General Outline of Global Linkage Relationship and Mathematical Self-Consistency Closed-Loop for Five Mathematical Constants

Project: W≡0 Global Topological Unified Field Theory System Construction ProjectStage: Stage 4 · Mathematical Precondition Layer (Final Conclusion & Locking of 4.0 Series) Abstract As a final locking special paper for the 4.0 Mathematical Precondition Layer of the W≡0 Global Topological Unified Field Theory System, this paper systematically summarizes and integrates all solid, traceable, and locked core achievements of the 4.00–4.08 series. The coverage includes the general order of system mathematical specifications, unified mathematical tool system, topological dimension standard system, independent topological origin of the five basic mathematical constants (0, 1, π, e, i) and the golden ratio constant φ, and the closed-loop system of Euler’s unified mathematical paradigm. Through systematized and standardized tabulation, this paper fully sorts out the six-layer hierarchical spectrum, non-cyclic derivation logic, global linkage constraints, and general applicable boundaries of the six core mathematical constants, constructing a rigorous and self-consistent constant linkage system. Meanwhile, it establishes a standardized, implementable, and traceable global mathematical self-consistency verification system. Via four core dimensions including definition consistency, acyclic derivation, tool compliance, and dimensional uniformity, supplemented by specific formula examples, terminology ledgers, and logical mapping, it completes the full-system self-consistency verification and strictly demonstrates the non-contradiction and completeness of the 4.0 mathematical system. This paper formally completes the standardization and locking finalization of all 4.0 series mathematical achievements, clarifies the core locking principles, detailed contents, and high-level revision mechanisms, refines the precise docking interfaces, invocation specifications, and mathematical application templates between the 4.0 mathematical system and subsequent advanced mathematical research and field theory deduction, and fills the connection gap between the precondition layer and high-level research. Ultimately, it constructs a complete, self-consistent, perfect, reusable, and traceable underlying mathematical axiom system, providing a unique, rigid, and standardized precondition mathematical foundation for all subsequent mathematical modeling, constant deduction, field theory architecture, and advanced unified theoretical research of the entire system, and fulfilling all established research tasks of the Stage 4 Mathematical Precondition Layer. Keywords W≡0 conservation; five basic mathematical constants; golden ratio constant; global linkage; mathematical self-consistency closed-loop; topological mathematical system; locking specification; precondition foundation; hierarchical spectrum