Hunting for SAT's Blossom: Exact-Quotienting Candidates, Representational Counterkills, and Quotient Debt

This round first lets the Equals Team seriously build its weapons, then lets the Not-Equals Team dismantle them one by one. It examines, in turn, six real-world SAT-quotienting routes — variable elimination (limited by elimination width), OBDD/DNNF knowledge compilation, XOR/affine extraction, symmetry quotients, backdoor condensation, and CDCL learned-clause compression — each of which can drastically compress the search on specific structures, and each of which has an identifiable blowup parameter. This round's most important counterexample comes from OBDDs: certain output-bit functions of integer division require exponential-size OBDDs under any variable ordering — yet integer division itself is clearly computable in polynomial time. This proves that “a given exact-quotient representation is necessarily forced to blow up” cannot even establish that “the function is not in P” — there is no direct correspondence between representation size and algorithmic running time. Proposes a Quotient Debt resource ledger that puts the cost transfers of different SAT-compression methods on one common footing for comparison, while explicitly stating that it is not a proven conservation law.