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
| 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
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.