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...
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...
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...
Paper 12: Étale Differential Equations on UPGS — Continuum Limit of Random Walks and Heat Kernel, with Derivation of the Schrödinger Equation Author: Zhang SuhangAffiliation: Luoyang, HenanDate: May 25, 2026 --- Abstract In Papers 7 and 8, ...
DOG Discrete Lattice Unified Four-Force System: Completeness Conclusion for Quantitative Computation
Author: Zhang Suhang, Luoyang
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Core Conclusion
The unified four-force mathematical-physical system based on Discrete Order Geome...
--- Structural Shortcomings of Traditional Mathematical and Geometric Systems and the Systematic Complementation by the DOG Paradigm Author: Zhang SuhangLuoyang Abstract Modern mathematics, geometry, and celestial mechanics have, over centurie...
--- Theoretical Support of Poisson Mechanics for the Geometric Progressive Conservation Law (GPCL)
Author: Zhang Suhang
Affiliation: Luoyang, Henan
Abstract
Based on the core geometric axiom that "linear motion is equivalent to circul...
The Complete Closed Proof of the Riemann Hypothesis (UCE Coordinated Version) Author: Zhang Suhang(Independent Researcher, Luoyang) System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical ParadigmSeries Number: Fourteenth Paper --- A...
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...
For years, I’ve been curious about why root crops like sweet potatoes and potatoes are so productive and grow so large. At first, I thought it was simply because they grow underground, sheltered from wind and rain, allowing them to expand freely. ...
MOC Differential Geometry (Multiple Origins with Higher Dimensions) Axiom 1 — Hierarchical Multiple Origins Axiom Space contains hierarchically nested origins, such as the Galactic origin, the Solar origin, and the Earth origin. Each origin is i...
--- Conclusion: Low-Energy Approximation in the DOG System Simultaneously Conforms to the MIE Extremum Criterion and the ECS Symmetric Equilibrium Steady State — A Triple Self-Consistent Closed Loop Author: Zhang Suhang, Luoyang, Henan --- I. ...
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...
A Physical Proof of the Isoperimetric Problem —— On the Isomorphism with the Method for the Poincaré Conjecture Abstract This paper presents a complete proof strategy for the isoperimetric problem: by introducing the potential energy E = ...
The constant rush of travel left Wei Ling exhausted yet fulfilled. He had no desire to...
Lorentz Covariant Extension of the Geometric Progressive Conservation Law: Unification of Classical and Relativistic Conservation Author: Zhang SuhangAffiliation: Luoyang, Henan --- Abstract The Geometric Progressive Conservation Law (GPCL)...
Part Three: Fractal-Coefficient Coupled Evolution —— Synchronous Mapping from Numerical Parameters to Graphical Forms
Author: Zhang Suhang (Luoyang, Henan)
Abstract Based on the analogical framework and axiomatic system establish...
Here is the English translation of the MOC Five Axioms, rendered in a style suitable for a formal manifesto or a Meditations on Science equivalent. --- MOC: Multi-Origin High-Dimensional Geometry · Five Axioms Axiom I: Set Defines Domain The f...
Multi-Origin High-Dimensional Geometry and the Chip Revolution: From the Two-Dimensional Dead End to One-Stroke High-Dimensional ConnectivityAll core bottlenecks of modern chips—routing congestion, signal interference, heat concentration, timing d...
Paper 3-3: Ramanujan's Series for 1/\pi and Higher-Order Periodic Channels of the \Pi Operator
Author: Zhang Suhang (Luoyang School of Mathematics）
Ramanujan derived numerous elegant and rapidly convergent series for 1/\pi, wh...
Axiom of Maximum Information Efficiency (II): Derivation of Conservation Laws and Symmetries
Abstract: Noether's theorem reveals the one-to-one correspondence between continuous symmetries and conservation laws, forming a cornerstone of theoret...
Numbers are dancing points.Functions are floating lines.Geometry is manifolds and fluids.
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 Pacific Ocean is a gift from God. The circular motion of ocean currents, combined with the rotation of the Earth, produces two superimposed centrifugal effects. Together they create exactly the same phenomenon as Newton’s bucket experiment. ...
Paper E4-4: Generator Relations between Euler’s Formula and the Π-Operator
Author: Suhang Zhang (Luoyang School of Mathematics）
Euler’s formula e^{i\theta}=\cos\theta+i\sin\theta intrinsically links complex exponentials to circu...
--- Resolution of the Barber Paradox within the MOC (Multi-Origin Curvature) Geometric Framework
The Barber paradox (a popular version of Russell's paradox) reveals the logical contradiction arising from "se...
Chapter 5 The Emergence of Binary: Symbolization of the Law of Excluded Middle — Binary is the minimal symbol set of the law of excluded middle, and numeral systems are counting modes after projection Author: Zhang Suhang (Luoyang, Hena...
Pure Theoretical Derivation of the Coupling Perturbation Term \delta\vec{K}_{ij} and Three-Body Closure Proof in the MOC System
Author: Zhang Suhang Affiliation: Independent Researcher (Luoyang)
Based on the three ...
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...
Paper 1-1: Core Definition and Symbol System of the \mathcal{\Pi} Operator
Author: Zhang Suhang Founder of the Luoyang School of Mathematics
As one of the most vital constants in the history of mathematics, \pi has long been c...