# C162 — Two distinct source mechanisms supply the same numerical 460

23 September 2026 · Step 7 of 50, continuing C155.

**The regular profile residual is 650−190=460; the cumulative Cainan insertion is a 460-year lifespan.** Their equality connects the regular and cumulative constructions, while their operations remain different.

In the regular comparison, 650 comes from SP–MT Noah birth coordinates, and 190 from MT Cainan/Terah switches. In the cumulative comparison, removing Cainan subtracts his lifespan 460 from the relevant upstream chain. It does not subtract the regular begetting insertion 130.

At the next-Gear selection, the regular Noah/Flood comparison is 600−2=598. Thus 598+460=1058=2K. This is the same source-sensitive identity already recorded in C08/C10, now grounded in the table inputs before comparing with K.

The equality provides a bridge of lengths. It does not identify a regular profile change with a cumulative lifespan operator, or prove why the chronology inputs take these values.

## 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.