General Outline of Stage 2: Methodology for Verification of Existing Theories and Boundary Judgment Criteria

Abstract After a century of development, modern physics has formed several relatively independent branches, including classical physics, relativity, quantum mechanics, and particle physics. However, profound paradigm fragmentation and ambiguous boundaries exist among these branches, and no unified fundamental criterion exists to define their scopes of validity and approximation conditions. This situation not only hinders the development of a unified field theory but also leads to unnecessary academic disputes and theoretical inconsistencies. As the opening general article of Stage 2 of the W≡0 Global Topological Theory of Everything, this paper inherits the permanently archived core achievements of Stage 1: the W≡0 axiom system, Boolean mapping methodology, first-order fundamental iron laws, and TOE admission criteria. It establishes for the first time a reusable, quantifiable, and operable methodological framework for verifying existing physical theories. This paper proposes the Three-Dimensional Verification Method, consisting of implicit assumption screening, tracing of approximation conditions, and special case adaptation verification, with clear operational rules, checklists, and branch-adaptive quantitative judgment criteria. Four core principles for theory verification are established, the research scope and forbidden areas of this stage are clearly defined, and the standard logical and mathematical norms for deriving "mature physical theories as low-energy special cases of the W≡0 system" are specified. The core contribution of this paper is to provide unified "constitutional" guidance for all subsequent verification work in Stage 2, ensuring consistency and comparability across branches. It establishes preliminary criteria for distinguishing Local Background Effective Theories from Global Universal Fundamental Theories, laying a methodological foundation for resolving paradigm conflicts in modern physics. Keywords: W≡0 axiom; verification of existing theories; boundary judgment; special case derivation; methodological system