# C49 — 6877 sits inside 10051 with a 339-year centre offset

22 September 2026 · Step 27 of the authorized 30-step Mirror continuation (C23–C52).

On each full Creation branch, the new 19-fold interval [u,s] contains the original 13-fold interval [b,f]. Its flanks are

\[
b-u=4K-p=1926,\qquad s-f=2K+p=1248.
\]

Together they remove 6K=3174 from 19K=10051, leaving 13K=6877. The 13-fold centre lies **K−p=339 years to the right** of the 19-fold centre.

| Branch | 19-fold centre | 13-fold centre | Offset |
| --- | --- | --- | --- |
| N02 | -2639/2 | -1961/2 | 339 |
| N04 | -2635/2 | -1957/2 | 339 |

This differs from the 13-within-17 geometry, where the same 13-fold centre lies 190 years to the left of the enclosing centre. Extending the left endpoint from c to u by 2K moves the outer centre left by K; therefore the offset changes from −p to K−p. No new date assignment is needed.

The left 1926 flank is the old 868 attachment plus the cumulative 1058 prefix. The right 1248 flank remains unchanged. This makes the integration explicit: 6877 is the same qualified Creation-to-reflected-Flood interval in both enclosures, not a different interval manufactured to fit 19.

The number 339 here is a geometric displacement derived from K and p. No further named event or lifespan relationship is inferred from its value. All endpoint admissions, including the local 299+299+650 Noah expansion, remain those of N02/N04.

**Validation.** 8 exact arithmetic/structural checks passed. The ten frozen dependencies passed hash verification; all three generated outputs replayed byte for byte in isolation, and the original dependencies remained unchanged. This step reads completed certificates and does not execute their campaigns.

**Scope and provenance.** Controlling File_18 and File_09 remain unchanged. Regular Gears apply only to Noah/Shem/Flood; SP person companions only to Noah/Shem. Creation and Conquest fields remain fixed. Native LXX ON, explicitly derived OFF, independent Flood start/close, and paired suffix inversion at January AD 1 remain in force. No civil year zero, upstream Gear transport, primers, Rounded campaign, or localized −33 is introduced. These are new continuation reports, not recovered historical Reports 11–25. Evidence is conditional on the supplied project model, not a proof of literary intention or independent historical dating.

**Source locators.** File_09 §3.1 (paired Mirror); File_18 §§2.1.3, 3.1–3.2, 6B and 6D (qualified regular and cumulative fields); frozen C15 typed graph, C16 domain certificate, and C22 reduced scale/constraint certificates.

**Best next bounded step — High sufficient.** Assemble an exact endpoint atlas for the two full 6877 branches and the N01 24-fold branch.