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...
Axioms and Definitions of the MOC Core — Paradigm Substitution of Classical Mechanical Quantities by Multi-Origin Vector Curvature Author: Zhang Suhang, LuoyangAbstractThis paper formally establishes the axiomatic foundation of the MOC (Multi-Or...
Higher-degree equations are shaped by curves swaying back and forth.Sway more intensely, and you get surfaces.Sway even more wildly, and you get solids.Orderly swaying creates geometric symmetry and is solvable.Chaotic swaying produces bizarre, ir...
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: Based on the MOC curvature vector conservation and ECS coupling balan...
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: History, Frameworks, and New Paradigms
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This paper is a review and applications paper in the series on th...
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...
Paper 2-4: Quadratic Solids of Revolution: Generalization of the Π Operator for Ellipsoids and Analysis of Eccentricity Effects Author: Zhang Suhang (Heluo Mathematical School) 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...
The elementary‑wave combination principles and consciousness encoding structure revealed by this theory can be directly integrated with brain‑computer interface (BCI) technology. By acquiring brain signals via EEG devices and performing Fourier de...
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...
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...
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
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The Ultimate Position of Functional Analysis in MOC Traditional Functional Analysis: Function → Infinite-dimensional vector space → Operator → Norm → Weak convergence → Hilbert space Everything is built upon: a single origin, a global linear ...
--- Binary is suitable for describing discrete systems, corresponding to logic.Decimal is suitable for describing continuous systems, corresponding to functions. Binary → Discrete system → Corresponds to formal logicDecimal → Continuous system →...
1. The Second Law of Thermodynamics Heat can only spontaneously flow from a hotter object to a colder one, and cannot spontaneously flow from a colder object to a hotter one. 2. The Principle of Air Conditioning In winter, an air condi...
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 12: Étale Differential Equations on UPGS — Continuum Limit of Random Walks and Heat Kernel, with Derivation of the Schrödinger Equation Author: Zhang SuhangAffiliation: Luoyang, HenanDate: May 25, 2026 --- Abstract In Papers 7 and 8, ...
--- 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...