Here is the English translation of your third paper: Author: Zhang Suhang, Luoyang Second Paper (corresponding to 3.2): Statistical Exclusion – Handling of the Law of Large Numbers and Parity Correlations Axiomatic Reconstruction of the Collatz...
Relationship Between Curvature, Revolution and RotationSince real celestial bodies are not ideal rigid spheres, their mass distribution, tidal deformation, and fluid motions make the intrinsic relation between curvature and rotation difficult to v...
Hypothetical Cosmological Model Our universe does not expand forever in one direction. Instead, it follows the laws of energy conservation and the balance between gravity and repulsion, undergoing an eternal cyclic motion of expansion and contrac...
Lin Hai stood in the command vehicle three hundred meters away, observing the fire through a...
Supplemental Paper S‑02: Definition of Generalized Π Operators under the MOC (Multi‑Origin Curvature Geometry) Framework
Author: Suhang Zhang
Abstract
The canonical three-channel Π operator system established in the preceding 19 core m...
Paper 3-2: Composite Transformations and the Structure of Dimensional Transformation Group
Author: Suhang Zhang （Luoyang School of Mathematics）
The core function of the \Pi-operator is to perform mapping operations between spa...
ECS-Hodge Correspondence Categorical Equivalence Between Symmetric Conservation Modes and Hodge Classes Author: Suhang Zhang Address: Luoyang, Henan Abstract Hodge classes serve as core objects in algebraic geometry, defined as ra...
--- 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...
Mark stood at the observation window, staring at the creature moulting inside the cultivation...
The first light of dawn pierced through Amazon’s dense canopy, dappling the damp earth with...
Embedding Mapping Derivation of the Standard Model Gauge Group \boldsymbol{U(1)\times SU(2)\times SU(3)} within the Global Discrete Parent Group (Zhang Group)Author: Suhang Zhang, Luoyang, HenanAbstractThe gauge group of the Standard Model G_{\t...
Discrete Order Geometry (DOG) and Knot Topology: From Continued Fraction Recursion to Interdisciplinary Topological Applications
Author: Zhang Suhang Address: Luoyang, Henan
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Knot topology has long been regarded as a branc...
Yang–Mills Equation Derived Core Formulas for Spectral Counting
Consistent with the DOG/MOC/ECS/MIE framework, this paper starts from the fundamental Yang–Mills equations an...
Differential Equations as the Continuum Limit of DOG Discrete Order
Differential equations are the mainstream mathematical tool for describing the evolution of continuous syste...
DOG Primitive Theorem: Natural Emergence of Algebraic Cycles in Discrete Order Geometry
Algebraic cycles (algebraic subvarieties) are the central objects of the Hodge conjectur...
Discrete Order Geometry (DOG) and Matrix Algebra: Essential Correspondence and Paradigm Reconstruction （ Part Two）
Author: Zhang Suhang Affiliation: Independent Researcher, Luoyang
Based on the axiomatic system of Discrete Or...
193 Cross-Disciplinary Unification via the Axiom of Maximum Information Efficiency: Murray's Law, Polyhedron Formula, and Fermat's Principle Author: Zhang Suhang, Luoyang Abstract: The Axiom of Maximum Information Efficiency (MIE), established...
Theoretical Division and Complementary Relationship between MOC and MIEAuthor: Suhang Zhang, LuoyangWithin the present theoretical framework, Multi-Origin Curvature (MOC) and Maximum Information Efficiency (MIE) constitute two axiomatic systems wi...
Author: Zhang Suhang, Luoyang Third Paper (corresponding to 3.3): A Dynamic Model of Inevitable Convergence Axiomatic Reconstruction of the Collatz Conjecture (III): Comprehensive Proof of Convergence Necessity --- Abstract Based on the pre...
I believe magnetic monopoles do not exist. The reasoning is as follows:
Maxwell's equations in vacuum indeed possess an electric–magnetic dual symmetry (E → B, B → –E). However, once electric charges are introduced as sources, this symmetry is ...
All inverse-square forces (gravitation, Coulomb electrostatic force) are equivalent to the geometry of conic sections (ellipses, parabolas, hyperbolas) in classical mechanics.
- Attraction ⇒ ellipse (or circle) - Repulsion ⇒ hyperbola - Bound...
Unification of the Four Fundamental Forces Gauge fields have unified the weak force, strong force, and electromagnetic force. However, they have not unified gravity and electromagnetic force. I have unified gravity and electromagnetism using...
Paper 13: The Trinity of Frequency, Probability, and Geometric Measure — From Discrete Order Geometry to Étale Schemes
Author: Zhang Suhang Affiliation: Luoyang, Henan
This paper achieves a seamless connection between ...
Paradigm Incorporation of the Hodge Conjecture – Natural Dissolution within the MOC‑DOG‑ECS Framework
The Hodge conjecture is one of the seven Millennium Prize Problems. Tradi...
Mellin Transform and Z-Transform: Projections in Multiplicative and Discrete Geometries
Within the MOC framework, the Fourier, Laplace, wavelet, and Gabor transforms correspond to structures on the Euclidean line, characterized by additive tran...
Since the beginning of systematic observations of natural motions, “force” has always been the core concept used to explain all changes in the world. From the movement of celestial bodies to the falling of objects, from electromagnetic induction t...
My view is different.Rotation of the bucket creates a centrifugal force directed outward from the center.Rotation of the Earth produces a centrifugal force acting upward from the ground.The superposition of these two effects produces the phenomeno...
Mass, Charge and Color Charge as Progressive Manifestations of EnergyMass, charge and color charge are not mutually independent intrinsic properties of matter. Instead, they are external manifestations and progressive forms of energy emerging at d...
Why are gravitational force and Coulomb force so similar?
The first scientist to explore this phenomenon was the famous Michael Faraday, though he obtained no conclusive results.
Later, people explained this phenomenon with the following r...
A Universal Resolution Theory for Self-Reference Paradoxes Based on MOC Multi-Origin Curvature Geometry
Author: Zhang Suhang (Founder of the Heluo Mathematical School)
Self-reference paradoxes have stood as a core conundrum pla...