A SRE-Dynamics Inspired Multipath Topological Flow Purification Architecture and Localized Operator Implementation Theoretical Paradigm: Status-Relational Entropy (SRE) Dynamics Methodological Base: Localized Eigen-Space Rank Variation & Heuristic Spectral Sieve

Based on the conceptual framework of Status-Relational Entropy (SRE) Dynamics, this paper presents a localized, computationally efficient multipath topological flow purification architecture and universal mathematical toolbox. In highly distributed networks, traditional global multipath cancellation methods suffer from high computational complexity and boundary mathematical truncation due to their reliance on a complete global connection matrix. Breaking away from global prior constraints, this framework abstracts the localized multipath propagation network into a discrete complex cross-spectral operator. By evaluating the rank variation and eigen-space configurations of a  localized correlation matrix, this method effectively distinguishes single-path direct causal flows (Rank-1 degradation) from chaotic multipath superpositions (Full-Rank expansion). Utilizing first-order algebraic closed-form solutions, the system introduces a heuristic topological sieve inspired by the Gaussian Unitary Ensemble (GUE) and Poisson distributions from Random Matrix Theory (RMT). Finally, we demonstrate the architectural pipeline for stream execution, offering an ultra-low-latency solution for modern signal and information processing.