Determine whether HermNet achieves superiority under Gaussian-energy ring classification

Determine whether HermNet achieves superior classification performance under Gaussian spectral-energy conditions on ring graphs in the common-basis comparison.

Background

The paper evaluates HermNet against several complete polynomial bases and native graph architectures across synthetic graph families, spectral-energy distributions, and teacher responses. Although an enhanced HermNet advantage is reported for a ring/uniform/wave setting, the corresponding Gaussian-energy ring comparison does not yield a resolved superiority result. The unresolved comparison concerns whether the observed behavior transfers from the favorable uniform-energy regime to Gaussian spectral-energy conditions on ring graphs.