C46 — The added families expose one already retained endpoint match
22 September 2026 · Step 24 of the authorized 30-step Mirror continuation (C23–C52).
Release the selected-length match by writing
Retain the old partition assignments A=−s−3K, Z=−s+7K and H=A−2K, and define U=−u. Exact subtraction gives:
| Paths | Residual from their labelled multiple |
|---|---|
| old 17; new 15 intersection; old 20 and old 22 | ρ |
| new u→v 17; u→s 19; right 12 and 22; joined 24 | ρ+m |
The source has m=0: the cumulative c−cm length and the selected regular comparison are both 598. This is the C20/C12 retained match, now visible in the extended paths. With that match held, every new right-side residual is simply ρ, so the additions provide no new scalar calibration beyond the existing 17-fold closure.
If m is independently released, an old 17-fold residual and a new 19-fold residual have rank two in (ρ,m). Their difference measures m. That is a useful conditional diagnostic, not evidence that the original source values were independently predicted twice.
The reduced C22 constraints still supply ρ=2ω−C/2. The new graph therefore preserves the distinction between primitive source balances, the regular/cumulative endpoint binding, and dependent family widths.
Validation. 4 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. Build a bounded residual diagnosis that distinguishes width errors from endpoint-binding errors.