Over the past several weeks I have started to compile some of the work, namely definitions and some algorithms that can be used to construct a combinatorial space oracle. I have hit a point though where proof techniques will be implemented to demonstrate the witnessing of some expression directly with syntax. This is required and must be rigorous; thus much care to detail must be accounted for; and the outcome is to demonstrate the collapse of PH. Thus, I am in a phase of learning, specifically the details of formally communicating proofs.
In the mean time with the current semester over halfway done, my grades must remain a priority. And homework remains to supersede work.
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