C35 — A reflected ON Shem endpoint extends the registered graph

22 September 2026 · Step 13 of the authorized 30-step Mirror continuation (C23–C52).

Define U=−u, the canonical paired reflection of the existing native-ON cumulative Shem member. This adds four typed reflected nodes to the selected graph:

Each source endpoint was already admitted in C15, and each lies in the retained 6350–6343 BC ON Shem envelope. Reflection changes its projection, not its profile, named role or field membership. The certificate retains the original node ID as reflection_of.

U is not the reflection of the optional left head H. In the compact form u=−12K+j and H=−12K−j, so those source coordinates differ by 2j. On N01 the source u is 6346 BC while H is 6350 BC. U therefore reflects 6346, not 6350.

This is a bounded four-node graph extension. It does not search for another Shem date, vary Cainan, introduce a regular Gear on the cumulative chain, or treat every point in a cumulative field as an interchangeable endpoint. The admitted u binding is carried through unchanged.

Validation. 13 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. Measure the new right-hand 12-fold spans from the retained comparison landings to U.