Does the emission of anything after lowering the gaze or after attempting to cut off thoughts invalidate the fast?

The emission of pre-seminal fluid (madhy) does not invalidate the fast, whether it is due to thinking, kissing, or other reasons. This is the view of the Shafi'i and Hanafi schools, some Hanbalis, and the preferred opinion of Sheikh Ibn Uthaymeen. Their argument is that there is no evidence to suggest that this invalidates the fast.