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...
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 tripartite unifying framework of probabil...
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...
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...
Applications of the UPG Framework: Central Limit Theorem, Statistical Inference, Machine Learning and Quantum Physics Author: Zhang Suhang Affiliation: Luoyang, Henan Abstract This paper serves as an application article for the Unifie...
--- Part One Title: The Geometric Foundation and Model Transformation of the Kakeya Conjecture via DOG-MOC
Author: Zhang Suhang (Bosley Zhang) Location: Luoyang, Henan, China Date: May 2026
Under the framework of Multi-Origin...
The Final Destination of Energy: Origin of Dark Matter and Dark Energy via Energy‑Level Degradation
Author: Zhang Suhang Affiliation: Luoyang, Henan Date: August 2026
In the standard Λ‑CDM cosmological model, ordinary matter, d...
Geometry and Mechanics
Author: Suhang Zhang, Luoyang, Henan
---
The two core frameworks of modern fundamental physics are both built upon geometric models: Riemannian geometry serves as the spacetime model of general relativit...
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...
Paper 6: Dynamic Midpoint Extremum Theorem: The Dynamic Tripartite Unification of Probability–Geometry–Algebra (UPG) Author: Zhang Suhang Affiliation: Luoyang, Henan Abstract This paper establishes the Dynamic Midpoint Extremum Theore...
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...
UPG and the Connection to ∞-Toposes: Construction of Weighted ∞-Toposes (UPGT) Author: Suhang ZhangAffiliation: Luoyang, Henan --- Abstract This paper establishes a connection between the Probability–Geometry Unified Framework (UPG) and Lurie'...
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
...
From the largest to the smallest — from celestial bodies down to particles — all things are discrete. Order, or law, connects all things. ———SuHang Zhang Within DOG, this connection is precisely encoded as a three‑...
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...
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 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...
Elliptic Function Interpretation of the Four Fundamental Forces1. General PrincipleMathematically: Trigonometric functions are only a degenerate special case of elliptic functions; elliptic functions are the general mother structure.Physically: Th...
"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...
Applications of Multi-Origin High-Dimensional Geometry1. Interstellar coordinate system2. Celestial motion research3. Interstellar spacecraft trajectory design4. Optimal design of steel wire ropes (for hoisting, ropeways, bridges, tower cranes)- T...
"The Golden Ratio, Fibonacci Numbers, and Euler’s Polyhedron Formula Under the Maximum Information Efficiency Axiom: Hierarchy, Association, and a Unified Perspective" Author: Zhang Suhang, Luoyang Core Axiom: Maximum Information Efficiency (M...
The Planckian Homunculus – A Different Kind of Observation If we could shrink ourselves down to the Planck scale – that extreme microscopic world where space is as small as 10^{-35} meters and time as short as 10^{-43} seconds – and become, so to...
The Intuitive Unification of Macroscopic and Microscopic Curvature Spacetime curves. Fields also curve. For a long time, physics has treated the curvature of macroscopic spacetime and the intrinsic curvature of microscopic fields as two separate...
--- 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...