C60 — The 24-fold closure does not independently determine the six-year gap
22 September 2026 · Step 8 of the authorized ten-step Mirror continuation (C53–C62).
Hold the retained interval formulas and LXX source fields fixed, but formally release the MT-ON/LXX-OFF Moses-base displacement Δ. The MT ON membership condition becomes
The other three cumulative fields still require 0≤j≤2 jointly. The regular Noah join selects j=2, which is admitted precisely when 2≤Δ≤9.
| Formal Δ | Four-field cumulative j values | Joined j values | MT member offset at j=2 |
|---|---|---|---|
| 1 | [0, 1] | [] | 6 |
| 2 | [0, 1, 2] | [2] | 5 |
| 4 | [0, 1, 2] | [2] | 3 |
| 5 | [0, 1, 2] | [2] | 2 |
| 6 | [0, 1, 2] | [2] | 1 |
| 7 | [0, 1, 2] | [2] | 0 |
| 9 | [2] | [2] | -2 |
| 10 | [] | [] | -3 |
Therefore the existing 24-fold closure and endpoint bounds do not recover Δ=6 uniquely. Even requiring all four N01 offsets to lie in the 2+2+3 cut set permits Δ=2,4,6,9. The actual six-year value is supplied by the named source balance 460−454, not independently predicted by this family label or boundary classification.
At the source, the MT member and lower ON Shem member both have Moses-relative offset +1. Requiring that extra offset equality at j=2 would select Δ=6, but the equality would itself be an additional condition; it cannot be counted as a second derivation from the already selected endpoints.
These controls shift only a formal MT cumulative field while leaving the geometric construction fixed. They are not proposed chronology variants and do not alter any source lifespan. Their purpose is to distinguish a source explanation from an overstrong inverse claim.
Validation. 18 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. Audit the 6348 whole-year member and 6348.5 Aaron phase in the exact paired Mirror coordinates.