The Ultimate Coupling Law of 8-Ridge Conch Topology and π³ Third-Order Field — A Complete Closed System of 100 Prime-π Topology Weld Points, 100 Formulas and 100 Primitive Constants (Final PDSM System)

Abstract

Based on the primitive core system of PDSM (Prime-π Dimension Symmetry Mechanism), this paper systematically constructs a complete ultimate topological welding system of 100 groups of prime-π (π-P) topological coupling nodes, together with a full set of 100 exclusive topological formulas and 100 primitive topological constants, taking the dual symbiotic mechanism of two-dimensional 8-ridge conch rotational topological manifold and three-dimensional π³ closed-loop field as the core theoretical framework. This paper rigorously proves that the ordered nature of π decimals, the apparent pseudo-random phenomenon, global uniform distribution, and discrete resonance anchoring of primes all originate from the 24-dimensional intrinsic eigen lattice formed by the orthogonal coupling of 3–8 coprime dimensions. Serving as the unique interactive medium connecting the continuous π field and the discrete prime number theory system, the 100 topological weld points realize five core functions: dimensional anchoring, phase meshing, field conservation locking, singularity penetration, and bidirectional reversible mapping. This research thoroughly establishes the underlying unified logic bridging topological field theory and fundamental number theory. All derived formulas contain no artificial fitting parameters or empirical corrections and are purely deduced from primitive topological structures, exhibiting strict mathematical self-consistency and universal applicability.