C44 — Two valid Shem members cannot be silently identified
22 September 2026 · Step 22 of the authorized 30-step Mirror continuation (C23–C52).
The old head H and the existing earlier endpoint u share a named cumulative role but differ by 2j. On N01 they are 6350 BC and 6346 BC, both inside the native-ON field. The correct 24-fold interval uses H on the BC side and the reflection of u on the AD side.
| Branch | u self-Mirror width | Residual from 24K | Head self-Mirror formula | Residual | Head actually admitted |
|---|---|---|---|---|---|
| N01 | 12692 | -4 | 12700 | 4 | yes |
| N02 | 12690 | -6 | 12702 | 6 | no: formal only |
| N03 | 12688 | -8 | 12704 | 8 | no: formal only |
| N04 | 12686 | -10 | 12706 | 10 | no: formal only |
On N01, replacing H with u gives 12692, four short of 12696. Reflecting H instead of u gives 12700, four too long. The corresponding mistaken right 22-fold endpoint overshoots by four as well.
The u self-Mirror intervals are valid reflections of actual members, but their lengths are not 24K on these four branches. The head-self formulas on N02–N04 are only diagnostic because those heads are outside the field. Membership alone is insufficient even on N01: the correct member binding must also be preserved.
The ±2j signature distinguishes this conflation from a wrong 529 unit or a changed cumulative lifespan. It is a phase error between two endpoints, not an invitation to repair the source by shifting a date.
Validation. 6 exact arithmetic/structural checks passed. The ten 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 §3.1 (paired Mirror); File_18 §§2.1.3, 3.1–3.2, 6B and 6D (qualified regular and cumulative fields); frozen C15 typed graph, C16 domain certificate, and C22 reduced scale/constraint certificates.
Best next bounded step — High sufficient. Measure what happens when the native-ON endpoint is replaced by its derived-OFF counterpart.