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 ...
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 ...
--- 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...
Paper 4-3: A Study on the Complementarity between the Π-Operator and Classical Differential OperatorsAuthor: Suhang Zhang (Luoyang School of Mathematics）Abstract Classical differential operators including gradient, divergence, curl, Laplacia...
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 ...
Understanding Lease Return Inspections Lease agreements typically outline acceptable wear and tear. However, what may appear minor to an owner can be interpreted differently during inspection. Inspectors evaluate: Exterior paint conditionSurface...
It was the weekend again. Wei Ling lay sprawled on the sofa, scrolling through his...
Wei Ling set a small bunch of white chrysanthemums against the rail of Hongqiao Bridge. The river...
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...
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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...
The Impact of Multi-Origin High-Dimensional Geometry on Radar DesignIn modern national defense and detection systems, radar has long been more than a device for detecting targets. It serves as a core strategic equipment supporting battlefield situ...
The Possibility of Consciousness Uploading Within the framework of the Primitive Wave Combinatorial Consciousness Theory, consciousness uploading is no longer mere science fiction, but an achievable goal with a clear theoretical path. Since any ...
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...
Inside the abandoned factory stood a small meeting room, perfect for gatherings. Its floor was...
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...
Curvature-Driven Fluid Equation Verification via Discrete Order Geometry: A Numerical Case Study
Author: Zhang Suhang (Independent Researcher, Luoyang, Henan)
Within the Multi-Origin Curvature (MOC) framework, the stea...
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 ...
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 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...
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...
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 ...
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 ...
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...
Matrix and Multi-Origin High-Dimensional Geometry —— MOC System Axiom V: The Matrix is the Low-Dimensional Projection, the High-Dimensional Noumenon Traditional linear algebra has committed a categorical error that has persisted for three centur...
Paper 2-1: Dual-Channel Transformation of the Π Operator for Cylindrical Bodies
A cylinder is the simplest non-spherical solid of revolution. Its formation intrinsically corre...
When Wei Ling received the distress signal from Proxima b, the alien script looked...
Hui Li was jolted awake. The tremor surged from deep within the Earth’s crust,...
Paper 5-2: Historical Review on the Evolution of π Research: From Euler and Ramanujan to the Formulation of the Π Operator System
Author: Suhang Zhang ( Luoyang School of Mathematics )
The cognitive history of π consists of thr...
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...
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...
