Proof of the BSD Conjecture within the DOG/MOC/ECS/MIE Framework
Author: Zhang Suhang Address: Luoyang, Henan
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Abstract
The BSD (Birch and Swinnerton-Dyer) conjecture is a Millennium Problem in number theory concerning the equal...
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Differential Equations as the Continuum Limit of DOG Discrete Order
Differential equations are the mainstream mathematical tool for describing the evolution of continuous syste...
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 ...
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DOG Discrete Order Geometry and Group Theory: The Origin of Symmetry in Constant-Coefficient Recursion
Group theory is the core language for describing symmetry in modern mathe...
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DOG Discrete Order Geometry and Modular Forms: The Recursive Nature of Coefficient Sequences
Modular forms are central objects in number theory and algebraic geometry; their Fo...
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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 ...
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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...
DOG Primitive Theorem: Natural Emergence of Algebraic Cycles in Discrete Order Geometry
Algebraic cycles (algebraic subvarieties) are the central objects of the Hodge conjectur...
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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...
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...
The Origin of the Natural Constant e in Spacetime Geometry within the DOG Discrete Order Geometry Framework
The natural constant e is a fundamental constant underlying m...
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The Origin of π in Spacetime Geometry within the DOG Discrete Order Geometry Framework
Since ancient times, humanity has understood the circumference ratio π only throug...
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Title: Under the DOG Discrete Order Geometry Framework, the Yang–Mills Equation Is No Longer a Foundational Challenge but a Natural Emergent Result of Spacetime Steady States
Author: Zhang Suhang
Address: Luoyang, Henan, China
Abstract ...
--- 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. ...
Conclusion: Low-Energy Approximation in the DOG System Strictly Conforms to the MIE Core Paradigm
Author: Zhang Suhang, Luoyang, Henan
I. Core Correspondence
1. Essence of MIE
MIE is the universal steady-state extremal ev...
--- 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...
DOG-FCE and MOC-UCE: Two Equivalent Physical Representations of the Same Unified Field Essence
Author: Zhang Suhang, Luoyang (Independent Researcher)
Within the axiomatic DOG-MOC grand unified system, there exist two co...
DOG Discrete Lattice Unified Four-Force System: Completeness Conclusion for Quantitative Computation
Author: Zhang Suhang, Luoyang
Core Conclusion
The unified four-force mathematical-physical system based on Discrete Order Geome...
