Duality

In response to the previous post, I may have some insight on the structure of the oracle spaces. This is not rigorous and the definitions will continue to evolve.

Lets say that we have constructed our oracle space and SAT space. We can now transform the SAT space into an oracle space for itself, but witness satisfiability of those expressions from our previous oracle space.
This would in essence, take each conjunction and expand to be itself a combinatorial space from this set of k, generating 2^k combinations. We could then consider if one of these strands would be satisfiable by witnessing through the terms of our previous oracle space.

I still favor the previous method, as it lessens confusion, and for the instance that one of these new SAT spaces, our old oracle space, could overlap, thus providing false witnessing. That is not good! Although with rigor, I do believe this is the same arena that our duality will occur; with refinement and time, determined to be finite by our finite space bounds...