# C33 — A qualified 19-fold Mirror interval from cumulative Shem to Noah

22 September 2026 · Step 11 of the authorized 30-step Mirror continuation (C23–C52).

The retained native-ON cumulative Shem endpoint u supplies a **19×529=10051** Mirror width to reflected SP Noah s:

\[
s-u=(c-u)+(s-c)=2K+17K=19K.
\]

| Branch | ON cumulative Shem BC numeral | Reflected SP Noah numeral | Width | Full Creation expansion |
| --- | --- | --- | --- | --- |
| N01 | 6346 | 3705 | 10051 | no |
| N02 | 6345 | 3706 | 10051 | yes |
| N03 | 6344 | 3707 | 10051 | no |
| N04 | 6343 | 3708 | 10051 | yes |

These are already qualified endpoints in the C15 graph. The new work composes the existing 2-fold cumulative prefix and 17-fold Mirror path through their common c node. No endpoint search, extra Gear, or new chronology profile is required.

For N02 the actual paired interval is 6346t/6345n BC to AD 3706t/3707n. Either same-season civil count gives 10051. N04 gives the corresponding 6343/3708 coordinate magnitudes. N01/N03 also support the 19-fold path, even though their full Creation expansion lacks an admissible MT Noah birth.

This is a new explicit dependent family in this continuation's selected register; it was not one of C15's eight enumerated family labels. Its value is forced by 2+17, so it does not add an independent calibration or witness. It does add a concrete, source-qualified endpoint relationship to the synthesis around 6877.

**Validation.** 12 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.** Inspect the overlapping 17-fold paths and their source-qualified 15-fold intersection.