DOG Primitive Theorem: Natural Emergence of Algebraic Cycles in Discrete Order Geometry
Author: Zhang Suhang Address: Luoyang, Henan
---
Abstract
Algebraic cycles (algebraic subvarieties) are the central objects of the Hodge conjectur...
--- Reconstructed Axioms of Set Theory under the MOC Multi-Origin High-Dimensional Framework Within the MOC multi-origin high-dimensional framework, we first establish the top-level paradigmatic axiomatic outline of set theory. The following fiv...
Matrix and Multi-Origin High-Dimensional Geometry —— MOC System Axiom V: The Matrix is the Low-Dimensional Projection, the High-Dimensional Noumenon Traditional linear algebra has committed a categorical error that has persisted for three centur...
First-Principles Derivation of the Schrödinger Equation via Discrete Order Geometry (DOG): From Discrete Recursion to Continuous Wave Mechanics Author: Zhang Suhang Independent Researcher, Luoyang Abstract Based on the matrix evolu...
--- The Four Great Lineages of Calculus: A Unified Classification Framework for Lines, Loops, Surfaces, and Volumes Author: Zhang Suhang (Luoyang) Abstract: Classical calculus presents a vast array of integral forms — ordinary definite integral...
Limit Argument for Conservation Law Preservation Author: Suhang Zhang Affiliation: Luoyang, Independent Private Researcher Abstract This paper investigates the preservation of conservation quantities for discrete dynamical systems in ...
--- 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...
DOG Discrete Order Geometry and Group Theory: The Origin of Symmetry in Constant-Coefficient Recursion
Group theory is the core language for describing symmetry in modern mathe...
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...
Weak Convergence and Ergodic Limit of Stochastic ECS Systems Author: Zhang Suhang Luoyang, Independent Researcher Abstract This paper extends the Extremum-Conservation-Symmetry (ECS) framework to discrete stochastic linear dynamical s...
Convergence of the Solution to the Discrete Riccati Equation with Respect to Sampling Period Author: Suhang Zhang Luoyang Abstract
This paper rigorously proves that as the sampling period h\to 0^+, the solution of the disc...
--- Clarification on the Relationship Between MIE and the Maximum Entropy Principle To avoid theoretical misunderstandings and academic ambiguity, this section specifically clarifies the intrinsic relationship between the Maximum Information Eff...
The Optimal Solution for Interstellar Colonization: Nuclear Power + Interstellar Corridor + Human Cryopreservation + Fertilized Eggs + Artificial Womb Author: Zhang Suhang Under the realistic constraints of an unbreakable speed of light and th...
Interstellar Corridor (Part I): A Foundational Theory of Low-Energy Interstellar Travel Based on Natural Spacetime Curvature Gradients Author: Zhang Suhang, Luoyang Abstract Current interstellar travel theories face core dilemmas: extremely l...
Unification of Honeycomb and Leaf Vein under the Axiom of Maximum Information EfficiencyAuthor: Suhang Zhang AbstractThe honeycomb uses the least beeswax to enclose the maximum volume. Leaf veins use a limited network of vessels to cover the maxim...
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...
--- 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...
Discrete Order Geometry (DOG) and Quantum Mechanics: Ontological Unification from Discrete Lattices to Quantum Representation
Author: Zhang Suhang Affiliation: Luoyang
Since its inception, quantum mechanics has been regarded as ...
Numbers are dancing points.Functions are floating lines.Geometry is manifolds and fluids.
Prospects for the Application of MOC in Magnetic Resonance Imaging (MRI)Magnetic resonance imaging is essentially a high-dimensional system that acquires and reconstructs massive proton spin signals in an inhomogeneous magnetic field. Its core cha...
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...
--- DOG Discrete Order Geometry and Its Coupling with Discrete Mathematics:Completing the Missing Discrete Spatial Geometric Foundation of Modern Mathematics Author: Zhang SuhangLuoyang Abstract Modern mathematics has long been divided into tw...
Global Data Verification of the System and Summary of Paradigm Applications Author: Zhang Suhang(Independent Researcher, Luoyang) System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical ParadigmSeries Number: Sixteenth Paper --- Abst...
--- 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 →...
Proof of Global Smooth Solutions to the Navier-Stokes Equations within the DOG/MOC/ECS/MIE Framework
The existence of global smooth solutions to the Navier-Stokes (NS) equati...
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...
Frequency as the Origin of Probability: From Discrete Order Geometry (DOG) to a Quantitative Derivation Where Frequency Difference Determines Probability
Author: Zhang Suhang, Luoyang, Henan
The origin of probability is...
Discrete Order Geometry (DOG) and Matrix Algebra: Essential Correspondence and Paradigm Reconstruction （Part One）
This paper systematically reveals the intrinsic isomorphic relationship...
Theoretical Calculation of Mercury’s Perihelion Precession under the Multi-Origin Curvature (MOC) Framework Author: Zhang Suhang (Luoyang, Henan)Affiliation: Independent Researcher Abstract: Based on the Multi-Origin Curvature (MOC) theory, this...
Frequency Difference Determines Probability: Geometric Proof of God Does Not Play Dice from the Perspective of Discrete Order Geometry Author: Zhang Suhang Address: Luoyang, Henan, China Abstract The intrinsic randomness of probabi...