C89 — The complete 2-fold sequence 1058→1150→1250 has retained endpoint pairs
22 September 2026 · Step 7 of the authorized ten-step Mirror continuation (C83–C92).
N02 and N04 now support all three stages of the 2-fold expansion with named endpoint pairs. Hold the ordinary Creation member and apply the same phase-preserving 25/23 map to both ends of each interval:
| Branch | 1058=2×529 | 1150=2×575 | 1250=2×625 |
|---|---|---|---|
| N02 | 1400→2458 | 1906→3056 | 2456→3706 |
| N04 | 1402→2460 | 1908→3058 | 2458→3708 |
The source roles progress as follows:
| Stage | Left reflected endpoint | Right reflected endpoint |
|---|---|---|
| 1058 | Fixed Conquest member | Upper-Gear MT Flood start |
| 1150 | Original backward cumulative Joseph head | Lower-Gear MT Noah birth |
| 1250 | Lower-Gear MT Flood start | Same-Gear SP primary Noah birth |
This source qualification is specific to the present placement. C09's scalar table listed 1150 and 1250 as generated in its original 2-fold construction. The present interval realization follows from the newly named 11-fold endpoints together with the retained 13-fold endpoints. It does not retroactively transfer these identities to every expansion of a1058 interval.
The first product grid, measured from fixed Creation, is
Its row differences are 506/598 and column differences 1058/1150. The determinant vanishes because the two rows share 25/23, so the 22–24–26 progression is a dependent consequence of this grid.
The second 1250 interval also has the already verified same-Gear dissection 600+650. Interval widths grow by 92 and 100 because their right endpoints move 598/650 while their left endpoints move 506/550. This preserves the distinction between endpoint motion and the width of the moving interval.
The exact bounded source domains differ by stage:
| Stage | Admitted j | Qualification |
|---|---|---|
| 1058 | [2, 3, 4, 5] | Both Conquest and upper Flood present |
| 1150 | [3, 5, 7] | Joseph and MT primary Noah present |
| 1250 | [2, 3, 4, 5, 6, 7] | Lower MT Flood plus SP primary/companion Noah |
| All three | [3, 5] | N02/N04 only |
For the three close-ending 1250 rows, the SP Noah endpoint is the corresponding SP person companion. That is an authorized SP-only binding, not an MT companion or a Flood person rail. The MT Noah endpoint needed by 1150 is absent on those close rows. G3 admits the 1150/1250 tail, while its 1058 head lacks upper Flood 2462.
Both endpoints and both seasonal components pass the two exact affine maps. These are source-qualified interval images; they do not license transporting unrelated records by a whole-chronology dilation.
Validation. 18 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. Compare this 506+552 dissection of 1058 with the retained cumulative 460+598 dissection, keeping endpoint frames distinct.