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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Abstract
Knot topology has long been regarded as a branc...
Differential Equations as the Continuum Limit of DOG Discrete Order
Differential equations are the mainstream mathematical tool for describing the evolution of continuous syste...
The Origin of the Natural Constant e in Spacetime Geometry within the DOG Discrete Order Geometry Framework
The natural constant e is a fundamental constant underlying m...
Batch Incubation & Age-Staggered Development Protocol 1. Staged activation: Fertilized eggs are thawed and incubated in timed batches, with intervals of 1–3 years between groups, avoiding population and care overload. 2. Age-hierarchy ...
Supplemental Paper S‑02: Definition of Generalized Π Operators under the MOC (Multi‑Origin Curvature Geometry) Framework
Author: Suhang Zhang
The canonical three-channel Π operator system established in the preceding 19 core m...
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...
DOG Primitive Theorem: Natural Emergence of Algebraic Cycles in Discrete Order Geometry
Algebraic cycles (algebraic subvarieties) are the central objects of the Hodge conjectur...
DOG Discrete Order Geometry: A Minimal Mathematical Paradigm for Unifying the Four Fundamental Interactions
Author: Zhang Suhang, Luoyang
I. Fundamental Unified Substrate
Let the set of all discrete spacetime lattice points in t...
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...
--- 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...
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...
Unification Under the Maximum Information Efficiency Axiom: Homology Between Murray’s Law and Polyhedron LawAuthor: Suhang Zhang, LuoyangAbstractMurray’s law describes the cubic scaling relation of vessel diameters in biological branching networks...
Theory of Biomimetic Fractal Topological Coupling and Dimensional Gradient Transition Transmission I. Core Theoretical Essence This theory takes the natural fractal structures of tree roots and leaf veins as its fundamental logical origin. It br...
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...
The first light of dawn pierced through Amazon’s dense canopy, dappling the damp earth with...
The wheels spun wildly! From Haicheng to Lincheng, westbound, day and night. Wind...
Discrete Order Geometry (DOG) and Harmonic Analysis: A Unified Framework for Decomposition and Reconstruction of Smooth Fields
Author: Zhang Suhang Independent Researcher · Luoyang
This paper establishes a fundamental com...
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...
A Quantitative Model for Axial Obliquity under the Pure MOC Framework
Author: Zhang Suhang (Luoyang, Henan) Affiliation: Independent Researcher
Based on the Multi-Origin Curvature (MOC) paradigm, this paper presents a com...
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...
Mark stood at the observation window, staring at the creature moulting inside the cultivation...
Lin Hai stood in the command vehicle three hundred meters away, observing the fire through a...
The First Love --- Some social news left Wei Ling with a tangled mess of feelings. He couldn't...
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...
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...
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...
Numerical Validation of the Extremum-Conservation-Symmetry System and a Case Study on Symmetry Group Extension
Author: Suhang Zhang Affiliation: Luoyang, Independent Researcher
This paper systematically conducts numerical...
I. Difference Is Potential, Which Is EnergyAt the fundamental structure of the physical world, difference itself corresponds to a potential field, and potential field is directly equivalent to energy. This relation should not be regarded as a man-...