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...
Derivation of the Four Fundamental Interactions from the Unified Recursive Field Equation (URFE)
Author: Zhang Suhang
Abstract: Based on the Unified Recursive Field Equation (URFE), parameter partitioning, group subspace projection, and b...
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...
--- Integrating All Physical Elements and Factors into the Geometric Recursive Conservation Chain（UGSL）: A Unified Logical Framework
I. General Outline: The Universal Conservation Rule for All Physical Elements
Core ...
Markov Theory as a Strict Special Case of the UPGS Universal Axiom System
Author: Zhang Suhang (Founder of the He-Luo Mathematical School)
Abstract
This paper independently, purely, and rigorously demonstrates the axiomatic hierarchy a...
--- Mapping–Number Theory Bottom-Layer Unified Explanation Based on Projection, Dynamic Slope, and MOC Curvature Geometry
Author: Zhang Suhang Founder of the Heluo Mathematical School
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In traditional mathematics, mapping ...
--- MOC Coordinate System: Geometric Definition of Multi-Origin Hierarchical Nesting and Classical Coordinate Degeneration
Based on the Multi-Origin Curvature...
--- 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
This paper ad...
--- 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...
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...
--- Resolution of the Barber Paradox within the MOC (Multi-Origin Curvature) Geometric Framework
The Barber paradox (a popular version of Russell's paradox) reveals ...
--- High-Dimensional Truth Gap: The Geometric Root of Gödel Incompleteness and Quantum Uncertainty
Author: Zhang Suhang, Luoyang, Henan
Gödel's incompleteness theorems reveal the existence of undecidable propositions in f...
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 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...
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 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 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...
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 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...
Tree Root-Shoot Isomorphism: A Natural Empirical Validation of Information Topology Author: Zhang Suhang --- Abstract This paper does not aim to investigate the growth patterns of plant organs. Rather, it selects the reversible transformation ...
--- 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...
--- Part III: Subordination Relations, Nesting Rules, and Cross-Layer Mapping Systems for Hierarchical Sets Author: Zhang Suhang, Luoyang, Henan Abstract Building upon the establishment of the hierarchically nested set paradigm and the three-l...
--- 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...
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 ...
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...
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...
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...
Proof that Continuous Lie Groups are Special Cases of Discrete Groups from a Recursive Geometry Perspective
Classical group theory divides discrete groups and continuous Lie groups into two ...
Geometric Recursive Conservation Chain System: Reframing and Extending Classical Group Symmetry Theory
Classical physics established a binding paradigm of continuous symmetry group – Noethe...
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...