{"id": "c650", "title": "C650 — Locate the common coarse rail", "filename": "C650.md", "role": "Research action", "step": 650, "sha256": "7128de41c2c69b4a02d90a51f4b44ad1a4505146e73092ef270c7d8fe8de164a", "bytes": 1575, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C650"], "download": "/sources/7128de41c2c69b4a02d90a51f4b44ad1a4505146e73092ef270c7d8fe8de164a.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "Which supplied triples share the same bilateral projection?", "content": "# C650 — Locate the common coarse rail\n\n## Question\n\nWhich supplied triples share the same bilateral projection?\n\n## Inputs\n\n```json\n{\n  \"triples\": [\n    [\n      4121,\n      4114,\n      4107\n    ],\n    [\n      4251,\n      4244,\n      4237\n    ],\n    [\n      2296,\n      2226,\n      2156\n    ],\n    [\n      1929,\n      1922,\n      1915\n    ],\n    [\n      1885,\n      1878,\n      1871\n    ]\n  ],\n  \"centers\": [\n    4114,\n    4244,\n    2226,\n    1922,\n    1878\n  ],\n  \"steps\": [\n    7,\n    7,\n    70,\n    7,\n    7\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"File70 §§3–6; A.3,A.5,A.6\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:04:52.873999+00:00\n\n## Results\n\n```json\n{\n  \"normalized\": [\n    [\n      1,\n      0,\n      -1\n    ],\n    [\n      1,\n      0,\n      -1\n    ],\n    [\n      1,\n      0,\n      -1\n    ],\n    [\n      1,\n      0,\n      -1\n    ],\n    [\n      1,\n      0,\n      -1\n    ]\n  ],\n  \"refinement_projection\": [\n    0,\n    2,\n    4\n  ]\n}\n```\n\n## Finding\n\nAll five supplied triples normalize to1|0|-1. Creation and Terah additionally share the five-node refinement; Jacob and Joseph establish the coarse rail only. A shared outer shape does not supply missing inner events.\n\n## Reassessment\n\nConsolidate the first20 steps into an explanation of geometry versus selected calendar placement.\n\n## Checks\n\n```json\n{\n  \"all_triples\": true,\n  \"projection\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:04:52.874257+00:00\n\n## Record provenance\n\nExact record hash: `e4c24280b4d4426f3ceec817198a956ebe03ed332b45f3e95d2b601944e35429`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json", "evidenceLinks": [{"id": "d-0fa80217c94b3951", "title": "File 70"}]}