Does the emission of pre-seminal fluid (madhy) or semen (maniy) due to fantasies invalidate the fast and necessitate expiation?

The majority of scholars hold that the emission of mani (sperm/seminal fluid) or madhy (pre-seminal fluid) due to mere thought does not invalidate the fast. However, the Malikis are of the opinion that if one experiences an emission of mani solely due to thought without persistence, their fast is invalidated, and they must make up for it. If one persists in such thoughts until emission occurs, and it is their habit to experience emission through such persistence, then they must offer expiation (kaffara); otherwise, they do not. As for madhy, it only necessitates making up the fast.