# C164 — Two cumulative candidates fail only at the Noah attachment

23 September 2026 · Step 9 of 50, continuing C155.

**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.**

| U | D | Required M | Required X | Complete square? |
|---|---|---|---|---|
| 6348 | 5290 | 2645 | 3703 | False |
| 6347 | 5289 | 2646 | 3704 | False |
| 6346 | 5288 | 2647 | 3705 | True |
| 6345 | 5287 | 2648 | 3706 | True |
| 6344 | 5286 | 2649 | 3707 | True |
| 6343 | 5285 | 2650 | 3708 | True |

The 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.

This 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.

## Evidence and scope

K=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.

Regular 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.

Sources: 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.