Adaptive Structural Convergence (A-SSC): A Polynomial-Time Framework for Structured NP-Complete Instances

This paper presents the Adaptive Structural Convergence (A-SSC) framework, a rigorous polynomial-time approach for solving structured NP-complete instances such as low-rank constraints or symmetric graphs. By combining localized recursive simplicial partitioning with the Localized Lasserre Hierarchy, the framework guarantees zero-gap solutions within polynomial bounds P for these structured classes. We provide a mathematical characterization of the Bayesian-Hessian flow, demonstrating how latent structures guide the search through complex manifolds while bypassing non-contributing regions of the solution space.