The basic structure of reality as we know from the Ari is the ten sepherot. But Rav Shalom Sharabi [from Yemen and then Jerusalem] showed how that boils down to five Partzufim [פרצופים] and from there down to three.

I had a few thoughts--but nothing really worked out.

Hegel's triadic (three fold) structure which he acknowledged came from Plato and obviously Kant. To me it is seems certain that to some degree he was inspired by Isaac Luria. The basic structure of reality as we know from the Ari is the ten sepherot. But Rav Shalom Sharabi [from Yemen and then Jerusalem] showed how that boils down to five Partzufim [פרצופים] and from there down to three. That is right at the beginning of the book Nahar Shalom.
To some degree it is possible to see the importance of the triads of Hegel by means of the Cantor set. In the Cantor set you keep taking out the middle third and if you go to infinity it turns out that the Lebesque measure intersection of all the subsets is zero. 

Which simply means if you take out the middle term you get no connection between the first and third.