DOG Discrete Order Geometry: A Minimal Mathematical Paradigm for Unifying the Four Fundamental Interactions

Author: Zhang Suhang, Luoyang

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I. Fundamental Unified Substrate

Let the set of all discrete spacetime lattice points in t...

Unified Theory of the Four Fundamental Interactions under the Discrete Lattice Paradigm of the DOG Universe
Author: Zhang Suhang, Luoyang, Henan
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Core Synopsis
The entirety of spacetime is fundamentally a giant discrete DOG cosmic lattice. ...

Title: The Geometric Positioning of the Probability Formula P = 1/(1+(\Delta\nu)^2) in DOG Spacetime
Author: Zhang Suhang
Address: Luoyang, Henan
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Abstract
Within the framework of Discrete Order Geometry (DOG), the observed probability ...

Frequency as the Origin of Probability: From Discrete Order Geometry (DOG) to a Quantitative Derivation Where Frequency Difference Determines Probability

Author: Zhang Suhang, Luoyang, Henan

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Abstract

The origin of probability is...

I got pulled into this project where we needed reliable industrial supply backing, you know the kind that sticks. At the start I assumed it would be almost simple, compare suppliers, check pricing, sort out the dispatch, done.
But then in meeting...

DOG Discrete Order Geometry and Hilbert Space: Bidirectional Isomorphism, Limit Correspondence, and Paradigm Bridging Theory

Author: Zhang Suhang, Luoyang

Abstract

Traditional discrete combinatorial geometry and continuous functional a...

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...

Every business industry needs to store things in the packaging and trash very smoothly and cleanly. No matter which category of business you have, like warehouse, shop, office, logistics, retail, whatever, packing materials you are using and durab...

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Discrete Order Geometry (DOG): A New View of Spacetime — Space as Matrix and Time as Fiber Bundle

Author: Zhang Suhang (Luoyang, Independent Researcher)

Abstract: Discrete Order Geometry (DOG) fundamentally reconstructs the picture of...

From the largest to the smallest — from celestial bodies down to particles — all things are discrete. Order, or law, connects all things.
                             ———SuHang Zhang

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Discrete Order Geometry (DOG) Unifies Gauge Field Theory – A Unified Framework for Universal Field Theory Based on the Microscopic Discrete Primordial

Author: Zhang Suhang (Luoyang, Henan)

Abstract

Modern gauge field theory, built ...

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Discrete Order Geometry (DOG): Primitive Inclusion and Paradigm Incorporation of Fiber Bundle Theory – A Unified Geometric Architecture with Discrete Connection as the Primordial Source and Smooth Connection as the Continuous Special Case
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The Combinatorial Axiom Foundation of Discrete Order Geometry (DOG) – Construction of a High-Order Arrangement and Combination System for Geometric Configurations

Author: Zhang Suhang (Luoyang, Henan)

Abstract

Classical geometry an...

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The Underlying Disruptive Impact of the DOG Paradigm on Universal Modular Systems

Author: Zhang Suhang, Luoyang

Abstract: Discrete Order Geometry (DOG) completely rewrites the underlying logic of modularity, transitioning from the old...

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...

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...

First-Principles Derivation of the Schrödinger Equation via Discrete Order Geometry (DOG): From Discrete Recursion to Continuous Wave Mechanics
 
Author: Zhang Suhang
Independent Researcher, Luoyang
 
Abstract
 
Based on the matrix evolu...

Discrete Order Geometry (DOG) and Matrix Algebra: Essential Correspondence and Paradigm Reconstruction  （ Part Two）

Author: Zhang Suhang
Affiliation: Independent Researcher, Luoyang

Abstract

Based on the axiomatic system of Discrete Or...

Discrete Order Geometry (DOG) and Matrix Algebra: Essential Correspondence and Paradigm Reconstruction  （Part One）

Author: Zhang Suhang
Affiliation: Luoyang

Abstract

This paper systematically reveals the intrinsic isomorphic relationship...

Discrete Order Geometry (DOG) and Quantum Mechanics: Ontological Unification from Discrete Lattices to Quantum Representation

Author: Zhang Suhang
Affiliation: Luoyang

Abstract

Since its inception, quantum mechanics has been regarded as ...

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Discrete Order Geometry (DOG) and Classical Fractal Geometry: Paradigm Comparison and Pain Point Resolution

Author: Zhang Suhang
Luoyang

Abstract: Classical fractal geometry, with its core assumptions of infinite self‑similarity and ...

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A Complete Solution System for the Three‑Body Problem within the Framework of Discrete Order Geometry (DOG)
Author: Zhang SuhangLuoyang
Abstract: Under the classical Newtonian continuous geometry system, the three‑body problem has been defi...

Hardware innovation plays a crucial role alongside software and cloud solutions. From IoT devices and embedded systems to consumer electronics and industrial machines, hardware development is shaping the future. Publishing a Hardware development g...

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Discrete Order Geometry (DOG) and Topology: A Preliminary Exploration of the Structured Description of Non‑Connected Spaces

Author: Zhang Suhang
Luoyang

Abstract

The establishment of Discrete Order Geometry (DOG) removes spatial c...

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Structural Shortcomings of Traditional Mathematical and Geometric Systems and the Systematic Complementation by the DOG Paradigm
Author: Zhang SuhangLuoyang
Abstract
Modern mathematics, geometry, and celestial mechanics have, over centurie...

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Discrete Order Geometry (DOG): A Study of Its Universal Application System
Author: Zhang SuhangLuoyang
Abstract
After establishing the definition of Discrete Order Geometry and demonstrating its coupling with the discrete mathematics syste...

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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...

Discrete Order Geometry (DOG): A Geometric Paradigm Based on Fractal Nesting and Continued Fraction Scaling

Author: Zhang Suhang
Luoyang

Abstract

Traditional geometric systems (Euclidean geometry, Riemannian geometry) and classical fract...

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
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Abst...