Is (u, v) always an f-corner in the disjoint sum G+H?

Ascertain whether, for DFAs G and H over the same alphabet Ψ that each admit an f-corner u in G and an f-corner v in H, the pair (u, v) is necessarily an f-corner of the disjoint-sum DFA G+H.

Background

The authors show that if G and H have f-corners u and v, then the disjoint sum G+H is (u, v)-synchronizable. However, they do not establish whether (u, v) is itself an f-corner in G+H, which would allow a direct application of the cornering strategy and potentially yield sharper bounds.

Clarifying whether the corner structure lifts under disjoint sum would strengthen the theoretical framework for simultaneous synchronization across multiple DFAs driven by a common input alphabet.