Systematic Derivation of First-Order Basic Laws Based on the W≡0 Fundamental Axiom

Abstract As the sole underlying foundation of the entire theoretical system, the W≡0 Global Topological Polarity Conservation Axiom manifests its theoretical value through systematic logical derivation. Following the zero additional physical hypotheses principle, this paper systematically derives four first-order basic laws solely from the mathematical expression and textual definition of the W≡0 Axiom via one-step core logical/mathematical transformations: the Absolute Balance of Global Polarity, Inevitable Global Compensation for Local Polarity Breaking, Irreducibility of Polarity Duality, and Global Invariance of Topological Structure. This paper adopts a two-column derivation format, with pure mathematical/logical derivation chains in the left column and corresponding physical interpretations in the right column, ensuring full transparency and no hidden assumptions. All laws are pre-validated through the Boolean Logic Ontology Line constructed in Paper 2 before formal mathematical derivation to guarantee logical consistency. Furthermore, this paper supplements each law with an independent logical proof and multi-path mathematical proofs, doubly locking its absolute truth from both qualitative and quantitative dimensions. A comparative analysis of axiom economy between the W≡0 system and mainstream unified field theories (e.g., General Relativity, Quantum Field Theory, String Theory) intuitively highlights the core advantage of the W≡0 system: all physical laws derive from a single axiom. Finally, this paper completes the self-consistency verification of the first-order basic law system and the discrimination of core confusing concepts, clarifying the applicable boundaries and future extensions of the laws. The first-order basic law system established in this paper serves as the primary bridge from the W≡0 Axiom to concrete physical laws, laying a solid logical foundation for the derivation of second-order laws, the construction of space-time architecture, and the generation of particle spectra in subsequent stages. Keywords: W≡0 Axiom; First-Order Basic Laws; Zero Additional Hypotheses; Two-Column Derivation; Multi-Path Proof; Axiom Economy; Logical Pre-Validation