Does merely thinking about sexual fantasies, without intention or pleasure, and without the occurrence of vibrations or the emission of semen, invalidate the fast of one who is struggling to abstain from these thoughts?

Fasting is not invalidated by the aforementioned thoughts, even if madhy (pre-seminal fluid) or maniy (seminal fluid) is discharged. The emission of madhy nullifies wudu (ablution), and the emission of maniy necessitates ghusl (ritual bath). However, if nothing is discharged, wudu is not nullified merely by thoughts, and the fasting person will be rewarded for striving against their self to divert it from such thoughts.