# C85 — The 1058 midpoint completes a formal 11–12–13 ladder

22 September 2026 · Step 3 of the authorized ten-step Mirror continuation (C83–C92).

The original Joseph head is not the midpoint of the 1058 Conquest-to-upper-Flood interval. It lies 23 before that midpoint:

\[
506=529-23,\qquad 552=529+23.
\]

For the 1056 lower-Flood interval, its midpoint lies 22 beyond Joseph and splits 528+528. Thus changing the Flood endpoint by 2 moves the midpoint by 1.

| Branch | Conquest | Joseph | Lower midpoint | Upper midpoint | Upper Flood |
| --- | --- | --- | --- | --- | --- |
| N01 | 1399 | 1905 | 1927 | 1928 | 2457 |
| N02 | 1400 | 1906 | 1928 | 1929 | 2458 |
| N03 | 1401 | 1907 | 1929 | 1930 | 2459 |
| N04 | 1402 | 1908 | 1930 | 1931 | 2460 |

Against the same fixed Creation member, the upper midpoint has width 6348=12×529. This places it exactly between the already admitted 11×529 Conquest and 13×529 Flood endpoints:

\[
5819\ \xrightarrow{529}\ 6348\ \xrightarrow{529}\ 6877.
\]

The lower midpoint instead has Creation width 6347=12×529−1. Both are exact component-wise midpoints under the declared paired representation; reflection supplies their corresponding BC-side comparisons.

This step establishes the midpoint coordinates 1928/1929/1930/1931 and their arithmetic. It does not yet assign an event name merely from a number. The existing 12-fold family has other certified endpoints, and its event identities do not transfer automatically to these new coordinates. C86 checks a bounded candidate catalog in the already consulted File_61 and File_18.

**Validation.** 17 exact arithmetic/structural checks passed. The 16 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.** Check these midpoint coordinates against fixed Jacob-in-Haran and cumulative Levi records, preserving their distinct source classes.