# C180 — Noah complements lie just below one 529-unit

23 September 2026 · Step 25 of 50, continuing C155.

**The six sourced SP Noah birth bases are 7K+s, with s=2,…,7; their8K complements are K−s.** This includes the sourced G3 primary boundary separately from the five admitted cumulative3K-start rows.

| Noah X | s | Generated S(X) | Cumulative3K start admitted? |
|---|---|---|---|
| 3705 | 2 | 527 | True |
| 3706 | 3 | 526 | True |
| 3707 | 4 | 525 | True |
| 3708 | 5 | 524 | True |
| 3709 | 6 | 523 | True |
| 3710 | 7 | 522 | False |

For the thirty aligned comparisons, s=d+1 and δ=s−j. The reversed complement interval is

\[
S(M)-S(X)=(3K-j)-(K-s)=2K+\delta.
\]

The offset from a pure529 multiple is therefore retained exactly under the complement. These522–527 coordinates are generated images of Noah source stations; this step does not identify them with later historical events or turn numerical proximity to a known era into source evidence.

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