Definition of virginity (especially regarding Mary)

What does virginity really mean? It appears to me either not to be a categorical variable, or an arbitrary state. My commonplace understanding of virginity would mean that someone had no sex so far; that would lead to virginity being a continuous variable instead of a categorical one, as sex can mean anything between fingering, licking, masturbation, penetration and so on. In the reception history, virginity seems to be a testable claim (see e.g. Jeanne d'Arc). We know now that there is no test for virginity. We could also assume that virginity is a state of mind, but that would make it kind of arbitrary if we do not assume asexuality. There could be another definition, but I doubt that that is how it could be interpreted in our times, and that would be based on the value of a woman for marriage, which would boil down either to the possibility of pregnancy outside of wedlock or sexual experience of any sort, depending on why virginity has such a high value in certain cultures regarding marriage. I am sure I missed something. How do different denominations teach this? What errors did I make in my naive pre-assessment?