Summer Vacation Ended Quietly The summer vacation had slipped away without a sound. ...
--- Part Two A Rigorous Global Proof of the Kakeya Conjecture via DOG-MOC Author: Zhang Suhang (Bosley Zhang) Location: Luoyang, Henan, China Date: May 2026 Abstract This paper, based on the self-developed Discrete Order Geometry (DOG) cov...
Basic Coupling Equation of Discrete Order Geometry (DOG): Generative Construction from Zhang's Matrix to FCE
Author: Zhang Suhang (Luoyang, Henan)
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Abstract
Discrete Order Geometry (DOG) takes discrete lattice points, hierarchical ...
It was June, the height of summer, and the heat hung thick and suffocating. The university...
Operator Algebra Structures in Discrete Order Geometry (DOG)
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Discrete Order Geometry (DOG) takes finite discrete lattices, order nesting, and local correlation as its ontology. This pap...
Discrete Numerical Verification and Symmetry Group Case Studies for Extremal–Conservation–Symmetry Systems
Author: Zhang Suhang Affiliation: Luoyang, Independent Researcher
Within the framework of Extremal–Conservation–Sy...
Group-Theoretic Unification of the Three Symmetries and the Euclidean GroupWithin the framework of Euclidean geometry and classical group theory, the three fundamental symmetries—translation, rotation, and reflection (folding)—are not independent ...
A Topological Extremum‑Seeking Solver for the NS Equations Based on the MOC‑DOG‑ECS‑MlE Framework 1 Introduction The Navier‑Stokes (NS) equations constitute the core governing system of viscous fluid dynamics. Conventional CFD solvers are ...
Dynamic Vector Geometry（DVG）: A Research Programme
Author: Zhang Suhang Luoyang School of Mathematics September 2026
This paper proposes a research programme aimed at generalizing the fundamental objects of geometry from...
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...
From Newton to Riemann, from fluxions to manifolds. Everything flows, nothing stands still. Is mathematics really so dull and boring? I don't think so!
Unified Geometric Extremal Physics（UGEP）
Solution to the Plateau Problem under the Unified Geometric Extremal Physics （UGEP）Framework
— Physical Restatement, Paradigm Reduction, and Its Isomorphism with the Isoperimetric Problem and the Poin...
On the Central Position of Geometry in Mathematics
For a long time, many people merely regard mathematics as a tool for calculation and problem-solving, which greatly narrows its true meaning. Mathematics is essentially an organic and vibran...
Nature and Science reprinted the paper on their front pages. MIT, Stanford, Oxford, Cambridge—...
God first noticed the problem thirty-five billion years after Creation. Or rather, not...
UPGS: A Preliminary FrameworkUPGS: Extending and Interfacing the UPG Framework with Scheme Theory Author: Zhang SuhangAffiliation: Luoyang, Henan --- Abstract This paper establishes an interface between UPG and scheme theory, embedding the pro...
Willett’s perspective was strikingly original. The pursuit of novelty and transformation was the...
Recasting the Hodge Conjecture in an Extended Geometric Framework Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract The Hodge conjecture is usually stated as follows: on a smooth complex projective algebraic variety, every (p,p)-type ra...
God makes all things with the greatest economy and efficiency. That is the essence of MlE. MlE provides mathematical support for Darwin's theory of evolution. Redundant structures that serve no purpose and consume resources t...
--- Curvature-Dependent Local Logical Rules — A Concept Demonstration within the MOC Framework Abstract Within the MOC (multi-origin coordinates) framework, this paper constructs a minimal schematic model. By introducing an origin curvature par...
What is defined is:**Hierarchical Structure of Multi-Origin Geometry- Embedding of Fractal Dimension- Recursive Mapping of Continued Fractions**It satisfies the three criteria for establishing a new branch of mathematics:1. Independent fundamenta...
Relativity and quantum mechanics each have their own domains of application.In my view, relativity is better suited to explaining the behavior of macroscopic objects and celestial bodies, while quantum mechanics is more appropriate for describing ...
The summer sun blazed mercilessly in the afternoon. The asphalt had grown soft under the heat,...
--- 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
Under the framework of Multi-Origin...
The Combinatorial Axiomatic Basis of Discrete Order Geometry (DOG)
— A Preliminary Exploration of a Combinatorial Generative Framework for Geometric Configurations
Classical geomet...
The Sun and the Earth would never claim this child as their own. Not for lack of love, but out of...
Chen Guo was born into a working-class family on an old street. His father, Chen Guang, was quiet...
Reinterpretation of Set Theory within the MOC (Multi-Origin Coordinates) High-Dimensional Framework
I. Core Stance
Classical set theory is single-origin, single-universe, and static in its hierarchy. Under MOC, set theory becomes multi-orig...
Multi-Origin Curvature (MOC) Framework: Basic Definitions and Geometric Conservation Law
Author: Zhang Suhang, Luoyang
This paper establishes the basic geometric definitions of the Multi-Origin Curvature (MOC) framework. Three co...
Multi-Origin High-Dimensional Geometry and TopologyIn the landscape of classical mathematics, topology is devoted to the study of properties preserved under continuous deformations of space. It concerns connectivity, compactness, genus, parity, an...