This paper studies XOR signals on the Johnson slice and shows that the classical balanced parity-selection phenomenon is part of a broader Hermite structure. The analysis also reveals a new n^(-3) scaling law at the first Hermite-zero degeneracy point, where the generic behavior breaks down. More broadly, the results identify I S_n I \ asymp \ sqrt n as the transition scale between balanced and bias-dominated behavior. Together, these results exhibit a unified Hermite structure underlying Johnson spectral leakage for XOR signals.
Publication Date: 2026-06-19