{"id": "c178", "title": "C178 — The Flood complement gives a residual-aware palindrome", "filename": "490d_C178_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 178, "sha256": "5e78c3dd3fdd7443c4490b5e40e1c6a7d40ec23987e20c0385542d146011fb5d", "bytes": 2139, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C178/490d_C178_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/5e78c3dd3fdd7443c4490b5e40e1c6a7d40ec23987e20c0385542d146011fb5d.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C178 — The Flood complement gives a residual-aware palindrome\n\n23 September 2026 · Step 23 of 50, continuing C155.\n\nThe Conquest complement window admits an ordered q→S(f)→f→S(q) palindrome. Its inner boundaries respond to δ while its outer width stays fixed for a held q.\n\n\\\n(6K-2q+\\delta)+(2q-4K-2\\delta)+(6K-2q+\\delta", "content": "# C178 — The Flood complement gives a residual-aware palindrome\n\n23 September 2026 · Step 23 of 50, continuing C155.\n\n**The Conquest complement window admits an ordered q→S(f)→f→S(q) palindrome.** Its inner boundaries respond to δ while its outer width stays fixed for a held q.\n\n\\[\n(6K-2q+\\delta)+(2q-4K-2\\delta)+(6K-2q+\\delta)=8K-2q.\n\\]\n\nFor P6's admitted G3 start, the AD paired bases are **1403→1772→2460→2829**, giving **369+688+369=1426**. The q and f stations are reflected sources; S(f) and S(q) are generated complements. They are not newly identified historical events at1772 or2829.\n\nThis supplies a precise way to place the deformed Flood route inside the same4K-centered architecture used for Moses and Peleg. The palindrome follows from applying one complement to the endpoints; its symmetry is not a new independent numerical witness.\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. **79 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"}]}