{"id": "c219", "title": "C219 — A fixed 650 translation does not commute with expansion", "filename": "490d_C219_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 219, "sha256": "9dd9373e0bff1a73383d0bc8dc2857b109219335536c21fded022588bdec54f3", "bytes": 1953, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C206_C265_529_Expansion_Centers_20260923/C219/490d_C219_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/9dd9373e0bff1a73383d0bc8dc2857b109219335536c21fded022588bdec54f3.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C219 — A fixed 650 translation does not commute with expansion\n\n23 September 2026 · Step 14 of 60, continuing C205.\n\nKeeping the translation amount unchanged changes the operation. Pₐ∘T₆₅₀−T₆₅₀∘Pₐ=1300/23, while the analogous fixed-598 commutator is 52.\n\n| Chain | 650 commutator |\n|---|---|\n| 3 | 1300/23 |\n| 5 | 1300/2", "content": "# C219 — A fixed 650 translation does not commute with expansion\n\n23 September 2026 · Step 14 of 60, continuing C205.\n\nKeeping the translation amount unchanged changes the operation. Pₐ∘T₆₅₀−T₆₅₀∘Pₐ=1300/23, while the analogous fixed-598 commutator is 52.\n\n| Chain | 650 commutator |\n|---|---|\n| 3 | 1300/23 |\n| 5 | 1300/23 |\n\nC218’s intertwining works because the translation itself scales from 598 to 650. It is not ordinary commutation with either fixed source displacement. This matters when combining the source rectangle with the expansion ladder: rearranging the operations without changing the translation introduces a real residual, which cannot be removed by a seasonal convention.\n\n## Evidence and scope\n\nK=529 and r=25/23. BC base B means (B+1)t/Bn BC; reflected AD base A means AD At/(A+1)n. Their civil span is B+A in both seasonal components, with no year zero. Signed paired centers are −B and +A; the center model uses components ±1/4 and restores this separation after dilation. An interval center is geometry, not an event or a proposed universal Mirror axis.\n\nRegular Gears are restricted to Noah/Shem/Flood. Creation and Conquest retain fixed source-field members; no fourth Gear is admitted. Generated coordinates, source-field membership and stored graph incidence are distinct. File_18/File_09 and the frozen C127 graph are unchanged. Earlier N01/N03 qualifications, the missing Shem join, closed primers and unestablished original Reports 11–25 remain unchanged. This packet selectively uses prior evidence; it does not rerun completed campaigns. Assertions and alternative placements are not independent historical witness counts.\n\n**5 step-specific checks and 19 frozen-input checks passed.** Exact inputs, results and predecessor hashes are in the accompanying JSON records; calculation code is in the evidence archive. Source dependencies are identified in the body and frozen in `sources/`.\n", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}]}