{"id": "c721", "title": "C721 — Relate the two exact phase charts", "filename": "C721.md", "role": "Research action", "step": 721, "sha256": "9ca746c834806440d3ac3ae02c1a31358d9446a06a4bb5eb802d2fe34414f4b1", "bytes": 1399, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C721"], "download": "/sources/9ca746c834806440d3ac3ae02c1a31358d9446a06a4bb5eb802d2fe34414f4b1.md", "format": "md", "derived": true, "tags": [], "excerpt": "How does the earlier positiveBC phase chart connect to the fixed-set signed chart?", "content": "# C721 — Relate the two exact phase charts\n\n## Question\n\nHow does the earlier positiveBC phase chart connect to the fixed-set signed chart?\n\n## Inputs\n\n```json\n{\n  \"earlier_chart\": \"q(Bn)=B; q(Bt)=B−1/2\",\n  \"signed_chart\": \"x(Bn)=−B+1/4; x(Bt)=−B+3/4\",\n  \"Short_center_labels\": [\n    \"2922t\",\n    \"2921n\"\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"Supplement A §§4.1,13.1–13.2; reviewer C692–C709\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:26:27.475595+00:00\n\n## Results\n\n```json\n{\n  \"chart_map\": \"x=1/4−q\",\n  \"sample_T_x\": \"-11753/4\",\n  \"sample_N_x\": \"-11755/4\",\n  \"center_pair_q\": [\n    \"5843/2\",\n    2921\n  ],\n  \"center_pair_x\": [\n    \"-11685/4\",\n    \"-11683/4\"\n  ],\n  \"January_center\": -2921\n}\n```\n\n## Finding\n\nThe charts are related by x=1/4−q. The2922t/2921n center pair brackets the January instant−2921 by a quarter-year on either side; neither labeled phase position alone is that instant. This resolves the chart relation without changing the source phases.\n\n## Reassessment\n\nApply all independent review refinements to the final integrated manuscript.\n\n## Checks\n\n```json\n{\n  \"T_rule\": true,\n  \"N_rule\": true,\n  \"center_pair\": true,\n  \"January_center\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:26:27.476086+00:00\n\n## Record provenance\n\nExact record hash: `05c0c928fe5398864d7f4c46c6e269862338e93e8a75004bf6efec16ae1258e5`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}