Self-Consistency Verification of the W≡0 Axiom Foundation and Discrimination of Frequently Confused Core Concepts

Abstract Self-consistency is the primary requirement for any fundamental physical theory. A theory containing internal logical contradictions, circular definitions, or implicit assumptions cannot be a valid Theory of Everything. As an entirely new theoretical paradigm, the self-consistency of the W≡0 Global Topological Polarity Conservation axiom system must undergo rigorous and systematic verification to serve as a reliable foundation for all subsequent research. This paper establishes for the first time a formalized methodological system for self-consistency verification in fundamental physics, including circular-definition-free verification (concept dependency directed graph method), internal-contradiction-free verification (reasoning path consistency method), and implicit-assumption-free verification (term tracing method), and converts these methods into actionable checklists. On this basis, a full-dimensional self-consistency verification of the W≡0 axiom system is performed. The results show that the conceptual system of the W≡0 axiom system forms a circular-free directed acyclic graph, its logical system contains no internal contradictions, the axiom system has no implicit physical assumptions beyond W≡0 itself, and the first-order inference system is fully self-consistent and mutually compatible. To address widespread misunderstandings in theoretical communication, this paper systematically discriminates four pairs of the most frequently confused core concepts: global topological zero-state basis vs. physical vacuum energy, global polarity conservation vs. local matter asymmetry, topological intrinsic opposition vs. artificial symmetry breaking, and first-order primitive inferences vs. second-order derived conclusions. For each pair, strict definitions, essential differences, and analyses of typical misstatements are provided. Meanwhile, this paper responds to the three most common academic objections—axiom self-reference, unfalsifiability, and excessive abstraction—clarifying misunderstandings from logical and methodological perspectives. As the closing paper of Stage 1, this paper systematically summarizes all achievements of Stage 1, formally declares that the meta-foundation and judgment criteria of the W≡0 Unified Field Theory have been permanently established, and specifies the connection points to Stage 3. The completion of this paper marks the successful conclusion of all tasks in Stage 1, laying an unshakable logical foundation for research in subsequent stages. Keywords: W≡0 Axiom; Self-Consistency Verification; Concept Discrimination; Response to Academic Objections; Stage 1 Summary