Is the thick, yellow fluid that emerged after thoughts of lust semen, necessitating a full month of fasting as expiation for a vow of masturbation, or is it madhy (pre-ejaculate)?

The practice of masturbation is Haram (forbidden) in Islamic law, naturally repulsive, and has health detriments. One must repent from it. A vow made by a person to prevent themselves from it (a vow of contention/rage) does not necessitate fulfillment upon breaking it. Rather, its maker has the choice between fulfilling the vow or offering an expiation for an oath. Thinking that does not intend the emission of semen is not considered a breach (of the vow), and the emission of the mentioned fluid does not constitute a breach if it was not intended for the fulfillment of lust. The best way to prevent oneself from what is forbidden is through mindfulness of Allah Almighty, marriage, or fasting.