Okay, so I'm quite interested in this myself (writing Fate fanfics with a bunch of unique magus) So I wanna see if I'm understanding this by way of metaphor. So, your Magical Foundation is like the school of science you use to approach a problem, the mystery is the formula you use to reach the answer and the mechanics is the answer itself? So like for example -
Foundation = Mathematics = Rune Magecraft
Mystery = Pythagorean Theorum = Blood Ritual
Mechanism = Length of the Hypotanuse = Conversion magecraft
Anyone would be able to tell by observing your magecraft that you reached a certain conclusion, 42 is the same number regardless of the school of thought used to reach it, and depending on the framing, might be able to tell your Foundation, but unless they know your formula, they won't be able to get from Foundation to Mechanism by themselves, thus maintaining the mystery of a given mage's research? Sorry if that sounds a bit asinine, I'm just trying to frame it in a way I can understand.