The Sea of Paradigms: From Grothendieck to the Dissolution of Hard Problems in a New Geometric Framework Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract Grothendieck once likened his mathematical method to a "rising tide": instead of ...
Discrete Order Geometry (DOG) Framework for the Geometric Origin of Weak Interactions: From Discrete Chiral Lattice Points to the V–A Current Author: Zhang Suhang(Luoyang, Independent Researcher) Abstract: Based on the four‑dimensional discre...
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...
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...
Yang–Mills Equation Derived Core Formulas for Spectral Counting
Author: Zhang Suhang Address: Luoyang, Henan
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Consistent with the DOG/MOC/ECS/MIE framework, this paper starts from the fundamental Yang–Mills equations an...
The Dual Constant Dynamic-Static Unification Principle in the DOG System
Within the complete framework of DOG discrete order geometry, the universe's two most fundamenta...
DOG Discrete Order Geometry: An Endogenous Unification of Hilbert Space and Probability System Author: Zhang Suhang Affiliation: Luoyang (Independent Researcher) Abstract Traditional modern mathematical physics suffers from three fundamenta...
Discrete Order Geometry (DOG) and Quantum Mechanics: Ontological Unification from Discrete Lattices to Quantum Representation
Author: Zhang Suhang Affiliation: Luoyang
Since its inception, quantum mechanics has been regarded as ...
Paper 5-3: Prospect of System Expansion: Interdisciplinary Developments toward Non-Euclidean Manifolds, Quantum Field Theory and Advanced Number Theory Author: Suhang Zhang (Heluo School of Mathematics) Abstract The Π operator frame...
Paper 13: The Trinity of Frequency, Probability, and Geometric Measure — From Discrete Order Geometry to Étale Schemes
This paper achieves a seamless connection between ...
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
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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...
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...
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...
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...
From the largest to the smallest — from celestial bodies down to particles — all things are discrete. Order, or law, connects all things. ———SuHang Zhang
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...
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 ...
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 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...
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-...
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...
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...
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...
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...
--- 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...
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...
--- 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...
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...
What Is Engine Detailing, Really? Engine detailing is the careful cleaning, degreasing, and dressing of the engine bay and its components. Done correctly, it removes built-up dirt, oil residue, and debris without harming sensitive parts like elec...
