Verification of Classical Physics System: Boundary Definition and Special Case Proof of Newtonian Mechanics, Electromagnetism, Thermodynamics and Statistical Mechanics

Abstract As the cornerstone of modern science and technology, the classical physics system has achieved unparalleled empirical success over the past four centuries. However, its theoretical limitations have become increasingly prominent with the development of physics: it lacks a unified fundamental foundation, cannot be compatible with modern physical theories such as relativity and quantum mechanics, and there are implicit boundary conflicts between its branches. As the first part of Stage 2 of the W≡0 Global Topological Theory of Everything, this paper systematically verifies the four core branches of classical physics—Newtonian mechanics, electromagnetism, thermodynamics, and statistical mechanics—strictly following the Three-Dimensional Verification Method (Implicit Assumption Screening, Tracing of Approximation Conditions, and Special Case Adaptation Verification) established in Paper 2.1. This paper screens the implicit assumptions of each branch, traces the topological approximation conditions required for their validity, supplements the complete mathematical derivation chains of Newtonian mechanics, the first law of thermodynamics, and the Boltzmann distribution, rigorously proves that all four branches are approximate special cases of the W≡0 global topological system under macroscopic scale, low-energy limit, and weak polarity gradient, and completes three levels of verification: mathematical equivalence, numerical error, and experimental matching.Note: Numerical derivation of fundamental physical constants, rigorous proof of the topological nature of electromagnetic fields, and derivation of quantum statistical mechanics will be completed in subsequent Stages 3, 4, and 7. This verification result shows that classical physics is not an ultimate description of the origin of the universe, but an effective approximation of W≡0 topological constraints at the scale of human daily experience. This paper clarifies the precise applicable boundaries and failure scenarios of each branch, provides a fundamental explanation for the unification of classical and modern physics, and lays the foundation for the subsequent verification of the modern physics system. Keywords: Classical physics; Newtonian mechanics; Electromagnetism; Thermodynamics; Statistical mechanics; Boundary verification; W≡0 special case; Three-Dimensional Verification Method