Benchmark Constant 0: Complete Topological Origin Deduction of Global Polarity Equilibrium System

Project: W≡0 Global Topological Unified Field Theory System Construction Project Stage: Stage 4 · Mathematical Precondition Layer Abstract Based on the first principle axiom of W≡0 global polarity conservation and the XYZ+T four-dimensional compact connected topological spacetime framework, this paper completes the full-chain native topological deduction of constant 0 from cosmic topological ontology to complete mathematical properties. Abandoning the instrumental and artificially defined cognition of constant 0 in traditional mathematics, we adopt a three-path deduction framework of body-phase-utility to prove that constant 0 is not absolute emptiness, but the ultimate equilibrium state constant formed by the complete cancellation of global positive and negative polarities and zero total kinetic variation, acting as the natural mathematical embodiment of the W≡0 conservation law. Relying entirely on the locked and finalized mathematical achievements of the 4.0 series, this paper standardizes topological terminology and operational rules, formally defines the local polarity assignment function and topological perturbation evolution equation, and systematically deduces the ontological attributes, polarity generation-annihilation cycle mechanism, and endogenous topological operational rules of constant 0. Strict mathematical demonstration distinguishes global net zero from local non-zero states, fundamentally avoiding the theoretical trivialization problem. Through multi-dimensional comparison, this paper verifies the compatibility and hierarchical differences between the topological intrinsic zero of this system and classical mathematical zero, confirming the absolute benchmark status of constant 0 for the four subsequent innate constants π, e, φ, and 1. This work forms a complete logical closed loop of deriving a complete mathematical benchmark from the single W≡0 axiom, laying a solid core foundation for the five fundamental mathematical constant system of the W≡0 theory. Keywords: W≡0 Theory; topological origin; benchmark constant 0; polarity conservation; body-phase-utility deduction; four-dimensional topological spacetime; Lyapunov stability; topological zero element