Preliminary Exploration of the Fusion Configuration as a Concrete Prototype of Fiber Bundles Author: Zhang Suhang, Luoyang, Henan
--- Abstract Based on previous research results on spherical cap‑derived self‑similar geometry (SCD‑SG), thi...
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...
Paper 3-1: Basic Algebraic Operations of the Π Operator: Scalar Multiplication, Addition and Inverse Elements
Author: Zhang Suhang （Luoyang School of Mathematics） Abstract
As a core tool for dimensional transformation, the algebraic struct...
--- Resolution of the Barber Paradox within the MOC (Multi-Origin Curvature) Geometric Framework
Author: Zhang Suhang
The Barber paradox (a popular version of Russell's paradox) reveals the logical contradiction arising from "se...
The Complete Closed Proof of the Riemann Hypothesis (UCE Coordinated Version) Author: Zhang Suhang(Independent Researcher, Luoyang) System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical ParadigmSeries Number: Fourteenth Paper --- A...
Multi-Origin High-Dimensional Geometric Neural Networks All current neural networks are fundamentally locked into two-dimensional planes, a single origin, and matrix tiling operations. No matter how large or deep the models become, they merely st...
Introduction Women’s health is a vital aspect of overall well-being, and having access to reliable and professional medical care is essential. From adolescence to motherhood and beyond, every stage of a woman’s life requires special...
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 ...
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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 ...
Discrete Order Geometry (DOG) and Topology: A Preliminary Exploration of the Structured Description of Non‑Connected Spaces
The establishment of Discrete Order Geometry (DOG) removes spatial c...
Wavelet Transform = Projection of MOC under Scale Shrinkage + Local Origin Keep the same style as before, while marking heuristic steps. --- 1. Intuitive Correspondence · Fourier: single origin + no scale + flat space· Wavelet: single origin...
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...
--- 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...
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 ...
Scientific Implications of Frequency Difference Determining Probability: God Does Not Play Dice This conclusion settles the long-standing debate between Bohr and Einstein. If we follow Bohr’s standpoint, the universe would descend into chaos. ...
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
Address: Luoyang, Henan, China
Abstract ...
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...
Wei Ling set a small bunch of white chrysanthemums against the rail of Hongqiao Bridge. The river...
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...
--- Geometric Progressive Conservation Chain in Curved Spacetime: Spacetime Curvature and Conservation Transmission Mechanism
Author: Zhang Suhang Affiliation: Luoyang, Henan
Classical general relativity establishes a...
The Global Law of MIE Optimal Integral Evolution
Author: Zhang Suhang (Independent Researcher, Luoyang) System Affiliation: MOC‑MIE‑ECS‑UCE Unified Mathematical‑Physical Paradigm Series Number: Paper No. 4 ---
The class...
Paper E1-4: Euler's Identity as the Minimal Closure Instance of the Π Operator System
Author: Suhang Zhang （Luoyang School of Mathematics） Abstract
Renowned as the most elegant formula in mathematics, Euler's identity e^{i\pi}+1=0 unifie...
Paper E4-4: Generator Relations between Euler’s Formula and the Π-Operator
Author: Suhang Zhang (Luoyang School of Mathematics）
Euler’s formula e^{i\theta}=\cos\theta+i\sin\theta intrinsically links complex exponentials to circu...
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...
Dynamics and Multi-Origin High-Dimensional Geometry Classical dynamics, based on a single-origin flat coordinate system, describes motion with all forces, displacements, and rotations normalized to a single coordinate reference. Motion evolution ...
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...
--- 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...
The constant rush of travel left Wei Ling exhausted yet fulfilled. He had no desire to...
Direct Derivation of the Functional Equation from Curvature Dual Symmetry Author: Zhang Suhang(Independent Researcher, Luoyang) System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical ParadigmSeries Number: Twelfth Paper --- Abstract...
Introduction: Why Characters Matter in Every Story In every great story, characters play the most important role. A strong plot may attract readers, but it is the characters that make them stay. Readers remember how characters made them feel, how...
