I am trying to figure out how a magus could create a new Hermetic virtue and teach that via a mystery cult. For example, say a Verditius magus wishes to create a virtue that increases the number of pawns that can be used to open an invested item based on her craft score (instead of reducing the number of pawns based on craft score).
My initial thought is that she would need to experiment when creating items in order to accumulate enough points for a breakthrough. Then, once she has a breakthrough, she would need to create an initiation script to teach the virtue to other people.
Does that approach make sense? Or is there a more correct way to do it?
First, it looks like you are trying to emulate Item Attunement (HoH-MC p135), but with a more limited scope.
I sounds like a Major Breakthrough - it is pushing the limit of hermetic theory (or in this case, Verditius virtue), without breaking it.
Following this path, she needs to accumulate enough research point, following either the original research approach or by following clues and studying item that could lead to an improvement of the theory. Then, it is up to your saga to decide: since it is only a tweaking of what Verditius can do, once the research is done, it does not need to be integrated. She only needs to write a tractatus about it and any Verditius reading will be able to perfom it. That's what I would go for.
You/your troop feel it is of significant importance or she wants to make it available to the whole Order, then:
she has to Integrate it (basically, redoing the step of the discovery to build up RP just to integrate it this time) - then anybody, without Initiation would be able to learn the trick by reading a tractatus on it or
there is an Initiation step required - and in this case, the petitioner needs to have some Verditius Lore unless she creates another Cult (allowing her to share her discovery to non-Verditius members, with all the political ramifications it can have).
There could be a third way of doing it though: through self-initiation (p14, The Mysteries). The script could be do find out some long forgotten notes of Verditius, possibly to sacrifice the existing Verditius virtue (Major Ordeal) to gain a new one - in this case she won't be able anymore to reduce the amount of vis used to open an item, but she will trade it for the ability to open an item with more pawns. If she wants the ability to perform both, then the new script needs to allow her to gain enough initiation point.
Here again, you need to have discussion with your troop: is it reasonable that she can self-initiate a virtue that is in no books ? For me, it looks close enough and not game breaking, so I would be fine (and it fits very much House Verditius list of Mysteries). It looks like a short-cut from the Breakthrough system, but there is more potential for story (researching old ritual, discovering forgotten notes), so that would be my favorite option just because of that.
I like this approach, it's the one that I'd take if I were the story guide.
I wouldn't do it too frequently though. A given mystery knowledge skill should not be able to be used for any virtue that the player wants. The virtue has to be a good fit for the mystery cult. But you can go too far in that direction too, a set of several virtues that amount to "make me even more awesome in that areas where I already rule" can very often be thematically consistent yet stacking virtue upon virtue upon virtue for the same thing isn't normally conducive to having a fun game.