The Hilbert-Smith Conjecture for Four-Manifolds: A Proof via the GM2 Module

This is the earliest technical validation paper that can be released as preprint regarding an attempt on discussing the four-dimensional Hilbert-Smith conjecture.  It attempts to construct a formally logically closed proof framework using technical details that are not proved to be rigorously feasible. This version focuses on the construction of the framework and the exploration of technical challenges in its implementation, through discussion, we can basically conclude that this framework is hopeful to be feasible and the path to a complete proof is viable. While this paper is being developed, a version that truly attempts to rigorously prove the four-dimensional Hilbert-Smith conjecture, based on this framework and technological accumulation, is also under development.