Quadratic variations of rough generalized Hermite processes: hidden long memory and a universal Gaussian boundary field

We study centered quadratic variations of fractionally filtered generalized Hermite processes. For every chaos order $q\ge2$, every admissible anisotropic monomial kernel $g_{\boldsymbolγ}$, and every fixed $0<h\le1/2$, we prove that $N^{2h+θ-1}V_N$ converges to a Rosenblatt process with self-simila