Hegel's geist has no process. One may think "surely he gives some kind of process for this..." but actually, no. Hegel basically just asserts that concepts generate their opposites through contradiction. When pressed on the mechanism, he ends up with circular explanations that amount to "the dialectic works because that's how Spirit evolves, and we know Spirit evolves this way because of the dialectic." When we look for the actual is_a relationships that would explain:

How a concept has the power to generate anything

What determines its opposite

Why this happens necessarily

How contradiction leads to synthesis

We find Hegel just assumes these relationships exist rather than explaining how they bootstrap into existence. He's basically hiding the lack of grounding behind complex terminology and elaborate systematic claims.

Now, if you assert something happens through contradiction, the law of contradictory explosion appears to invert but that is a tautological claim because it is true by law of contradictory explosion and has infinite regress of anything transformations...

except, the law of contradictory explosion is itself wrong. from a contradiction, not anything follows (because that would logically mean that a contradiction could literally instantiate anything in reality. more accurately, and we know this and it isnt new); from a contradiction, ignorance follows.
