Multi-Origin High-Dimensional Geometric Neural Networks All current neural networks are fundamentally locked into two-dimensional planes, a single origin, and matrix tiling operations. No matter how large or deep the models become, they merely st...
The Essential Meaning of Sets in the Multi-Origin High-Dimensional SystemIn traditional Euclidean geometry and classical set theory, a set is merely a container for points and elements, attached to a single global origin. All coordinates, metrics,...
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...
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...
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...
Core Applications of MOC Multi-Origin High-Dimensional Geometry in Giant Satellite Constellation Networking 1. Pain Points and Root Causes Low-Earth orbit (LEO) giant constellations (Starlink, China Starnet, etc.) face three rigid constrai...
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 ...
Wavelet Transform = Projection of MOC under Scale Shrinkage + Local Origin Keep the same style as before, while marking heuristic steps. --- 1. Intuitive Correspondence · Fourier: single origin + no scale + flat space· Wavelet: single origin...
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...
Geometric Origin of the Weak Interaction: From Curvature-Frequency Transitions to a Unified FrameworkAuthor: Suhang ZhangLuoyang, ChinaAbstractBased on the author’s previously established MOC-MIE axiomatic system and the equivalence relation betwe...
--- Unified Derivation of Inverse-Square Interactions under the Geometric Extremum Principle (GEP) Framework Abstract Based on the Geometric Extremum Principle (GEP) and taking spatial curvature as the fundamental field variable, this paper, to...
Matrices handle multivariate problems.Group theory solves higher-order equations.
2. Change Formula\dot\kappa_I = \mathcal F_I(\dots)One sentence:How things change, move, and are acted upon by forces is entirely determined by their interactions.- Universal Gravitation Formula- Coulomb's Law- Ohm's Law I=U/R- Kinematic equations...
1. Rule Formula (规矩公式) \mathcal{D}\star\mathcal{R}=0 One sentence:Things do not disappear out of nowhere; total quantities are conserved, and nothing behaves arbitrarily.- Energy Conservation能量守恒- Charge Conservation电荷守恒- Momentum Conservation动量...
Multi-Origin Curvature Fractal Topology with Continuous Dimensional Transition A Pure Mathematical Study on Structure-Preserving Morphing Between High-Dimensional and Low-Dimensional Fractals Abstract This paper establishes a unified m...
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 ...
Force as Potential Difference: A Theorem in Geometric Extremum Physics Abstract Based on the framework of Multiple-Origin Curvature (MOC) and the axiom of Maximum Information Efficiency (MIE), this paper rigorously proves that physical intera...
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...
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...
"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...
Mathematical Innovation Abstract(Purely Mathematical Formulation, Directly Usable in Academic Papers)This paper introduces a new class of fractal geometric transformations: continuous dimensional gradient transformations from three-dimensional spa...
--- Force as Potential Gradient: A Universal Theorem in Geometric Extremum Physics and a Unified Framework for Conservative Interactions (Revised Edition)
Abstract Based on the Multi-Origin Curvature (MOC) axiom of spatial description and the...
Information Ecological Topology2D Information Reception and 3D Material Absorption in Trees: Inverse Coupling under the Maximum Information Efficiency AxiomAuthor: Suhang ZhangLuoyang AbstractBased on Axiom III of Geometric Field Theory—the Maximu...
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 ...
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...
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...
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...
Numbers are dancing points.Functions are floating lines.Geometry is manifolds and fluids.
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...
Geometric Equivalence of Frequency Gradient and Force: Extension of the MOC-MIE Axiomatic System and Implications for Unification of Weak InteractionAuthor: Suhang ZhangLuoyangAbstractBased on the author’s previously established axiomatic system o...