C58 — The two equal 1058 prefixes use different source decompositions
22 September 2026 · Step 6 of the authorized ten-step Mirror continuation (C53–C62).
Write positive BC numerals as F₋=5290−j (LXX OFF Flood), F₊=5290+j (MT ON Flood), S₋=6348−j and S₊=6348+j (two native-ON Shem members). These subscripts describe the index sign, not Cainan state or a regular Gear.
Their Moses-side gaps differ. ON Shem minus LXX OFF Flood is 1060; ON Shem minus MT ON Flood is 1054. The retained member selections compensate:
The first prefix uses a two-year reduction from its Moses-side gap. The second uses a four-year increase. The difference between these adjustments is six, exactly the source displacement Δ=460−454.
| j | LXX Flood offset | Lower Shem offset | MT Flood offset | Upper Shem offset |
|---|---|---|---|---|
| 0 | 5 | 3 | -1 | 3 |
| 1 | 4 | 2 | 0 | 4 |
| 2 | 3 | 1 | 1 | 5 |
At N01 (j=2), these offsets are +3,+1,+1,+5. The right prefix spans the +3/+1 selection; the left spans +5/+1 across its differently based source rows. Both use positions in the 2+2+3 numeric template, but that does not assign this cumulative template to regular Gear 2.
This explains the equal margins of the 20/24 construction without pretending their source mechanisms are identical. Since 454=460−6 and the endpoints were already linked, the two decompositions do not add independent unit determinations. Their value is to preserve the actual chronology and member roles behind the equality.
Validation. 9 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. Intersect all four cumulative source fields and identify the shared week-boundary template of the joined N01 rectangle.