{"id": "c190", "title": "C190 — Conjugation preserves the ratio while transporting its anchor", "filename": "490d_C190_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 190, "sha256": "a61003c4dfecb7e63dfcafa6e66b425b9335c715e6b575afabc666ba12c99158", "bytes": 2052, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C190/490d_C190_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/a61003c4dfecb7e63dfcafa6e66b425b9335c715e6b575afabc666ba12c99158.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C190 — Conjugation preserves the ratio while transporting its anchor\n\n23 September 2026 · Step 35 of 50, continuing C155.\n\nThe exact operator relation is S∘Pₐ∘S=Pₛ₍ₐ₎. Complementing a dilation preserves its ratio and moves the anchor to8K−a.\n\nC05's−4444 anchor therefore moves to+8676. The algebra remains valid, but the", "content": "# C190 — Conjugation preserves the ratio while transporting its anchor\n\n23 September 2026 · Step 35 of 50, continuing C155.\n\n**The exact operator relation is S∘Pₐ∘S=Pₛ₍ₐ₎.** Complementing a dilation preserves its ratio and moves the anchor to8K−a.\n\nC05's−4444 anchor therefore moves to+8676. The algebra remains valid, but the transported anchor is generated and is not a member of the held apparent SP Creation field. At a=2116 the anchor is fixed, recovering the commutation in C189.\n\nThis separates formal closure of affine operations from closure of a chronology's source domain. A conjugate map can exist mathematically even when the source record that would justify its anchor is absent. The canonical Mirror axis and source profiles remain unchanged.\n\n## Evidence and scope\n\nK=529. Positive BC base B denotes (B+1)t/Bn BC; reflected AD base A denotes AD At/(A+1)n. Their same-season civil span is B+A, after the no-year-zero correction. AD source projections are not historical AD occurrences. Generated coordinates and interval midpoints do not acquire event identity from numerical coincidence.\n\nRegular Gears remain confined to Noah/Shem/Flood. Creation and Conquest use fixed source-field members; no fourth Gear is admitted. File_18/File_09 and the C127 graph are unchanged. C133–C155 source corrections remain controlling, with the C10 ancestry of the next-Flood-Gear rule now explicit. No historical campaign is rerun, no quarantined primer is reopened, and no N01/N03 expansion or missing Shem join is repaired. Original Reports 01–10 remain previously verified; interrupted original Reports 11–25 remain unestablished.\n\nSources: controlling File_18 §§2–3, 6A–6D; File_09 paired Mirror rules; selectively retained C05, C08, C10, C123, C128 and C133–C155 evidence. Specific dependencies are named in the body/certificate. **32 assertions passed**; see `RESULTS.json` and `CERTIFICATE.json`. Assertions, selected field combinations and inherited identities are not independent historical witness counts.\n", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}]}