Part One: Analogical Foundation in Number Theory —— The Fractal Generation Logic of Composite Numbers
Author: Zhang Suhang, Luoyang, Henan
Abstract Starting from the constructive processes of number theory and fractal geometry, this paper ...
Paper 4-2: Integral Channel: Cross-Dimensional Π Mapping of Scalar and Vector FieldsAuthor: Suhang Zhang, Heluo Mathematical SchoolReferences: OmittedAbstractThe Channel III of the Π operator relies on integral-type π quantities (Gaussian integral...
--- High-Dimensional Truth Gap: The Geometric Root of Gödel Incompleteness and Quantum Uncertainty
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Abstract
Gödel's incompleteness theorems reveal the existence of undecidable propositions in f...
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 ...
Instability and Divergence Principle of Deviated States
Author: Zhang Suhang (Independent Researcher, Luoyang)
System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical Paradigm Series Number: Ninth Paper
This...
Numerical Cases and Analysis of Two Basic Navier-Stokes Formulas Author: Zhang Suhang Version 1: Basic Paradigm (ECS + DOG + MlE) boldsymbol{U}^{n+1} =mathop{argmin}{boldsymbol{U}inmathcal{H}} mathcal{E}big(boldsymbol{U},nablaboldsymbol{U}big) ...
Paper 3-3: Ramanujan's Series for 1/\pi and Higher-Order Periodic Channels of the \Pi Operator Author: Zhang Suhang (Heluo Mathematical School) Abstract Ramanujan derived numerous elegant and rapidly convergent series for 1/\pi, who...
--- Resolution of the Barber Paradox within the MOC (Multi-Origin Curvature) Geometric Framework
Author: Zhang Suhang Founder of the Heluo Mathematical School
The Barber paradox (a popular version of Russell's paradox) reveals ...
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 ...
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 ...
Conclusion: Low-Energy Approximation in the DOG System Strictly Conforms to the MIE Core Paradigm
I. Core Correspondence
1. Essence of MIE
MIE is the universal steady-state extremal ev...
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...
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...
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...
The day Liu Ezi went to the school to see Teacher Zhang, she had discussed it with Yan...
Geometric Recursive Conservation Chain System: Reframing and Extending Classical Group Symmetry Theory
Classical physics established a binding paradigm of continuous symmetry group – Noethe...
--- Theoretical Support of Poisson Mechanics for the Geometric Progressive Conservation Law (GPCL)
Affiliation: Luoyang, Henan
Based on the core geometric axiom that "linear motion is equivalent to circul...
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...
--- 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...
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...
Paper 1-1: Core Definition and Symbol System of the \mathcal{\Pi} Operator
As one of the most vital constants in the history of mathematics, \pi has long been confi...
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...
--- 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. ...
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...
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. ...
Discrete Order Geometry (DOG): A Geometric Paradigm Based on Fractal Nesting and Continued Fraction Scaling
Author: Zhang Suhang Luoyang
Traditional geometric systems (Euclidean geometry, Riemannian geometry) and classical fract...
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...
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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 ...
