{"id": "c164", "title": "C164 — Two cumulative candidates fail only at the Noah attachment", "filename": "490d_C164_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 164, "sha256": "9900df688a44360bfabc159e5ca16ea42f55fc95065bfe22a35043f3f00ce330", "bytes": 2411, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C156_C205_529_Source_Grammar_20260923/C164/490d_C164_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/9900df688a44360bfabc159e5ca16ea42f55fc95065bfe22a35043f3f00ce330.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "C164 — Two cumulative candidates fail only at the Noah attachment\n\n23 September 2026 · Step 9 of 50, continuing C155.\n\nAll six cumulative 2K comparisons can attach a retained MT alternate Flood to a 17K diagonal, but only four can also attach the required SP Noah.\n\n| U | D | Required M | Required X | Complete square? |", "content": "# C164 — Two cumulative candidates fail only at the Noah attachment\n\n23 September 2026 · Step 9 of 50, continuing C155.\n\n**All six cumulative 2K comparisons can attach a retained MT alternate Flood to a 17K diagonal, but only four can also attach the required SP Noah.**\n\n| U | D | Required M | Required X | Complete square? |\n|---|---|---|---|---|\n| 6348 | 5290 | 2645 | 3703 | False |\n| 6347 | 5289 | 2646 | 3704 | False |\n| 6346 | 5288 | 2647 | 3705 | True |\n| 6345 | 5287 | 2648 | 3706 | True |\n| 6344 | 5286 | 2649 | 3707 | True |\n| 6343 | 5285 | 2650 | 3708 | True |\n\nThe first two cases require X3703 and X3704, outside the SP Noah field. The remaining four are exactly N01–N04. Thus the cumulative two-member displacement and the regular next-Gear selection meet on the same four finite source configurations.\n\nThis independently separates the sources of the exclusions. The cumulative 1058 equality is available in six places; the regular Noah birth field removes two. The resulting four-row match is a joint source intersection, not a universal claim that every cumulative 598 identifies a regular Noah–Flood event span.\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. **21 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"}]}