Infinite-Dimensional Levy Area and Spectral Ancestry

We relate primitive ancestry in free-Lie expansions of infinite-dimensional Lévy area to critical weak-Schatten spectra. For $L=\mathfrak L(V)$, $D=[L,L]$, and $J=\ker(T(V)\to S(V))$, we prove $L\cap J^r=γ_r(D)$ and identify the exact normal layers with $\mathfrak L_r(D/[D,D])$. Continuous Hilbert-m