--- 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...
First Avenue on the Fourth Ring Road had descended into total chaos. Hundreds of taxis...
Discrete Numerical Verification and Symmetry Group Case Studies for Extremal–Conservation–Symmetry Systems
Author: Zhang Suhang Affiliation: Luoyang, Independent Researcher
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Abstract
Within the framework of Extremal–Conservation–Sy...
Multiple Integrals in Multi-Origin Curvature (MOC) Geometry
(Including the Mathematical Definition of “Integrate First, Then Couple”)
Core Thesis: The classical multiple integral in a single‑origin Euclidean space is a degenerate special ca...
1. The Second Law of Thermodynamics Heat can only spontaneously flow from a hotter object to a colder one, and cannot spontaneously flow from a colder object to a hotter one. 2. The Principle of Air Conditioning In winter, an air condi...
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 ...
It was June, the height of summer, and the heat hung thick and suffocating. The university...
The Continuous Limit of Discrete Order Geometry (DOG): A Study of the Correspondence Between Discrete Evolution and Differential Equations
Author: Zhang Suhang (Luoyang, Henan)
Discrete Order Geometry (DOG) constructs a p...
Summer Vacation Ended Quietly The summer vacation had slipped away without a sound. ...
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...
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!
Basic Coupling Equation of Discrete Order Geometry (DOG): Generative Construction from Zhang's Matrix to FCE
Discrete Order Geometry (DOG) takes discrete lattice points, hierarchical ...
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...
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 ...
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...
Nature and Science reprinted the paper on their front pages. MIT, Stanford, Oxford, Cambridge—...
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...
God first noticed the problem thirty-five billion years after Creation. Or rather, not...
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...
On the Ontological Relationship among Geometry, Functions and Number Theory under the MOC System Within the framework of conventional mathematics, geometry, functions and number theory are relatively independent, each with its own scope of res...
The Sun and the Earth would never claim this child as their own. Not for lack of love, but out of...
--- 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...
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...
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,...
Willett’s perspective was strikingly original. The pursuit of novelty and transformation was the...
The Combinatorial Axiomatic Basis of Discrete Order Geometry (DOG)
— A Preliminary Exploration of a Combinatorial Generative Framework for Geometric Configurations
Classical geomet...
--- 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...
The delivery room door finally opened. A nurse came out holding a swaddled baby, her voice...
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...