FP definability throughout the positive class

Determine whether ordinary fixed-point logic (FP), rather than fixed-point logic with an ordered auxiliary number sort without counting (FP*), suffices for every finite-on-top-of-temporal CSP in the positive class.

Background

The main theorem establishes that every finite-on-top-of-temporal CSP that avoids the identified obstructions is definable in FP*. The conclusion notes that the stronger result using ordinary FP has not been established for the entire positive class. Thus, whether all positively classified CSPs admit FP definitions remains open.