Euclidean-Normalized Multivariate and Pearson Separations

Establish whether the multivariate and Pearson feature-priming rules admit lower bounds matching the unnormalized Hadamard separations when inputs are constrained by Euclidean normalization.

Background

The Hadamard constructions used for the main lower bounds employ sign-valued rows whose Euclidean norm is of order $\sqrt d$. The paper shows that the powered-univariate lower bound persists after normalizing the inputs to have Euclidean norm at most one, but it does not establish the analogous result for multivariate or Pearson priming.

This leaves unresolved whether comparable separations, and hence comparable worst-case frontiers, persist under the additional Euclidean constraint for those two rules.