# C54 — 1058 requires a two-year offset between the two cumulative members

22 September 2026 · Step 2 of the authorized ten-step Mirror continuation (C53–C62).

The two Moses-side bases differ by 600+460=1060:

\[
S_M=6345,\quad F_M=5285,\quad
S_M+b-(F_M+a)=1060+b-a.
\]

For this span to equal 1058=2K, the member offsets must satisfy **a−b=2**. Requiring both offsets to lie in the existing −2…+5 envelopes yields exactly six pairs:

| j | OFF Flood | Its offset a | ON Shem | Its offset b | Gap |
| --- | --- | --- | --- | --- | --- |
| 0 | 5290 | 5 | 6348 | 3 | 1058 |
| 1 | 5289 | 4 | 6347 | 2 | 1058 |
| 2 | 5288 | 3 | 6346 | 1 | 1058 |
| 3 | 5287 | 2 | 6345 | 0 | 1058 |
| 4 | 5286 | 1 | 6344 | -1 | 1058 |
| 5 | 5285 | 0 | 6343 | -2 | 1058 |

The j=0 row is OFF Flood opening 5290 and whole-year Aaron-side ON Shem 6348. The completed N01–N04 bindings are j=2,3,4,5. The j=1 pair is a valid cumulative-only pair; it does not supply the missing regular Noah join. j=6/7 fail this Shem binding because its required member lies below 6343.

Removing the source Cainan lifespan 460 from the ON Shem endpoint leaves a derived-OFF Shem endpoint exactly 598 from the selected OFF Flood member. The decomposition 1058=460+598 is therefore explicit for every row. The 598 is not the ordinary Shem lifespan: it compares differently positioned envelope members against the 600-year Moses-side separation.

The six pairs are related placements of one equation in fixed fields. Their number is not a count of independent confirmations, and the calculation does not assign regular Gear numbers to cumulative members.

**Validation.** 12 exact arithmetic/structural checks passed. The 13 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 §0.4 rules 21–22 and the Creation Cell / Aaron Phase guard (week anatomy), §3 (paired Mirror); File_18 §§4.2 and 6A–6D (lifespans and cumulative fields); frozen C15/C16/C22 and C43/C46/C48/C50/C52 certificates (retained graph, unit, and domains).

**Best next bounded step — High sufficient.** Distinguish envelope members from named cut boundaries under the three source-qualified week anatomies.