C38 — A joined 24-fold Mirror path is admitted on N01

22 September 2026 · Step 16 of the authorized 30-step Mirror continuation (C23–C52).

The qualified N01 left head H and the newly reflected Shem endpoint U give a 24×529=12696 interval:

Its two source coordinates belong to the native LXX cumulative ON Shem envelope. They are distinct members: H uses 6350 BC and U reflects 6346 BC.

The path has both decompositions 12K+12K and 22K+2K. The first uses the retained comparison landing at 3t/2n BC; the second follows the old 22-fold interval to reflected OFF Flood 5288 and adds the 1058 interval to reflected ON Shem 6346.

This is a new dependent family label in the selected graph. It follows from the existing left head plus the new reflection of an already qualified endpoint. It does not require another source scale or a new Gear.

Within the already joined N01–N04 paths, only N01 admits the old left head, so only N01 receives this complete 24-fold chain. That statement does not exclude simpler source-only 24-fold pairs elsewhere in the same Shem field. A later bounded domain calculation will separate those raw endpoint pairs from the full joined path.

Validation. 5 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. Compare the local centres of the new 24-fold and retained 20-fold intervals.