Proof of Global Smooth Solutions to the Navier-Stokes Equations within the DOG/MOC/ECS/MIE Framework
Author: Zhang Suhang Address: Luoyang, Henan
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Abstract
The existence of global smooth solutions to the Navier-Stokes (NS) equati...
Author: Zhang Suhang, Luoyang Part I (Corresponding to 3.1): Axiomatic Constraint – Maximum Information Efficiency (MIE) in the Collatz System Axiomatic Reconstruction of the Collatz Conjecture (I): The Maximum Information Efficiency Axiom as...
The Sphere Theorem as a Natural Consequence of Unified Geometric Extremal Physics in Three‑Dimensional Topology – More Fundamental and More “Foundational” than the Poincaré Conjecture 1. Standard Formulation of the Sphere Theorem in 3‑Manifolds ...
Projective Generation Theory of Multi-Origin High-Dimensional Geometry and the Ultimate Convergence Principle of Two-Dimensional Figures This chapter establishes the ontological foundation and the ultimate closed-loop structure of the entire theo...
A Physical Intuition Framework: Geometric Fundamentals Governing Quantum Phenomena This text does not seek to replace or negate the computational systems and experimental findings of established quantum mechanics, nor does it claim to have ach...
Energy-Fundamental Spacetime View: The Underlying Logic of Conservation and SymmetryMy spacetime view is grounded in the fundamental reality of physics, rejecting abstract, groundless deduction. It establishes a complete logical chain from essence...
After leaving the factory, Xiaoshuai searched everywhere for a job, but found nothing for more...
The First Love --- Some social news left Wei Ling with a tangled mess of feelings. He couldn't...
The gloom over the Southern Continent plummeted to its lowest point under the cruel backlash of the deadly rat poison. The ultimate poison bait Everett had created was nothing but drinking poison to quench thirst. The rat swarm was nearly wiped o...
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...
Why Do Vortices Pull Objects In? — A Challenge to the Bernoulli Explanation and a Multi-Origin Geometric ModelAbstractBernoulli’s principle is commonly used to explain why vortices draw objects inward, yet it only applies to two‑dimensional ideal ...
The Ultimate Unification of Four Symmetries: Rotational, Fractal, Hierarchical, and Multi‑Origin Coordinate Symmetry
I. Preface This paper proposes a research programme: an attempt to understand all laws of the universe as combin...
As the faint glow of the ionosphere washed over Yan Shifan’s soul, he still clung to the rage and...
"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...
The shadow of the rat plague had spread from the vast pastures to engulf every corner of the Southern Continent.
In just half a month, the rat population, growing at an exponential rate, burst past the boundaries between grasslands and towns. T...
Axiomatic Proof of the Goldbach Conjecture: Based on the ECS Framework (Extremum-Conservation-Symmetry)
Author: Zhang Suhang (Luoyang)
Abstract: The Goldbach Conjecture asserts that every even integer not less than 4 can be expressed as th...
The Meaning of Probability Theory in Multi-Origin High-Dimensional Geometry
In the classical framework of probability theory and single-origin Euclidean geometry, intrinsic randomness serves as the foundational presupposition of the theory. Pro...
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-...
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...
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...
After Mars was written off, God staked all his hopes on Earth. But even after he tweaked...
Numerical Cases and Analysis of Two Basic Navier-Stokes Formulas Author: Zhang Suhang Version 1: Basic Paradigm (ECS + DOG + MlE) boldsymbol{U}^{n+1} =mathop{argmin}{boldsymbol{U}inmathcal{H}} mathcal{E}big(boldsymbol{U},nablaboldsymbol{U}big) ...
Renormalization Group Equations for Quantum Gravity Based on the Discrete Parent GroupAuthor: Suhang Zhang, Luoyang, HenanAbstractThe ultraviolet divergences in quantum gravity originate from the assumption of infinitely differentiable continuo...
The Sea of Paradigms: From Grothendieck to the Dissolution of Problems in a New Geometric Framework
Author: Zhang Suhang Address: Luoyang, Henan, China
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Grothendieck once likened his mathematical method to a "rising tide": n...
Lattice Structure and Matrix Representation in Discrete Order Geometry Author: Zhang Suhang, Luoyang, Henan
Discrete Order Geometry (DOG) takes finite discrete lattice points and order nesting as its ontology, withou...
The Lower Half of Geometry – On the Number-Theoretic Foundation of Complex Structures
Riemann once said: All geometry is the local structure of a manifold. On this cornerstone, he unified the geometric world of the continuous, the smooth, and t...
On September 14, 2015, the LIGO detectors captured gravitational wave signals from the merger of two black holes 1.3 billion light‑years away. This landmark discovery not only verified the final prediction of Einstein’s general theory of relativit...
Dark Matter and Dark EnergyI. Dark MatterDark matter is a special form of matter that exists widely in the universe but cannot be directly observed. It is a key component of cosmic structure.Its most essential characteristic is that it has no elec...
URFE Calculates Celestial Orbits
Author: Zhang Suhang
Combining the Unified Recursive Field Equation (URFE) with scenario-based calculations for different gravitational field strengths, and following the previously defined symb...
Proof that Continuous Lie Groups Are Special Cases of Discrete Groups from a Recursive‑Geometric PerspectiveAuthor: Suhang Zhang(Luoyang, Henan, China)AbstractClassical group theory divides discrete groups and continuous Lie groups into two mutual...