For the longest time, I honestly thought all volleyball nets were basically the same. As long as the ball could go over and the poles stayed upright, I figured that was enough. A few months ago, my friends and I started playing more regularly on ...
Paper 5: Stochastic Processes and Geometric Flows: From Random Walks to Brownian Motion and Quantum Probability Author: Zhang Suhang Affiliation: Luoyang, Henan Abstract This paper extends the probability-geometry isomorphism frame...
Paper 4: Geometric Reconstruction of Probability Axiom System: Kolmogorov Axioms Equivalent to Geometric Measure Axioms
Author: Zhang Suhang Affiliation: Luoyang, Henan
Abstract
This paper accomplishes a landmark unification between pr...
Paper 3：Geometric Embedding of Multivariate Random Variables: A Unified Triple Operation of Joint Distribution, Marginalization, and Conditioning Author: Zhang Suhang Affiliation: Luoyang, Henan, China Abstract Building upon the algebraic-prob...
Paper 2: Geometric Realizations of One-Dimensional Probability Distributions: Bell Curve, Staircase, Lattice, and Fractal
Author: Zhang Suhang
Affiliation: Luoyang, Henan
Continuing the probabilistic-geometric isomorphism fr...
--- Paper 1: The Fundamental Paradigm of Probability-Geometry Isomorphism: From Gaussian Distributions to General Measure Correspondences
Author: Zhang Suhang, Luoyang, Henan
The probability density function of the Gaussian dist...
Scientific Implications of Frequency Difference Determining Probability: God Does Not Play Dice This conclusion settles the long-standing debate between Bohr and Einstein. If we follow Bohr’s standpoint, the universe would descend into chaos. ...
Frequency Difference Determines Probability: Geometric Proof of God Does Not Play Dice from the Perspective of Discrete Order Geometry Author: Zhang Suhang Address: Luoyang, Henan, China Abstract The intrinsic randomness of probabi...
Preliminary Exploration of the Fusion Configuration as a Concrete Prototype of Fiber Bundles Author: Zhang Suhang, Luoyang, Henan
--- Abstract Based on previous research results on spherical cap‑derived self‑similar geometry (SCD‑SG), thi...
Spherical-Cap Derived Self-Similar Geometry (SCD-SG): A New Natural Finite-Level Spherical Composite Solid Geometry Author: Zhang Suhang, Luoyang, Henan Abstract Nature abounds with three-dimensional composite configurations featuri...
Application Chapter —— Grounded Mapping of the Three‑Layer Number‑Theoretic Structure in Computing and Engineering
Author: Zhang Suhang (Luoyang, Henan)
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Abstract Based on the three‑layer structure of “prime primitive – regular co...
Part Three: Fractal-Coefficient Coupled Evolution —— Synchronous Mapping from Numerical Parameters to Graphical Forms
Abstract Based on the analogical framework and axiomatic system establish...
Part Two: Axioms and Mathematical Formulas —— Formal Foundations of the Composite Number Construction System
Abstract Based on the analogical framework of “primes–composites” and “fractal pri...
Part One: Analogical Foundation in Number Theory —— The Fractal Generation Logic of Composite Numbers
Abstract Starting from the constructive processes of number theory and fractal geometry, this paper ...
Frequency Difference Determines Probability Distribution: Empirical Verification Based on Multi‑Country Academic Dissemination Data Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract The core proposition of Discrete Order Geometry (DOG)—...
Curvature-Driven Fluid Equation Verification via Discrete Order Geometry: A Numerical Case Study
Author: Zhang Suhang (Independent Researcher, Luoyang, Henan)
Within the Multi-Origin Curvature (MOC) framework, the stea...
Proof of Global Smooth Solutions to the Navier-Stokes Equations within the DOG/MOC/ECS/MIE Framework
Author: Zhang Suhang Address: Luoyang, Henan
The existence of global smooth solutions to the Navier-Stokes (NS) equati...
Continuous-Limit Matching from FCE to the Weak Force Gauge Field Equation Author: Zhang Suhang (Luoyang, Henan) --- Abstract Discrete Order Geometry (DOG) takes the Fundamental Coupling Equation (FCE) as the native expression of its equation ...
From FCE to Field Equations: Continuous-Limit Matching in Discrete Order Geometry Author: Zhang Suhang (Luoyang, Henan) --- Abstract Discrete Order Geometry (DOG) takes the Fundamental Coupling Equation (FCE) as the native expression of its e...
Proof of Existence and Uniqueness of Smooth Solutions to Navier-Stokes Equations within DOG/MOC/ECS/MIE Framework (Supplemented Revised Version) Author: Zhang Suhang Luoyang, Henan Abstract The global existence of smooth solutions...
Proof of the ABC Conjecture within the DOG/MOC/ECS/MIE Framework
The ABC conjecture is a central problem in number theory. Shinichi Mochizuki attempted to prove it using his...
In today’s competitive industrial landscape, manufacturers are under constant pressure to increase productivity, reduce operational costs, maintain product consistency, and meet strict environmental and safety standards. One of the most overlooked...
Proof of the Twin Prime Conjecture within the DOG/MOC/ECS/MIE Framework
The twin prime conjecture is a century‑old core problem in analytic number theory. Its weak version, p...
Discrete Order Geometry (DOG) Fundamental Coupling Equation: Generative Construction from Zhang Matrix to FCE Author: Zhang Suhang (Luoyang, Henan) --- Abstract Discrete Order Geometry (DOG) takes discrete lattice points, hierarchical order, ...
Proof of the P vs. NP Problem within the DOG/MOC/ECS/MIE Framework
The P vs. NP problem is a central open question in theoretical computer science, asking whether every prob...
Proof of the BSD Conjecture within the DOG/MOC/ECS/MIE Framework
The BSD (Birch and Swinnerton-Dyer) conjecture is a Millennium Problem in number theory concerning the equal...
The Continuous Limit of Discrete Order Geometry (DOG): A Study of the Correspondence Between Discrete Evolution and Differential Equations
Discrete Order Geometry (DOG) constructs a p...
The Sea of Paradigms: From Grothendieck to the Dissolution of Problems in a New Geometric Framework
Author: Zhang Suhang Address: Luoyang, Henan, China
--- Abstract
Grothendieck once likened his mathematical method to a "rising tide": n...
Paradigm Incorporation of the Hodge Conjecture – Natural Dissolution within the MOC‑DOG‑ECS Framework
The Hodge conjecture is one of the seven Millennium Prize Problems. Tradi...
Foundations of Discrete Order Geometry (DOG): System Definition, Morphisms and Order Isomorphism — First Cornerstone Draft of the DOG Framework Author: Zhang Suhang (Luoyang, Henan) Remarks This paper lays the first foundati...