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...
--- Extended Discussion and Academic Boundaries of the MOC System Author: Zhang Suhang, Luoyang Abstract: This paper serves as a supplementary note to the first three papers of the MOC system. It accomplishes only two core tasks: first, it poin...
Paper 2: Geometric Realizations of One-Dimensional Probability Distributions: Bell Curve, Staircase, Lattice, and Fractal
Author: Zhang Suhang
Affiliation: Luoyang, Henan
Abstract
Continuing the probabilistic-geometric isomorphism fr...
Imaginary numbers represent direction. Rotation changes direction. Translation changes position. Ellipses and hyperbolas differ only in real versus imaginary directions. They are fundamentally unified. People have long treated the ellipse,...
--- Paper 1: The Fundamental Paradigm of Probability-Geometry Isomorphism: From Gaussian Distributions to General Measure Correspondences
Author: Zhang Suhang, Luoyang, Henan
The probability density function of the Gaussian dist...
Paper 5: Stochastic Processes and Geometric Flows: From Random Walks to Brownian Motion and Quantum Probability Author: Zhang Suhang Affiliation: Luoyang, Henan Abstract This paper extends the probability-geometry isomorphism frame...
Paper 3：Geometric Embedding of Multivariate Random Variables: A Unified Triple Operation of Joint Distribution, Marginalization, and Conditioning Author: Zhang Suhang Affiliation: Luoyang, Henan, China Abstract Building upon the algebraic-prob...
Title: The Essential Solution to the Three-Body Problem – Higher-Dimensional Curvature Vector Conservation and Coupled Steady State Author: Zhang Suhang, Luoyang Abstract: Based on the MOC (Multi-Origin Curvature) axiomatic system, this paper pr...
Paper 4: Geometric Reconstruction of Probability Axiom System: Kolmogorov Axioms Equivalent to Geometric Measure Axioms
Author: Zhang Suhang Affiliation: Luoyang, Henan
This paper accomplishes a landmark unification between pr...
The Unified Origin of Celestial Motion — Both Revolution and Rotation Are Inevitable Consequences of Curvature Vector Conservation Author: Zhang Suhang, Luoyang Abstract: Building upon the axiomatic system of MOC curvature vector conservation an...
Paper 7: Flat Probabilistic Schemes — Migration from Geometric Measure Spaces to Étale Sites
Author: Suhang Zhang, Luoyang, Henan Abstract
Based on the axiomatic system of probability geometry established in previous papers (Paper 1 & P...
Paper 6: The Unification of Algebra, Probability and Geometry: The New UPG Paradigm — History, Framework and Applications Author: Zhang Suhang
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This paper is a review and applications paper in...
Paper 2-4: Quadratic Solids of Revolution: Generalization of the Π Operator for Ellipsoids and Analysis of Eccentricity Effects
（Luoyang School of Mathematics） Abstract
An ellipsoid is a natural generalization of a...
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 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...
All Two-Dimensional Figures Ultimately Reduce to the Ellipse: A Universal Ontological Argument Based on Multi-Origin Geometry and High-Dimensional Fiber Bundles Abstract Traditional unified theories of planar geometry can only establish the prim...
Construction and Physical Implications of Symmetric Multi-Origin Curvature (SMOC) Geometry **Author:** Zhang Suhang *Independent Researcher* **Abstract:** Based on the Multi-Origin Curvature (MOC) spacetime framework, this paper constructs the...
Paper 8: Étale Random Walks and Arithmetic‑Quantum Unification under the UPGS Framework — Geometric Origins of Prime Distribution, Zeta Functions, and Born’s Rule Author: Zhang SuhangAffiliation: Luoyang, HenanDate: May 25, 2026 --- Abstrac...
Gabor Transform = Projection of MOC under "Fixed Scale + Gaussian Window + Single Origin" 1. Intuitive Correspondence - Fourier Transform: Global kernel e^{-i\omega t}, no localization. - Gabor Transform: Fourier kernel with a Gaussian wi...
MOC Differential Geometry (Multiple Origins with Higher Dimensions) Axiom 1 — Hierarchical Multiple Origins Axiom Space contains hierarchically nested origins, such as the Galactic origin, the Solar origin, and the Earth origin. Each origin is i...
Quantitative Orbital Calculation Capability of the MOC System: From Topological Criterion to Algebraic MappingAuthor: Zhang Suhang (Luoyang)AbstractBased on the axiomatic framework of the MOC system (curvature vector conservation + ECS coupling eq...
We often think that mass is an innate property of objects. A stone, a speck of dust—they all seem to possess weight and substantial existence by birth. But looking into the vast universe and tracing back to the very origin, mass is not inherent at...
Paper 9: The Riemann–Roch Theorem under UPGS — A Geometric Proof Based on the Étale Heat Kernel, MIE Variational Principle, and ECS Conservation Laws
Author: Zhang Suhang Affiliation: Luoyang, Henan Date: May 25, 2026
...
Global Fermat Number Cyclotomic Iterative Geometry
Fermat proposed the Fermat numbers F_k=2^{2^k}+1 and conjectured that all such numbers are prime. A century later, Gauss, in his Disquisitiones Arithmetic...
Paper 10: The Weil Conjectures under UPGS — Étale Random Walks, Curvature Duality, and ECS Stability
Within the UPGS (Étale Probability Schemes) fram...
Paper 11: Computation on UPGS — Algorithms, Complexity, and Numerical Implementation
UPGS (Étale Probability Schemes), as a unified theoretical frame...
Paper 13: The Trinity of Frequency, Probability, and Geometric Measure — From Discrete Order Geometry to Étale Schemes
This paper achieves a seamless connection between ...
"Heuristic Association Between Euler’s Polyhedron Formula and the Golden Ratio Under the Maximum Information Efficiency Axiom" Author: Zhang Suhang, Luoyang Core Axiom: Maximum Information Efficiency (MIE) Axiom --- Abstract Based on the Ma...
Derivation of Euler’s Formula from the Maximum Information Efficiency (MIE) Axiom Prerequisites · Consider a connected planar graph (nodes and edges without crossings). It may be the edge graph of a convex polyhedron, a leaf vein network, an e...
--- On the Essential Identity of Binary and the Law of Excluded Middle and Its Core Significance Abstract This paper aims to clarify the intrinsic relationship between binary (the binary numeral system) and the law of excluded middle (LEM). Bre...