# C36 — The 12-fold family gains four right-hand placements

22 September 2026 · Step 14 of the authorized 30-step Mirror continuation (C23–C52).

The newly reflected endpoint U=12K−j and retained landing Z=−j give

\[
U-Z=12K=6348.
\]

| Branch | Landing BC numeral | Reflected ON Shem numeral | Width |
| --- | --- | --- | --- |
| N01 | 2 | 6346 | 6348 |
| N02 | 3 | 6345 | 6348 |
| N03 | 4 | 6344 | 6348 |
| N04 | 5 | 6343 | 6348 |

All four joined N01–N04 branches admit this right-hand 12-fold interval. That differs from the old *left-head* 12-fold attachment H→Z, which is admitted only on N01. Equal family values do not make those two endpoint requirements equivalent.

The landing remains a retained Christ-period comparison coordinate, not an independently established historical birth date. For N02, 4t/3n BC to AD 6345t/6346n gives 6348 by either seasonal civil count.

The new span follows from the existing Shem member and the partition landing: it adds source-qualified placements, not a new unit or a new free equation. On N01 the left and right 12-fold intervals coexist. On N02/N03/N04 only this right-hand attachment is admitted within the selected construction.

**Validation.** 8 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.** Join the retained left 10-fold interval to the new right 12-fold interval.