{"id": "c672", "title": "C672 — Generate the complete phase bracket", "filename": "C672.md", "role": "Research action", "step": 672, "sha256": "3bc0243b7830df9fc413c5a1b49d58eb314488f9eb727e3d1173f35596396efc", "bytes": 1770, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C672"], "download": "/sources/3bc0243b7830df9fc413c5a1b49d58eb314488f9eb727e3d1173f35596396efc.md", "format": "md", "derived": true, "tags": [], "excerpt": "Can center, width and suffix offset recover all eight supplied endpoints?", "content": "# C672 — Generate the complete phase bracket\n\n## Question\n\nCan center, width and suffix offset recover all eight supplied endpoints?\n\n## Inputs\n\n```json\n{\n  \"base_center\": 2871,\n  \"widths\": [\n    34,\n    40\n  ],\n  \"phase_offsets\": {\n    \"n\": 0,\n    \"t\": \"1/2\"\n  },\n  \"BC_label_rule\": \"coord(tY)=Y−1/2\"\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §§4.1,4.3\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:10:25.916112+00:00\n\n## Results\n\n```json\n{\n  \"phase_rows\": [\n    {\n      \"width\": 34,\n      \"phase\": \"n\",\n      \"coordinates\": [\n        2888,\n        2854\n      ],\n      \"labels\": [\n        2888,\n        2854\n      ]\n    },\n    {\n      \"width\": 34,\n      \"phase\": \"t\",\n      \"coordinates\": [\n        \"5777/2\",\n        \"5709/2\"\n      ],\n      \"labels\": [\n        2889,\n        2855\n      ]\n    },\n    {\n      \"width\": 40,\n      \"phase\": \"n\",\n      \"coordinates\": [\n        2891,\n        2851\n      ],\n      \"labels\": [\n        2891,\n        2851\n      ]\n    },\n    {\n      \"width\": 40,\n      \"phase\": \"t\",\n      \"coordinates\": [\n        \"5783/2\",\n        \"5703/2\"\n      ],\n      \"labels\": [\n        2892,\n        2852\n      ]\n    }\n  ],\n  \"formula\": \"x=C+epsilon±w/2\"\n}\n```\n\n## Finding\n\nOne center/width/phase formula generates all eight before/after positions. Corresponding suffix widths are34 and40; Tishri and Nisan centers remain separated by half a year in exact coordinates.\n\n## Reassessment\n\nTest whether one global affine date map can perform this entire phase change.\n\n## Checks\n\n```json\n{\n  \"source_labels\": true,\n  \"fixed_phase\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:10:25.916432+00:00\n\n## Record provenance\n\nExact record hash: `7678cbcaa6477f93b68fab8add528ac5f16f45cd92d2602992138e0fc1a48d50`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}