--- Part One Title: The Geometric Foundation and Model Transformation of the Kakeya Conjecture via DOG-MOC
Author: Zhang Suhang (Bosley Zhang) Location: Luoyang, Henan, China Date: May 2026
Abstract
Under the framework of Multi-Origin...
Paper 13: The Trinity of Frequency, Probability, and Geometric Measure — From Discrete Order Geometry to Étale Schemes
Author: Zhang Suhang Affiliation: Luoyang, Henan
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This paper achieves a seamless connection between ...
Paper 12: Étale Differential Equations on UPGS — Continuum Limit of Random Walks and Heat Kernel, with Derivation of the Schrödinger Equation Author: Zhang SuhangAffiliation: Luoyang, HenanDate: May 25, 2026 --- Abstract In Papers 7 and 8, ...
Paper 11: Computation on UPGS — Algorithms, Complexity, and Numerical Implementation
Author: Zhang Suhang Affiliation: Luoyang, Henan Date: May 25, 2026
UPGS (Étale Probability Schemes), as a unified theoretical frame...
Paper 10: The Weil Conjectures under UPGS — Étale Random Walks, Curvature Duality, and ECS Stability
Within the UPGS (Étale Probability Schemes) fram...
Paper 9: The Riemann–Roch Theorem under UPGS — A Geometric Proof Based on the Étale Heat Kernel, MIE Variational Principle, and ECS Conservation Laws
...
Paper 8: Étale Random Walks and Arithmetic‑Quantum Unification under the UPGS Framework — Geometric Origins of Prime Distribution, Zeta Functions, and Born’s Rule Author: Zhang SuhangAffiliation: Luoyang, HenanDate: May 25, 2026 --- Abstrac...
Paper 7: Flat Probabilistic Schemes — Migration from Geometric Measure Spaces to Étale Sites
Author: Suhang Zhang, Luoyang, Henan Abstract
Based on the axiomatic system of probability geometry established in previous papers (Paper 1 & P...
Paper 6: The Unification of Algebra, Probability and Geometry: The New UPG Paradigm — History, Framework and Applications Author: Zhang Suhang
Affiliation: Luoyang, Henan
This paper is a review and applications paper in...
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
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
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)
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...
Discrete Order Geometry (DOG) and Knot Topology: From Continued Fraction Recursion to Interdisciplinary Topological Applications
Knot topology has long been regarded as a branc...
Discrete Order Geometry (DOG) and Harmonic Analysis: A Unified Framework for Decomposition and Reconstruction of Smooth Fields
Author: Zhang Suhang Independent Researcher · Luoyang
This paper establishes a fundamental com...
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...