# C168 — The 8K preimage carries the native 11K residual into its first leg

23 September 2026 · Step 13 of 50, continuing C155.

**An 8K preimage is exact by construction; it does not erase a mismatch in the native Creation–Conquest pairing.** With γ=b+q−11K and generated z=8K−q,

\[
b-z=3K+\gamma,
\qquad f-q=2K+\alpha-\eta-\delta-\rho-\gamma.
\]

Thus the generalized Creation route has a 3K+γ first leg, an exact generated 8K leg, and the stated final Flood leg. Opposite γ contributions cancel from the total b→f span, because q is an internal subdivision.

This is consistent with C128's earlier ε diagnostic at the Conquest boundary; γ is the same kind of native 11K residual in the expanded grammar. Generated preimages retain their comparison status. A sourced q endpoint does not independently attest z or make the first leg exactly 3K.

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