# 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

\[
m=\ell_{\rm cumulative}-\ell_{\rm regular},\qquad
u=c-(2K+m),\qquad B=17K+\rho.
\]

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.