# C87 — The 529 midpoint is four years below the Levi member aligned with Joseph

22 September 2026 · Step 5 of the authorized ten-step Mirror continuation (C83–C92).

The midpoint's source identity must be separated from the Levi member that generates the original Joseph portion. File_61 §11 gives the invariant same-member difference

\[
L-J=137-110=27.
\]

Since the 1058 midpoint is J+23, it lies L−4. The 1056 midpoint is J+22=L−5. These are comparisons between retained cumulative members, not new translations of the genealogy.

| j | Joseph head | Kohath boundary | Aligned Levi member | 1058 midpoint | 1056 midpoint |
| --- | --- | --- | --- | --- | --- |
| 2 | 1905 | 1795 | 1932 | 1928 | 1927 |
| 3 | 1906 | 1796 | 1933 | 1929 | 1928 |
| 4 | 1907 | 1797 | 1934 | 1930 | 1929 |
| 5 | 1908 | 1798 | 1935 | 1931 | 1930 |
| 6 | 1909 | 1799 | 1936 | 1932 | 1931 |
| 7 | 1910 | 1800 | 1937 | 1933 | 1932 |

N02's Joseph 1906 is aligned with Levi 1933 and Kohath 1796. Its upper midpoint 1929 is the separately fixed Jacob-Haran record, four below Levi. N04's Joseph 1908 is aligned with Levi 1935 and Kohath 1798, while its midpoint 1931 is a different Levi-envelope member. Identifying the 1931 midpoint with the 1935 source member would erase this four-year distinction.

The original Levi field 1931…1938 and its arithmetic image 1927…1934 overlap only at 1931…1934. That explains why a Levi label is admitted for only part of the midpoint catalog. It does not authorize moving Levi by−4 as a regular Gear operation.

The entire aligned Levi-to-Conquest interval is 533=506+27=529+4. Thus the same four-year difference appears whether read from Joseph's source lifespan contrast or from the proposed 529 midpoint. These equations express one source dependency; they should not be counted as separate confirmations. For j=6/7 the upper midpoint remains a formal midpoint coordinate because its upper Flood is absent, even when the coordinate itself matches a Levi member.

No H7/T14 portion, new birth rule, or upstream Gear movement is introduced. The original backward Joseph portion is sufficient for this distinction.

**Validation.** 21 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.** Extend the sourced 506+552 partition through the held MT Noah birth and test the 22–24–26 multiples-of 23 ladder.