{"id": "c177", "title": "C177 — The 8K insertion preserves the Flood residual", "filename": "490d_C177_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 177, "sha256": "ef878b9d17c8c330a68695bd4c6d2e38903856a84fcfdf3d84e0671f5d721e44", "bytes": 2180, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C177/490d_C177_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/ef878b9d17c8c330a68695bd4c6d2e38903856a84fcfdf3d84e0671f5d721e44.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C177 — The 8K insertion preserves the Flood residual\n\n23 September 2026 · Step 22 of 50, continuing C155.\n\nOn the retained alignment, every sourced Creation/Conquest/Flood choice has the refinement 3K+8K+(2K−δ). Inserting the generated 8K preimage preserves the actual 13K−δ total.\n\n\\\nb\\ \\textBC\\to z\\ \\textBC\\to q\\ \\tex", "content": "# C177 — The 8K insertion preserves the Flood residual\n\n23 September 2026 · Step 22 of 50, continuing C155.\n\n**On the retained alignment, every sourced Creation/Conquest/Flood choice has the refinement 3K+8K+(2K−δ).** Inserting the generated 8K preimage preserves the actual 13K−δ total.\n\n\\[\nb\\ \\text{BC}\\to z\\ \\text{BC}\\to q\\ \\text{AD}\\to f\\ \\text{AD},\n\\qquad 3K+8K+(2K-\\delta)=13K-\\delta.\n\\]\n\nP6's nearest admitted route is 4416→2829→AD1403→AD2460 in paired bases, with lengths 1587+4232+1057=6876. The missing exact Flood continuation cannot be supplied by the exactness of the middle 4232.\n\nThis extends the earlier exact C122 route to the now explicit residual family. The generated station remains generated, and the two sourced end-to-end comparisons retain their profiles. The 8K framework therefore connects naturally to the 529 analysis without hiding the one-year source boundary.\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"}]}