xiaogang shui

Prime Conch Geometry and Riemann Zeta Zero Analysis Based on Modulo-210 Periodic Vortex Topology (PDSM Framework)

Abstract: 1. This paper constructs the Prime Vortex Dynamic System (PDSM) and establishes an eight-ridge prime conch topological structure constrained by dual modulo-30 and modulo-210 periodic boundaries, breaking the coarse-grained limitations of traditional prime geometric mode...

Prime Conch Geometry and Riemann Zeta Zero Analysis Based on Modulo-210 Periodic Vortex Topology (PDSM Framework)

Abstract: 1. This paper constructs the Prime Vortex Dynamic System (PDSM) and establishes an eight-ridge prime conch topological structure constrained by dual modulo-30 and modulo-210 periodic boundaries, breaking the coarse-grained limitations of traditional prime geometric mode...

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)

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...

PDSM Vortex Field Conjecture on Geometric Emergence of Primes: Impossibility in Infinite Domain and Well-Posedness in Finite Domain

Abstract The long-standing dichotomy between discrete number theory and continuous differential geometry constitutes the core academic bottleneck restricting the research on prime distribution mechanisms. To break through this theoretical dilemma, this paper constructs an origina...

A Rigorous Proof of the Riemann Hypothesis Based on Primitive Vortex Geometry (PDSM)

The Riemann Hypothesis remains a core unsolved problem in analytic number theory spanning over 160 years. Classical complex analysis only establishes algebraic symmetric relations for the zeta function but fails to constrain zero-point positions from thegeometric essence. This pa...

Deep Topological Correlation Between π Ripple Scale, π Decimal Embedded Primes and Prime Gaps (Original PDSM Mechanism)

For more than a century, classical analytic number theory has adhered to the core premise of the random distribution of prime numbers, and the Riemann zeta function system and traditional sieve methods can only realize statistical fitting and approximate estimation of prime distr...

Primitive Vortex Mathematics (PDSM): Prime Singularities, Residues and Geometric Theory of the Riemann ζ-Function on Eight-Ridge Spiral Manifolds

Based on Primitive Vortex Mathematics (PDSM) and Vortex Dynamic Differential Geometry (V-DG), this paper constructs an eight-ridge spiral induced manifold as the geometric carrier of prime number distribution. Covariant vortex equations and intrinsic manifold covariant residues a...

Prime-Pi Dual-State Mathematics: Prime Conch Topology and Bidirectional Vortex Resonance Singularity Cluster Research

Based on the original theoretical framework of Prime-Pi Dual-State Mathematics, this paper proposes the intrinsic free-angle mapping rule for natural numbers and constructs an eight-ridge helical geometric structure constrained by prime residue classes modulo 30. The model define...

Prime-Pi Dual-State Mathematics: Prime Conch Topology and Bidirectional Vortex Resonance Singularity Cluster Research

Based on the original theoretical framework of Prime-Pi Dual-State Mathematics, this paper proposes the intrinsic free-angle mapping rule for natural numbers and constructs an eight-ridge helical geometric structure constrained by prime residue classes modulo 30. The model define...