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 ...
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 ...
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 Physical Solution to the Plateau Problem Under the Same Paradigm Author: Suhang ZhangLuoyang Abstract (brief)
By treating the surface area as a potential energy functional and applying the minimum energy principle, we show that the solu...
Numbers are dancing points.Functions are floating lines.Geometry is manifolds and fluids.
Matrices handle multivariate problems.Group theory solves higher-order equations. Higher-degree equations are shaped by curves swaying back and forth.Sway more intensely, and you get surfaces.Sway even more wildly, and you get solids. Orderly sw...
Generalized Upgrade of the Turing Computation Model: A Dimension-Ascension and Dimension-Reduction Dual Framework from One-Dimensional Sequential Computation to Multi-Dimensional Topological Parallel Computation Author: Zhang Suhang (Heluo School...
Structural Information Theory: The Dual-Layer Complementary Foundational Framework of Dimension-Preserving Topological Transport and Shannon Information Theory Author: Zhang Suhang (Heluo School of Mathematics) Abstract Shannon information theo...
Dimensionality Reduction Equals Flow Redistribution: The Engineering Essence of Point Set PlanarizationI. Engineering Essence of Dimensionality Reduction Transformation1.1 Engineering Mechanism of Topological Evolution in Dimensionality ReductionW...
The Topological Essence and Engineering Substance of Dimensional Ascent: Flux Expansion, Planar Point Spatialization, and the Maximum Information Efficiency Axiom from 2D to 3D
Author: Zhang Suhang
Core Axiomatic Support: Multi-Origin Curvat...
Information Topology: Theory of Reciprocal Topological Information Conservation Between High and Low Dimensions
Author: Zhang Suhang --- Abstract
Traditional geometry, fractal theory, and dimensionality reduction paradigms have long suffer...
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...
Bionic Fractal Topology for Wireless Power Transfer: A Technical Scheme of Stereo-to-Stereo Coupling and Dimensionality-Reduced DistributionAbstractAiming at the problems of difficult coil alignment, narrow spatial coverage, and low efficiency of ...
All Two-Dimensional Figures Ultimately Reduce to the Ellipse: A Universal Ontological Argument Based on Multi-Origin Geometry and High-Dimensional Fiber Bundles Abstract Traditional unified theories of planar geometry can only establish the prim...
Imaginary numbers represent direction. Rotation changes direction. Translation changes position. Ellipses and hyperbolas differ only in real versus imaginary directions. They are fundamentally unified. People have long treated the ellipse,...
Wireless Power Transmission: Perhaps the True Future of MOSTraditional power grids are wired, fixed-point, and unidirectional by nature. In essence, they force energy into one-dimensional transmission lines, resulting in high energy loss, vulnerab...
MOS (Multi-Origin High-Dimensional Geometry) Power Grid Design — Reconstructing the Spatial Philosophy and Design Paradigm of Power Grids, Breaking Free from the Rigid Path of “High-Voltage Dependence” --- 【Epigraph】This paper does not elaborat...
Mass Is Not Absolute: A Brief Reflection on Fields and Mass For a long time, people have regarded mass as an innate, fixed property of matter, as if it could exist absolutely, independent of its surroundings. But with deeper understanding of t...
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...
Multi-Origin Curvature (MOC): A Geometric Interpretation of Mass Transfer and Thermo-Hydrodynamic Coupling in Packed Towers — Three Longstanding Engineering Pain Points Abstract The mass transfer and reaction thermal effects in packed tow...
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 ...
Unified Geometric Axiom of Rectilinear and Circulating FlowAxiomatic StatementUnified Flow Axiom: For any steady or asymptotically stable flow, its trajectory satisfies the following in a local coordinate system:(i) Normal Boundedness – Displaceme...
Axiom 1 (Tangential Convergence)Fluid tangential motion is necessarily smooth, stable, and convergent.Axiom 2 (Normal Boundedness)Although fluid normal disturbances are disorderly, their intensity remains finite and bounded at all times. Correspon...
The Unification of Geometry, Function, and Number Theory under the MOC Framework
In traditional mathematics, geometry, function, and number theory stand as separate branches, connected by the function as a mapping between geometric forms and ar...
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...
The Core Logic of the Universe’s Eternal Motion Ultimate Minimal Axiom Force arises from potential difference.Parity is intrinsically broken.Potential difference never vanishes.Therefore, the world moves eternally. --- Layered Philosophical Ex...
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...
MOC: A Unified Curvature Framework with Multiple Origins as a Generalization of Hilbert Space Abstract The Hilbert space has long served as the foundational mathematical structure for harmonic analysis, functional analysis, signal processi...
Gabor Transform = Projection of MOC under "Fixed Scale + Gaussian Window + Single Origin" 1. Intuitive Correspondence - Fourier Transform: Global kernel e^{-i\omega t}, no localization. - Gabor Transform: Fourier kernel with a Gaussian wi...
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...