Verification of the Particle Physics System: Boundary Definition and Special Case Proof of the Standard Model and Grand Unified Theories

This paper is the fourth sub-thesis of Stage 2 (Verification of Existing Theories) in the project: W≡0 Global Topological Unified Field Theory. Stage Affiliation: W≡0 Global Topological Unified Field Theory · Stage 2 (Verification of Existing Theories) · Sub-paper 2.4 Abstract As the core phenomenological framework of contemporary particle physics, the Standard Model (SM) has achieved extremely high-precision experimental matching in the empirical verification of electromagnetic, weak, and strong interactions. However, it suffers from fundamental deficiencies, including an excessive number of empirical parameters, the absence of explanations for dark matter and dark energy, an unclear origin of particle masses, and incompatibility with gravity. Various Grand Unified Theories (GUTs) attempt to unify the three fundamental interactions through higher-order symmetries, yet they remain trapped in dilemmas such as arbitrary symmetry-breaking presuppositions, unconfirmed predicted particles, and disconnection from global physical constraints. Essentially, both the SM and GUTs lack a unified topological foundation. As the fourth sub-paper of Stage 2 of the W≡0 Global Topological Unified Field Theory, this paper systematically verifies the Standard Model and mainstream Grand Unified Theories using the Three-Dimensional Verification Method (implicit assumption screening, approximation condition tracing, and special case adaptation verification), combined with particle topology analysis and high-energy empirical data comparison. This paper screens all implicit assumptions of the two theoretical systems, traces the approximate conditions required for their validity, and proves that the Standard Model is an approximate special case of the W≡0 global topological polarity system under low-energy, weak topological polarity entanglement, and local particle steady-state conditions. It also points out that GUTs rely only on local symmetry constraints, exclude global polarity conservation and topological invariance, and thus represent incomplete local topological derivations. This work clarifies the applicable boundaries and fundamental causes of the inherent flaws of the Standard Model, identifies the logical loopholes and approximation deviations of GUTs, lays the foundation for the strict construction of the particle topology spectrum and fundamental topological configurations of elementary particles in Stage 5, and provides judgment criteria for the global topological reconstruction of the particle physics system. Keywords: particle physics; Standard Model; Grand Unified Theories; boundary verification; W≡0 special case; particle topology; topological polarity entanglement; global polarity conservation