I guess for me a core belief would be what a person wanted in a relationship for example. I.e. do they won a closely bonded relationship where you work together hang out all the time do everything together. Or does one person enjoy loads of time alone away from their partner and just want someone they hang out with in the evenings. Of course these kind of core beliefs and ideals can change but if they’re out of alignment for too long with your partner it’s going to be pretty miserable. Or things like are you willing to work through triggers to stay together or does one partner run away rather than deal with them. Does one partner want to date loads of people at the same time versus be completely monogamous. These types of beliefs are going to wear pretty thin after a while if they’re not in alignment.