{"id": "c174", "title": "C174 — Reflection exchanges diagonal defects and adjusts the side residual", "filename": "490d_C174_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 174, "sha256": "0cd706587e1df3141bfa9705b9b749ec47ddea47eed3b632e081a51d2dd87a3c", "bytes": 2130, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C174/490d_C174_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/0cd706587e1df3141bfa9705b9b749ec47ddea47eed3b632e081a51d2dd87a3c.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Inverse", "Mirror / 529"], "excerpt": "C174 — Reflection exchanges diagonal defects and adjusts the side residual\n\n23 September 2026 · Step 19 of 50, continuing C155.\n\nThe generalized square remains reflection-compatible, but its residual labels transform. Reflect all vertices, reverse event order, and use new BC rows X,M with new AD columns D,U. Then\n\n\\\n\\a", "content": "# C174 — Reflection exchanges diagonal defects and adjusts the side residual\n\n23 September 2026 · Step 19 of 50, continuing C155.\n\n**The generalized square remains reflection-compatible, but its residual labels transform.** Reflect all vertices, reverse event order, and use new BC rows X,M with new AD columns D,U. Then\n\n\\[\n\\alpha'=\\beta,\\qquad\\beta'=\\alpha,\\qquad\\delta'=\\delta+\\beta-\\alpha.\n\\]\n\nThe square matrix is numerically unchanged precisely when α=β; otherwise its unequal diagonal entries exchange places. C150's invariance is recovered at α=β=0.\n\nThis transforms the square's numerical roles, not regular source profiles into cumulative ones. The separate native Creation and ordinary-Flood residuals are not silently carried to new historical identities. All reflected pair components retain File_09's negation-and-order-reversal rule.\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. **101 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"}]}