Unified Geometric Extremal Physics Framework Solution to the Willmore Problem
— Physical Restatement, Paradigm Reduction, and Isomorphism with the Isoperimetric Problem, Plateau’s Problem, and the Poincaré Conjecture
Abstract Within the fra...
A Gentle Discussion on the Higgs Field and the Origin of Mass In popular science, the way the Higgs boson gives elementary particles their mass is often compared to a celebrity moving slowly through a crowd of fans. This analogy is vivid and e...
Applications of MOC Multi-Origin High-Dimensional Geometry in Earth–Moon Satellite Networking1. Pain PointsAt a distance of 380,000 kilometers, the Earth–Moon system contains multiple gravitational centers, including the Earth, the Moon, and the L...
All Functions Return to Elliptic Functions I. Proposition Within the unifying worldview that "geometry is the mapping of reality, ultimately culminating in number theory," the world of functions also has its ultimate destination: All functions ...
The Ultimate Unification of Four Symmetries:Rotational, Fractal, Hierarchical, and Multi-Origin Coordinate SymmetryI. Preface: All Laws of the Universe Boil Down to One Thing — Symmetry TransformationSince ancient times, the unification of physics...
The charge energy equation is derived from the law of conservation of energy, based on the annihilation of an electron and a positron into two photons. E = Kq，K=5.1×10⁵ J/C.
Charge also curves spacetime According to general relativity, gravity arises from the curvature of spacetime, and spacetime curvature is caused by mass. Similarly, I argue that electric charge curves the spacetime around it, and this curved ...
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...
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...
Dimensionality Reduction as Flow Allocation: The Engineering Essence of Point Set Flattening Within the framework of Multiple Origin Curvature (MOC), the continuous transition from three dimensions to two dimensions is essentially both a progr...
On Innovation Capacity and the Ineliminability of Process Some people imagine: using gene editing to create a child, then inputting Einstein’s consciousness into that child, and the child will become Einstein. This fantasy overlooks a most funda...
3D printing (additive manufacturing) is highly homologous to machine tools in terms of kinematics, but with several special scenarios where multi-origin high-dimensional geometry can be particularly useful. --- 1. The kinematic chain of 3D pri...
Brain waves can be rigorously decomposed using Fourier analysis, and consciousness can be mathematically described as the combinatorial coding of these primitive waves. This is not only valid but also cutting-edge in science. Let me explain ...
Conservation Laws Corresponding to the Four Fundamental Forces1. Strong Interaction- Corresponding conservation laws:- Color charge conservation- Baryon number conservation- Isospin conservation (under high-energy approximations)- Conservation of ...
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...
The Ultimate Position of Functional Analysis in MOC Traditional Functional Analysis: Function → Infinite-dimensional vector space → Operator → Norm → Weak convergence → Hilbert space Everything is built upon: a single origin, a global linear ...
Core Innovations & Complete DerivationEnglish Version0. Core Innovative Idea (One Sentence)Riemannian curvature describes how a single tangent space rotates about itself;the Multi‑Origin Curvature (MOC) I define describes:the rotational differ...
Multi-origin high-dimensional geometry is almost a coordinate description framework tailor-made for robotics (especially serial manipulators and mobile robots). In simple terms: a robot is a mobile, nestable "multi-origin system". 1. The esse...
Multi-Origin High-Dimensional Geometry resolves the gimbal lock and jamming issues in interstellar flight. Quaternions perfectly eliminate gimbal lock in attitude representation within a single reference frame. Multi-Origin High-Dimensional Geom...
1. Strong Interaction - Symmetry Group: SU(3) The gauge group of color charge, and the...
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...
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...
Formal Paradigm of Unified Geometric Extremal Physics 1. Abstract Definition of the Paradigm Definition (Unified Geometric Extremal Paradigm) A geometric extremal problem is said to admit a unified physical–geometric paradigm if there ...
Laplace Transform = Projection of MOC under "Half-Line Manifold + Complex Wave Number + Single Origin"1. Intuitive Correspondence- Fourier Transform: Euclidean manifold \mathbb{R}, real wave number k → oscillatory kernel e^{-ikx}.- Laplace Transfo...
MOC Multi-Origin High-Dimensional Geometry: Permutation and Combination – Rigorous Definitions, Five Fundamental Axioms, Core Formula System I. Core Rigorous Definitions (Pure Mathematics, No Embellishments) Definition 1: Multi-Origin Reference ...
One-Stroke Drawing Is Inevitably Valid Under the Multi-Origin High-Dimensional Framework I. Why Is One-Stroke Drawing Possible in High Dimensions? High-dimensional space provides extra degrees of freedom to bypass low-dimensional obstacles...
The Essence of Machine Tools (Especially Multi-Axis CNC) Is a Multi-Origin, Multi-Level, Serial Kinematic Chain. Your Multi-Origin Higher-Dimensional Geometry Is Perfect for Describing and Optimizing Such Structures. --- 1. The Kinematic Chain o...
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...
Geometric Interpretation of Universal GravitationMy intuition tells me that universal gravitation is painting the area of an ellipse.1. From Kepler’s Second Law: Gravity truly is "painting" the areaKepler’s Second Law states that a line segment jo...