Curvature-Driven Fluid Equation Verification via Discrete Order Geometry: A Numerical Case Study
Author: Zhang Suhang (Independent Researcher, Luoyang, Henan)
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Abstract
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...
Continuous-Limit Matching from FCE to the Weak Force Gauge Field Equation Author: Zhang Suhang (Luoyang, Henan) --- Abstract Discrete Order Geometry (DOG) takes the Fundamental Coupling Equation (FCE) as the native expression of its equation ...
From FCE to Field Equations: Continuous-Limit Matching in Discrete Order Geometry Author: Zhang Suhang (Luoyang, Henan) --- Abstract Discrete Order Geometry (DOG) takes the Fundamental Coupling Equation (FCE) as the native expression of its e...
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...
In today’s competitive industrial landscape, manufacturers are under constant pressure to increase productivity, reduce operational costs, maintain product consistency, and meet strict environmental and safety standards. One of the most overlooked...
Proof of the Twin Prime Conjecture within the DOG/MOC/ECS/MIE Framework
The twin prime conjecture is a century‑old core problem in analytic number theory. Its weak version, p...
Discrete Order Geometry (DOG) Fundamental Coupling Equation: Generative Construction from Zhang Matrix to FCE Author: Zhang Suhang (Luoyang, Henan) --- Abstract Discrete Order Geometry (DOG) takes discrete lattice points, hierarchical order, ...
Proof of the P vs. NP Problem within the DOG/MOC/ECS/MIE Framework
The P vs. NP problem is a central open question in theoretical computer science, asking whether every prob...
Proof of the BSD Conjecture within the DOG/MOC/ECS/MIE Framework
The BSD (Birch and Swinnerton-Dyer) conjecture is a Millennium Problem in number theory concerning the equal...
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...
The Sea of Paradigms: From Grothendieck to the Dissolution of Problems in a New Geometric Framework
Author: Zhang Suhang Address: Luoyang, Henan, China
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Grothendieck once likened his mathematical method to a "rising tide": n...
Paradigm Incorporation of the Hodge Conjecture – Natural Dissolution within the MOC‑DOG‑ECS Framework
The Hodge conjecture is one of the seven Millennium Prize Problems. Tradi...
Foundations of Discrete Order Geometry (DOG): System Definition, Morphisms and Order Isomorphism — First Cornerstone Draft of the DOG Framework Author: Zhang Suhang (Luoyang, Henan) Remarks This paper lays the first foundati...
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...
MOC Embedding Theorem: Embedding Representation of Complex Projective Algebraic Varieties in Multi-Origin Curvature Geometry Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract Traditional complex projective algebraic varieties are built ...
--- A Study of Fractal Order and Chaos Emergence Mechanisms Based on Finite-Level Continued Fraction Sequences Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract Fractal geometry and continued fractions belong respectively to the two ma...
Lattice Structure and Matrix Representation in Discrete Order Geometry Author: Zhang Suhang, Luoyang, Henan
Discrete Order Geometry (DOG) takes finite discrete lattice points and order nesting as its ontology, withou...
--- Conclusion: Low-Energy Approximation in the DOG System Simultaneously Conforms to the MIE Extremum Criterion and the ECS Symmetric Equilibrium Steady State — A Triple Self-Consistent Closed Loop Author: Zhang Suhang, Luoyang, Henan --- I. ...
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From the largest to the smallest — from celestial bodies down to particles — all things are discrete. Order, or law, connects all things. ———SuHang Zhang Within DOG, this connection is precisely encoded as a three‑...
The Combinatorial Axiomatic Foundation of Discrete Order Geometry (DOG) — A Preliminary Study of a Combinatorial Generation Framework for Geometric Configurations Author: Zhang Suhang(Luoyang, Henan) --- Abstract Classical geometry and modern...
Discrete‑Order Geometry (DOG) and Topology: An Open Research Framework for Disconnected Ordered SpacesAuthor: Zhang SuhangAffiliation: Luoyang, Henan, ChinaAbstractDiscrete‑Order Geometry (DOG) does not take spatial connectedness as a prerequisite...
Applicable Boundaries of Classical Geometric Systems and the Paradigmatic Complement of Discrete‑Order Geometry (DOG)Author: Zhang Suhang(Luoyang, Henan)AbstractClassical Euclidean geometry, Riemannian geometry and discrete mathematics constitute ...
Preliminary Exploration of Application Directions and Research Boundaries for Discrete‑Order Geometry (DOG)— Research NoteAuthor: Zhang SuhangLuoyangAbstractBased on the foundational definition of Discrete‑Order Geometry (DOG), this paper compiles...
--- DOG Discrete Order Geometry and Its Coupling with Discrete Mathematics Author: Zhang SuhangLuoyang Abstract Modern mathematics has long been divided into two fundamental branches: continuous mathematics and discrete mathematics. There exis...
Discrete Order Geometry (DOG): A Discrete Hierarchical Geometric Framework Based on Fractal Nesting and Continued-Fraction Scales Author: Zhang Suhang(Luoyang, Henan) Abstract Euclidean geometry and Riemannian geometry take continuous connected...
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...
Complete Exclusion of All Counterexample Paths at the Curvature Level Author: Zhang Suhang(Independent Researcher, Luoyang) System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical ParadigmSeries Number: Fifteenth Paper --- Abstract ...