Construction of Bidirectional Mapping Between Boolean Logic Ontology Line and Global Topological Physical System

Abstract The core dilemma behind the century-long exploration of unified field theories lies in the disconnection between qualitative logic and quantitative mathematics: numerous theories possess elegant mathematical forms yet suffer from ontological logical contradictions; many physical propositions are mathematically self-consistent but violate the most basic physical intuitions. Based on the W≡0 global topological polarity conservation axiom system, this paper academically operationalizes the "Dual-Line Research Paradigm" (Boolean Logic Ontology Line + Mathematical Deduction Phenomenon-Application Line) for the first time, and constructs a bidirectional mapping system between Boolean logic and the global topological physical system. This paper explicitly limits the mapping to classical propositional logic with preliminary extension to first-order predicate logic, proposes the mappability criterion for physical propositions and two core constraints (finite resolution constraint, global-local consistency constraint), establishes a complete three-layer mapping architecture (atomic proposition layer, logical connective layer, inference rule layer), releases the Boolean Proposition-Physical State Mapping Specification Table, and verifies the effectiveness of the mapping system through two full-process cases: the logical determination of the existence of isolated magnetic monopoles and the logical rejection of the spontaneous generation of net electric charge model. To ensure the absolute rigor, conceptual completeness, and axiomatic consistency of the methodology system, this paper embeds the self-consistency verification of the mapping system and the distinction of core easily confused concepts, thoroughly avoiding the conceptual misalignment, hierarchical confusion, and boundary ambiguity prevalent in contemporary physics. The mapping system constructed in this paper serves as the core methodological tool of the W≡0 theoretical system. As a "logical pre-filter", it can quickly eliminate logically inconsistent physical propositions before mathematical derivation, fundamentally avoiding the methodological trap of "mathematics for mathematics' sake", and providing a unified, self-consistent, and unambiguous logical verification standard for all subsequent theoretical deductions. Keywords: Dual-Line Research Paradigm; Boolean-Topological Mapping; Logical Pre-Verification; Mappability Criterion; W≡0 Axiom; Physical Causality; Methodological Self-Consistency