The Implicit Resolution of Combinatorial Complexity Part II

Abstract Following the finite quadratic limitations and the Implicit Domain Theorem established in Part I, this paper elevates the axiomatic framework to non-linear topologies and N-body interactions. We first formalize the measurement constraint, proving that purely quantum architectures face a fundamental extraction bottleneck, necessitating a hybrid extraction paradigm. We then discard the continuous Taylor expansion in favor of pseudo-Boolean algebra, proving that classical explicit trajectories face a combinatorial explosion governed by higher-order multi-linear tensors. Finally, we demonstrate that while quantum domains implicitly absorb these pseudo-Boolean topologies natively, physical hardware execution requires explicit quadratization via auxiliary gadgets, introducing severe thermodynamic, graph theoretic, and asymptotic analog precision constraints.