# C181 — The Noah partition crosses the axis after an 8K complement

23 September 2026 · Step 26 of 50, continuing C155.

**Applying S to the reflected Noah construction produces a generated cross-axis3+2+5 route with the same residual.** In increasing signed order its points are

\[
-2K-s\ \to K-s\ \to3K-j\ \to8K-s,
\]

with intervals **3K,2K+δ,5K−δ**. The first point is a BC center; the remaining three are AD centers. The total remains10K.

At P6's nearest boundary this gives signed centers −1064→523→1582→4226, with lengths1587+1059+2644. These are complements of the reflected source/comparison route, not a new historical sequence. In particular, the original Christ-period landing Z remains a comparison station, and its image is generated.

This links the8K operator to the Noah partition at the level of exact paired geometry. Source identity does not follow merely because the resulting route again has familiar529 coefficients.

## 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. **49 assertions passed**; see `RESULTS.json` and `CERTIFICATE.json`. Assertions, selected field combinations and inherited identities are not independent historical witness counts.