Practical necessity of core-conditioned selector

Determine whether the core-conditioned Togeari-M selector provides a practical advantage over the cheaper raw-factor Togeari-R selector across distinct physical regimes.

Background

Togeari-M selects contact combinations using the core-response Gram matrix $UM^{-1}U^T$, whereas Togeari-R uses the cheaper Euclidean Gram matrix $UU^T$. In the two tested contact-active extractions, both selectors produced the same five-vector Krylov basis and their retained subspaces were closely aligned.

The core-conditioned selector has the stronger conditional SPD theory, but the experiments do not establish that this theoretical advantage translates into better practical performance. The authors therefore leave its practical value unresolved across broader regimes.