Maybe soulmates, maybe university au?

I’ve been trying to remember the name of this fic for so long. Tbh, I don’t think I ever finished it. I only remember a small part of it and I’m not even sure it’s entirely accurate at this point. Anyway, here’s what I recall: it was a soulmate or marriage law trope, maybe even a university au? in the movie playing in my mind, I imagined this scene like Hermione sitting in a big lecture-style classroom and I think Draco is there too. The professor (or someone giving the lecture) was talking about a new spell or something that tested compatibility or found soulmates. I think Draco did the spell and Hermione’s charm bracelet (necklace?) was summoned to him. Or he described charms that were on it, maybe. I remember Hermione being very skeptical about the magic behind it all.

Sorry, I know that’s like bare bones information to go off of! Thanks!