{"id": "c685", "title": "C685 — Close the three-calendar micro triangle", "filename": "C685.md", "role": "Research action", "step": 685, "sha256": "0c4e0d9076a54766e9f785e161d46f440bbdf120b1f652397feb6798631e12b2", "bytes": 1212, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C685"], "download": "/sources/0c4e0d9076a54766e9f785e161d46f440bbdf120b1f652397feb6798631e12b2.md", "format": "md", "derived": true, "tags": ["Calendar Keys"], "excerpt": "Do all three existing Keys yield one calibrated volume at34.5?", "content": "# C685 — Close the three-calendar micro triangle\n\n## Question\n\nDo all three existing Keys yield one calibrated volume at34.5?\n\n## Inputs\n\n```json\n{\n  \"seed\": \"69/2\",\n  \"calendar_lengths\": [\n    336,\n    360,\n    364\n  ],\n  \"operators\": [\n    \"E\",\n    \"P\",\n    \"J\"\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §6; C631 common calibration\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:13:12.649245+00:00\n\n## Results\n\n```json\n{\n  \"converted_counts\": [\n    \"75/2\",\n    35,\n    \"450/13\"\n  ],\n  \"calendar_volumes\": [\n    12600,\n    12600,\n    12600\n  ],\n  \"common_volume\": 12600\n}\n```\n\n## Finding\n\nAt the micro seed34.5, all three calibrated routes meet at12600:336×E(s)=360×P(s)=364×J(s). The Priestly route completes the source’s P/J comparison using the already established common-calibration identity.\n\n## Reassessment\n\nExplain the exact twentyfold relation between the micro seed and the native690 core.\n\n## Checks\n\n```json\n{\n  \"three_routes\": true,\n  \"P_count\": true,\n  \"E_count\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:13:12.649489+00:00\n\n## Record provenance\n\nExact record hash: `2c656f9311602fd91e4ee680c5b909212683e2edf9709eb4e20b875e5be41f55`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}