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.