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...
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 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...
A Four-Dimensional Algebra Construction Adapted to Fibre Bundle Topology and Its Structural Correspondence to Fundamental Interactions Author: Zhang Suhang, Luoyang, Henan Abstract This paper proposes a four-dimensional algebraic la...
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...
On the Conditions for the Validity of the Law of Excluded Middle—The Mutual Reinforcement of Weyl’s Mathematical Boundary and the Spatiotemporal-Observation Boundary
Luoyang School of Mathematics
Since ...
Reduction of the Unified Curvature Equation to the Classical Limit: From UCE to General Relativity, Classical Field Theory and Mechanics Author: Zhang Suhang Affiliation: Luoyang School of Mathematics Abstract The Unified Curvature...
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...
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 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...
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'...
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...
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
Author: Zhang Suhang Affiliation: Luoyang, Henan Date: May 25, 2026
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...
Unified Curvature Equation (UCE): A Geometric Unification Framework for Spacetime Curvature and Gauge Curvature Author: Zhang Suhang Affiliation: Luoyang School of Mathematics Abstract Based on the two-layer geometric structure of Rie...
"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...
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...
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...
Methodological Reflections on the Study of the Collatz Conjecture: From Case Entanglement to Axiomatic Constraints Author: Zhang Suhang, Luoyang Abstract The Collatz conjecture, a classic open problem at the intersection of number theory and dy...
Multi-Origin Curvature (MOC) Framework: Basic Definitions and Geometric Conservation Law
Author: Zhang Suhang, Luoyang
This paper establishes the basic geometric definitions of the Multi-Origin Curvature (MOC) framework. Three co...
--- 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...