Proof that Continuous Lie Groups are Special Cases of Discrete Groups from a Recursive Geometry Perspective
Author: Zhang Suhang, Luoyang, Henan
Abstract
Classical group theory divides discrete groups and continuous Lie groups into two ...
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--- Part IV: Discrete Origin and Continuous Limit: The Unified Resolution of Binary Forms in the New Set Theory Author: Zhang Suhang, Luoyang, Henan Abstract The binary fragmentation between discrete and continuous is one of the longest-standi...
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...
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...
Algebraic Isomorphism Between Zhang Group and Continuous Lie Groups Under the Triple Limit Author: Suhang Zhang (Luoyang, Henan, China) Abstract Within the frameworks of Discrete Order Geometry (DOG) and Multi-Origin Recursive Geometry...
--- Chapter Two: Methodology – Mathematical Modeling Methods Adapted for Biological Topological Systems
A Mathematical Modeling System for 2D-3D Biological Topological Systems
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Core Task
Buil...
Geometric Recursive Conservation Chain System: Reframing and Extending Classical Group Symmetry Theory
Classical physics established a binding paradigm of continuous symmetry group – Noethe...
Lorentz Covariant Extension of the Geometric Progressive Conservation Law: Unification of Classical and Relativistic Conservation Author: Zhang SuhangAffiliation: Luoyang, Henan --- Abstract The Geometric Progressive Conservation Law (GPCL)...
--- Part II: Beyond the Flat Static Set View: Establishing a Hierarchically Nested Set System Author: Zhang Suhang, Luoyang, Henan Abstract Classical set theory, with its flat, single-layered, statically fixed conception of sets as its foundat...
So Mighty is the Pull: Reflections on Mechanics
So mighty is the pull, so vast its spirit. For millennia, humanity's quest to understand the forces of the universe has carried this indomitable resolve.
Starting from the sages who came before...
Chapter One: Theoretical Chapter – An Integrated Explanation of the Structure–Function Relationship from a Topological Perspective
An Integrated Explanation of the "Structure–Function" Relationship in Biological Morphology from a Topological Pe...
Part One：Structural Limitations of Classical Set Theory and the Necessity of Expanding the Hierarchically Nested Set Paradigm Author: Zhang Suhang, Luoyang, Henan Abstract Since the emergence of naive set theory and the establishment of the ...
For the longest time, I honestly thought all volleyball nets were basically the same. As long as the ball could go over and the poles stayed upright, I figured that was enough. A few months ago, my friends and I started playing more regularly on ...
--- Theoretical Support of Poisson Mechanics for the Geometric Progressive Conservation Law (GPCL)
Author: Zhang Suhang
Affiliation: Luoyang, Henan
Based on the core geometric axiom that "linear motion is equivalent to circul...
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...
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...
Chapter 7： Conclusions and Outlook: Classical Logic as a Special Case of MOC Logic — Toward a New Hierarchical Logic System Author: Zhang Suhang, Luoyang, Henan Abstract This is the final chapter of the series Geometric Origin of th...
Chapter 2: The Higher-Dimensional "OR" State: The Matrix of the Law of Excluded Middle Author: Zhang Suhang (Luoyang, Henan, China) Abstract This paper is the second installment in the research series Geometric Origin of the Law of Exc...
Chapter 4: Projection Mapping \boldsymbol{\Pi} and State Collapse Mechanism: \boldsymbol{\Pi: \mathcal{T}\to\{0,1\}}, Forced Binarization and Emergence of the Law of Excluded Middle Author: Zhang Suhang, Luoyang, Henan Abstract ...
Chapter 5 The Emergence of Binary: Symbolization of the Law of Excluded Middle — Binary is the minimal symbol set of the law of excluded middle, and numeral systems are counting modes after projection Author: Zhang Suhang (Luoyang, Hena...
Chapter 6 ：Reconstruction of the Three Fundamental Laws of Logic: The Law of Identity, the Law of Contradiction and the Law of Excluded Middle as Products of Low-Dimensional Projection Author: Zhang Suhang, Luoyang, Henan Abstract This...
--- Geometric Progressive Conservation Chain in Curved Spacetime: Spacetime Curvature and Conservation Transmission Mechanism
Author: Zhang Suhang Affiliation: Luoyang, Henan
Classical general relativity establishes a...
--- High-Dimensional Truth Gap: The Geometric Root of Gödel Incompleteness and Quantum Uncertainty
Gödel's incompleteness theorems reveal the existence of undecidable propositions in f...
Chapter 3: Three Non-Classical States of the High-Dimensional Truth Space \mathcal{T} Further elaboration: Definitions of truth-value gap, truth-value glut and indeterminate state Author: Zhang Suhang (Luoyang, Henan)
This pa...
--- The Dimensional Mapping Generative Principle of Number Bases: A Unified Geometric Origin of Discrete, Linear, and Periodic Numeral Systems
Founder of the Heluo Mathematical School
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--- The End of the Third Mathematical Crisis: MOC Multi-Origin Curvature Geometry and the Restructuring of Mathematical Foundations
Author: Zhang Suhang (Bosley Zhang)
Three foundation...
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A Universal Resolution Theory for Self-Reference Paradoxes Based on MOC Multi-Origin Curvature Geometry
Author: Zhang Suhang (Founder of the Heluo Mathematical School)
Self-reference paradoxes have stood as a core conundrum pla...
