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
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.