Limits of Transport-Equivalent Grouping in Radiation-Response Materials: Evidence for π-Class Structure

This preprint examines a bounded 5 MeV ten-material comparison and shows that Xi-based transport-equivalent grouping can preserve transport-side similarity while leaving a structured response-side remainder aligned with π-class membership. On the declared slice, a single fitted Kπ factor compresses the full-slice residual RMS from 19.61% to 0.35%. The manuscript also reports bounded leave-one-out robustness, a corrected 3/5/7 MeV cross-energy carry check, a same-family transport-side support band, and a broader 20-material support map that situates the 5 MeV wedge inside a wider classified field without promoting that wider field into a coequal claim packet. This record is posted to establish a public, citable timestamped priority record for the manuscript version dated 2026-06-18.