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...
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...
"The Golden Ratio, Fibonacci Numbers, and Euler’s Polyhedron Formula Under the Maximum Information Efficiency Axiom: Hierarchy, Association, and a Unified Perspective" Author: Zhang Suhang, Luoyang Core Axiom: Maximum Information Efficiency (M...
"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...
Derivation of Euler’s Formula from the Maximum Information Efficiency (MIE) Axiom Prerequisites · Consider a connected planar graph (nodes and edges without crossings). It may be the edge graph of a convex polyhedron, a leaf vein network, an e...
Unified Theory of Two Classes of Self-Similar Fractals Based on Continued Fraction Recursive Isomorphism Author: Zhang Suhang --- Abstract Classical fractal geometry has long maintained a division between two classes of self-similar geometric ...
Geometric Origin of Weak Interactions: From Curvature Frequency Transitions to a Unified Framework Author: Zhang Suhang, Luoyang Abstract Based on the previously established MOC-MIE axiomatic system and the equivalence relation between...
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...
--- 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...
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...
Unified Derivation of Inverse-Square Interactions under the Geometric Extremum Principle（GEP）
Abstract
Based on the Geometric Extremum Principle, this paper takes spatial curvature as the core fundamental field quantity and combines the Maxi...
Paper: Foundational Axioms and Isomorphism System of Fractal Continued-Fraction Geometry (FCFG)
In the existing mathematical framework, continued fractions belong to the domains of number theory and analytic approximation, while sel...
Unification of Honeycomb and Leaf Vein under the Axiom of Maximum Information EfficiencyAuthor: Suhang Zhang AbstractThe honeycomb uses the least beeswax to enclose the maximum volume. Leaf veins use a limited network of vessels to cover the maxim...
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 the...
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 framewo...
Unified Geometric Extremal Physics（UGEP）
Solution to the Plateau Problem under the Unified Geometric Extremal Physics （UGEP）Framework
— Physical Restatement, Paradigm Reduction, and Its Isomorphism with the Isoperimetric Problem and the Poin...
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 Abstract T...
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...
MOC 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 su...
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...
MOC (Multi-Origin Curvature) 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 elaborate on de...