# C88 — The sourced Mirror chain has 22–24–26 multiples of 23

22 September 2026 · Step 6 of the authorized ten-step Mirror continuation (C83–C92).

Extend the 506+552 Joseph partition through the already retained MT Noah birth. On both complete branches, the consecutive intervals are

\[
506, 552, 598=23\,(22, 24, 26).
\]

| Branch | Conquest | Joseph head | Upper MT Flood | Held MT Noah | Consecutive increments |
| --- | --- | --- | --- | --- | --- |
| N02 | 1400 | 1906 | 2458 | 3056 | [506, 552, 598] |
| N04 | 1402 | 1908 | 2460 | 3058 | [506, 552, 598] |

The sequence increases by 46=2×23 at each step and totals 1656=72×23. Its two overlapping two-edge intervals have widths

\[
506+552=1058=46\times 23,
\qquad 552+598=1150=50\times 23.
\]

Their ratio is 25/23. This gives the first expanded 2-fold width 1150 a precise endpoint comparison: reflected original cumulative Joseph head to reflected regular MT Noah birth. The two branches use 1906→3056 and 1908→3058.

The final 598 keeps its established cross-Gear identity: upper-Gear Flood start to lower-Gear Noah birth. It is not a shortened Noah lifespan or a same-Gear Noah–Flood span. Conquest and Joseph remain fixed field selections without regular Gears.

The arithmetic progression is a structured dissection of the admitted 11/13 constructions. Its three entries and two overlapping sums share the same four records, so they are not independent numerical witnesses. C89 tests the complete 2-fold expansion, including the second 1250 interval and the exact source domains.

**Validation.** 11 exact arithmetic/structural checks passed. The 17 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 and Appendix A (paired Mirror and exact phase); File_18 §§2.1.3, 2.4, 3.1 and 6/6A (regular fields and cumulative collateral source); File_61 §§3.3–3.4, 11.1–11.4 and 14.3 (fixed Jacob events, original Joseph portion and its 500-year Conquest comparison); File_62 collateral-scope guards; frozen C15/C16/C22/C43/C65/C74–C77/C82 dependencies (retained source, phase and family controls). The declared phase model does not infer an unstated birthday or event month from an annual source row.

**Best next bounded step — High sufficient.** Certify all three 2-fold expansion stages 1058→1150→1250 as interval images, including their distinct endpoint domains.