# C156 — 190 is a profile offset; 868 is a member alignment

23 September 2026 · Step 1 of 50, continuing C155.

**The offsets have different source origins.** File_18 gives the retained alternate MT comparison as ordinary MT plus regular Cainan 130 and Terah 60, hence **190=130+60** without using any target 529 equation.

The cumulative LXX OFF Moses-line Flood base is 5745−460=5285. The fixed SP full-430 Creation endpoint is 4199+215=4414. Their unselected base difference is **871**, not 868. Write a cumulative member D=5285+e (−2≤e≤5) and native Creation member b=4414+h (0≤h≤7). Then

\[
D-b=871+e-h=868\quad\Longleftrightarrow\quad h=e+3.
\]

P6 uses e=−1,h=2, giving 5284−4416=868. Thus 868 is a measured relation of aligned field members, not a universal translation between the two complete chronologies. Once selected, 868+190=1058=2K is exact.

The audit also identifies an inherited result: C10 already explicitly derived the next-Flood-Gear rule and 1058=598+460. C149 recovered that rule consistently; it should be counted as verification rather than a new independent discovery. This batch develops the source-selection conditions beyond that inherited result.

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