What is the ruling on someone who, during a period of divorce-related obsessive thoughts, swore that he would not break his fast with his friends, then broke his fast with one of them after his friend moved to live with him in his new residence?

An oath is bound by the intention of the one who makes it. Whoever swears an oath to do something and then violates it has broken their oath, and an expiation for breaking an oath becomes obligatory upon them. However, if one doubts whether they made an oath, nothing is incumbent upon them, because the default assumption is that no oath was made. Similarly, obsessive thoughts about divorce do not cause harm.

Accordingly, nothing is binding upon you if you doubt having sworn an oath, whether it was by divorce or otherwise. If you are certain that you swore an oath not to break your fast with any of your friends, without any restriction of time or place, and then you broke your fast with one of them in a place other than your first residence, then you have broken your oath, and an expiation for breaking an oath is incumbent upon you if the oath was by Allah. However, if the oath was by divorce, it is considered binding by the majority of scholars, while Ibn Taymiyyah holds that it necessitates an expiation for breaking an oath if divorce was not intended.

You do not break your oath if you intended not to break your fast with friends in a specific residence and then you broke your fast with one of them after moving to another residence, because an oath is based on the intention of the one who makes it. Likewise, you do not break your oath if the reason for the oath ceases to exist without any action on your part.

In your case, nothing is incumbent upon you as long as you do not remember having sworn an oath, for the default assumption is that no oath was made. It is advised to stay away from obsessive thoughts.