{"id": "c673", "title": "C673 — Test one-map compression of the phase family", "filename": "C673.md", "role": "Research action", "step": 673, "sha256": "9fc55595b09ecf2e53d0b2999c42f296bc0035d3e7ed849e719e322f3a4280b5", "bytes": 1237, "origins": ["C480–C1634/Research_Cycles/C0632_C0731/journal.json#C673"], "download": "/sources/9fc55595b09ecf2e53d0b2999c42f296bc0035d3e7ed849e719e322f3a4280b5.md", "format": "md", "derived": true, "tags": [], "excerpt": "Can one affine function change34 to40 while preserving every half-year phase separation?", "content": "# C673 — Test one-map compression of the phase family\n\n## Question\n\nCan one affine function change34 to40 while preserving every half-year phase separation?\n\n## Inputs\n\n```json\n{\n  \"width_change\": [\n    34,\n    40\n  ],\n  \"phase_change\": [\n    \"1/2\",\n    \"1/2\"\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"C672\",\n  \"Supplement A §4.3\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:10:37.837145+00:00\n\n## Results\n\n```json\n{\n  \"required_width_slope\": \"20/17\",\n  \"required_phase_slope\": 1,\n  \"false_global_phase_gap\": \"10/17\",\n  \"role_specific_rule\": \"C+epsilon+(20/17)(x−C−epsilon)\"\n}\n```\n\n## Finding\n\nA single affine date map is impossible: width demands slope20/17, while the preserved phase separation demands slope1. The valid expression dilates around each phase’s own center. This explains why the full object needs a phase coordinate.\n\n## Reassessment\n\nCompare the scalar34.5 Key input with the coordinate34-to40 construction.\n\n## Checks\n\n```json\n{\n  \"incompatible\": true,\n  \"phase_miss\": true,\n  \"phase_specific\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:10:37.837450+00:00\n\n## Record provenance\n\nExact record hash: `acb88dbed3d675e012284caf3a98ebde7ef4e3ebf8c24677937e2a5ce1694f19`\n\nSource journal: `Research_Cycles/C0632_C0731/journal.json`", "journalDownload": "/sources/f0643e934c6a7443706351fa40040684d915ed0ae25c0f9188a4c4dba12814ff.json"}