Paper 1-3: Architecture of Three Major Transformation Channels Based on Multiple Expressions of π
Author: Zhang Suhang (Heluo Mathematical School)
Abstract
The core innovation of the \mathcal{\Pi} operator lies in the fact that differe...
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 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...
The Dual Constant Dynamic-Static Unification Principle in the DOG System
Author: Zhang Suhang Address: Luoyang, Henan
Within the complete framework of DOG discrete order geometry, the universe's two most fundamenta...
--- DOG Discrete Order Geometry and Its Coupling with Discrete Mathematics:Completing the Missing Discrete Spatial Geometric Foundation of Modern Mathematics Author: Zhang SuhangLuoyang Abstract Modern mathematics has long been divided into tw...
URFE Calculates Celestial Orbits
Author: Zhang Suhang
Combining the Unified Recursive Field Equation (URFE) with scenario-based calculations for different gravitational field strengths, and following the previously defined symb...
Paper 9: The Riemann–Roch Theorem under UPGS — A Geometric Proof Based on the Étale Heat Kernel, MIE Variational Principle, and ECS Conservation Laws
Author: Zhang Suhang Affiliation: Luoyang, Henan Date: May 25, 2026
...
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...
Discrete Order Geometry (DOG) First‑Principles Derivation of the Dirac Equation: Spinor Order and Relativistic Discrete Evolution
Author: Zhang Suhang (Luoyang, Independent Researcher)
Abstract – Based on the unified discrete evolution p...
What is the AI in Reinforcement Learning Market? The AI in Reinforcement Learning Market refers to the global ecosystem of technologies, algorithms, platforms, and solutions that enable machines to learn optimal decision-making through trial-and-...
Complete Derivation of the Unified Recursive Field Equation (URFE) Author: Zhang Suhang
1. Core Prerequisite Theories
Foundation: MOC Multi-Origin Geometry, DOG Discrete Order Geometry, GPCL Geometric Recursive Conservation Chain, Unifie...
Chapter 1：Geometric Origin of the Law of Excluded Middle The Emergent Essence of Classical Logical Laws under the MOC Framework
Author: Zhang Suhang (Luoyang, Henan, China)
Chapter 1 Introduction: The Sanctity and Fractures of the L...
Part Two: Axioms and Mathematical Formulas —— Formal Foundations of the Composite Number Construction System
Author: Zhang Suhang (Luoyang, Henan)
Abstract Based on the analogical framework of “primes–composites” and “fractal pri...
Yang–Mills Equation Derived Core Formulas for Spectral Counting
Consistent with the DOG/MOC/ECS/MIE framework, this paper starts from the fundamental Yang–Mills equations an...
Global Data Verification of the System and Summary of Paradigm Applications Author: Zhang Suhang(Independent Researcher, Luoyang) System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical ParadigmSeries Number: Sixteenth Paper --- Abst...
Prospects for the Application of MOC in Magnetic Resonance Imaging (MRI)Magnetic resonance imaging is essentially a high-dimensional system that acquires and reconstructs massive proton spin signals in an inhomogeneous magnetic field. Its core cha...
Paper 4-3: A Study on the Complementarity between the Π-Operator and Classical Differential OperatorsAuthor: Suhang Zhang (Heluo School of Mathematics)AbstractClassical differential operators including gradient, divergence, curl, Laplacian, d'Ale...
--- Native Derivation of Yang-Mills Equations within the DOG Framework (Under the Unified Four-Force Paradigm) Author: Zhang SuhangAffiliation: Independent Researcher, Luoyang, Henan --- Abstract Traditional Yang-Mills theory is a field-theor...
Establishment of the Global Unified UCE Curvature Equation
Author: Zhang Suhang (Independent Researcher, Luoyang)
System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical Paradigm Series Number: Tenth Paper
T...
Construction of the Evolutionary Manifold of the Zeta Function
Author: Zhang Suhang (Independent Researcher, Luoyang) System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical‑Physical Paradigm Series Number: Paper No. 5
Abstract ...
Renormalization Group Equations for Quantum Gravity Based on the Discrete Parent GroupAuthor: Suhang Zhang, Luoyang, HenanAbstractThe ultraviolet divergences in quantum gravity originate from the assumption of infinitely differentiable continuo...
Embedding Mapping Derivation of the Standard Model Gauge Group \boldsymbol{U(1)\times SU(2)\times SU(3)} within the Global Discrete Parent Group (Zhang Group)Author: Suhang Zhang, Luoyang, HenanAbstractThe gauge group of the Standard Model G_{\t...
ECS-Hodge Correspondence Categorical Equivalence Between Symmetric Conservation Modes and Hodge Classes Author: Suhang Zhang Address: Luoyang, Henan Abstract Hodge classes serve as core objects in algebraic geometry, defined as ra...
From the largest to the smallest — from celestial bodies down to particles — all things are discrete. Order, or law, connects all things. ———SuHang Zhang
Winter is here, and while some of us are bundled up indoors, others are craving the rush of a snowy mountain. If the slopes are calling your name, but you're stuck at your desk, then Snow Rider 3D offers a surprisingly satisfying alternative. This...
Paper I：Rigorous Chain Mapping of Action–Potential Difference–Stability: The Local Reduction Essence of Symplectic Structure and Global Unification under ECS Author: Zhang Suhang (Heluo School of Mathematics) AbstractIn the classical mechanics s...
URFE Solves the Three-Body Problem Author: Zhang Suhang 1. First: What Makes the Classical "Three-Body Problem" Difficult Standard Conclusion (holds from 1880 to 2026): · No general elementary analytic solution: The positions cannot be express...
--- MOC Coordinate System: Geometric Definition of Multi-Origin Hierarchical Nesting and Classical Coordinate Degeneration
Author: Zhang Suhang Founder of the Heluo Mathematical School
Based on the Multi-Origin Curvature...
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...
DOG Discrete Order Geometry and Lattice Theory: Algebraic Representation of Order Structures Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract Lattice theory studies algebraic structures in which any two elements in a partially ordered ...
