Linear independence of classes from different cores

Determine whether fortuitous cohomology classes obtained from two different choices of nonabelian core are linearly independent.

Background

The all-rank construction embeds an SU(2) fortuitous core into higher-rank gauge groups, but it does not establish how many inequivalent classes arise from different core choices. In particular, the authors leave unresolved whether distinct core constructions necessarily produce linearly independent cohomology classes.