C150 — Paired reflection preserves the finite residual square
23 September 2026 · Bounded step 15 of 20 (C136–C155).
Reflecting all four vertices preserves the same numerical square when event order is restored. It exchanges the cumulative-side and regular-side roles; it does not identify them.
The original arrangement has BC rows U,D and reflected AD columns M,X. Global reflection gives BC rows X,M and reflected AD columns D,U. Its matrix is
The diagonal positions exchange, but their equal values make the displayed matrix unchanged. The two side lengths exchange roles and remain 2K+δ. This invariance follows from reflection and equal diagonals; it is not a second independent family of source witnesses.
The check uses File_09/C127's paired convention: BC base b has coordinates −b−¼, −b+¼, and reflected AD base b has b−¼, b+¼. Negation plus reversal of component order maps one pair to the other. Both corresponding civil-season counts remain b+a.
For retained U members without materialized graph nodes, the reflected display is a permitted projection of the admitted field member, not a newly stored historical event. The historical graph, axis and source profiles remain fixed.
Source and scope control
All numerical bases in this packet stand for paired coordinates: BC base B is (B+1)t/Bn BC; reflected AD base A is AD At/(A+1)n. Thus a cross-Mirror same-season span is B+A, after the civil no-year-zero subtraction. AD stations are reflected source events, not historical AD occurrences. K=529 throughout.
Regular Gears remain restricted to Noah/Shem/Flood. Creation and Conquest are fixed source-field selections. C133–C135 corrections remain controlling. The C127 graph and canonical controls are frozen; source-field admission is distinguished from an existing graph node and from a generated comparison coordinate. No wider N01/N03 expansion or missing N03 Shem join is repaired. Original Reports 01–10 remain previously verified references; interrupted original Reports 11–25 remain unestablished. Check counts are computational assertions, not independent historical witnesses.
Evidence: CERTIFICATE.json; 168 passing assertions in RESULTS.json. The assertion list identifies the actual tests.