C30 — A two-year branch change reverses under reflection

22 September 2026 · Step 8 of the authorized 30-step Mirror continuation (C23–C52).

For an abstract coordinate translation T_h(x)=x+h, the canonical reflection satisfies

Moving from N02 to N04 raises j from 3 to 5. The direct c,b,q,f,v,s points each rise by two, while their reflected and partition coordinates D,X,Y,A,Z fall by two. The same pattern holds from N01 to N03. Thus the whole display cannot be advanced by a single translation in the same direction on both sides of the Mirror.

In source terms, the primary N02→N04 comparison moves MT Noah and SP Noah from G1 to G2 and ordinary MT Flood from G2 to G3. Creation and Conquest select other members of their already fixed fields. That selection is not Gear transport of those fields. The SP companion-death support retains its own qualified station.

The algebra explains equal widths across the two full constructions while preserving their opposite movement under reflection. It does not authorize indefinite iteration: the third Gear and the cumulative field bounds terminate the source-qualified sequence.

Validation. 6 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. Distinguish the 23 lattice from the 529 lattice in the full Creation expansion.