The kernel F2 case for translation generalized quadrangles

Determine the structure and classification of translation generalized quadrangles of order (s, s²) in the unresolved case where the kernel is F2.

Background

The paper derives strong structural conclusions for translation generalized quadrangles of order (s, s²) when the kernel is not F2, including links with semifield-flock generalized quadrangles and classical generalized quadrangles. The exceptional kernel F2 case is not covered by those results and is explicitly left open.