triples\"\n}\n```\n\n## Finding\n\nA genuine C3 action rotates duration components and returns after three applications. It does not establish a permutation of historical people or complete chronology states.\n\n## Reassessment\n\nTest how whole-year and exact phase choices change crossed containers.\n\n## Checks\n\n```json\n{\n  \"all_rotations\": true,\n  \"third_power_identity\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T00:14:08.923700+00:00\n\n## Record provenance\n\nExact record hash: `a22fb0384fb192c1b75b6ee07ee84c20b8fb963fa4a8e3f94493c549c335dd5a`\n\nSource journal: `Research_Cycles/C0532_C0631/journal.json`", "journalDownload": "/sources/7a2e1117efc741218b68e2db8bb20eadd33cab34e00384e9b903708031da1d2d.json", "evidenceLinks": [{"id": "d-be42daca1d82dac9", "title": "File 62"}]}