You are defining a woman by her genes. So yes, I expect you to have a university degree to be able to make such an authoritative definition.
Several decades ago, the authorities on the subject regarded homosexuality as a mental disorder. Fortunately not all LGBT lay-people deferred to their judgements.
Just like I would expect you to have a degree in physics before making an authoritative definition based on properties of physics.
So I need a degree to say "E=mc2."
Believe it or not, Facebook University isn’t a real university.
I don't have a full definition, however, I think my parameters apply to >98% of women and >98% of those with XX chromosomes.
IIUC, your definition of a woman is a person who self-identifies as one, and currently at least, most of those who identify themselves as women have XX chromosomes, and for that matter, female genitalia, breasts disproportionately larger than men, and naturally talk at slightly higher pitches.
I also think that this will be the case for at least a few decades, though what do I know?
If someone with XY chromosomes and male genitalia wants to call thonself a woman, fine, it's (still) a (relatively) free country, but just don't expect me to always play along—and with that, I expect to be banned for transphobia, because not only do I don't completely agree with the so-called progressives, but that I posted such.