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.本文提出了自适应结构收敛（Adaptive Structural Convergence, A-SSC）框架，这是一种严谨的多项式时间求解方法，可用于求解低秩约束、对称图等结构化NP完全实例。该框架将局部递归单纯形划分与局部拉塞雷层级（Localized Lasserre Hierarchy）相结合，可为这类结构化问题类别在多项式界P内保证零间隙解。本文还对贝叶斯-海森流（Bayesian-Hessian flow）开展了数学表征，阐明了隐结构如何引导搜索遍历复杂流形，同时绕开解空间中的非贡献性区域。