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. ...
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...
DOG Discrete Order Geometry and Modular Forms: The Recursive Nature of Coefficient Sequences
Author: Zhang Suhang Address: Luoyang, Henan
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Abstract
Modular forms are central objects in number theory and algebraic geometry; their Fo...
Construction and Physical Implications of Symmetric Multi-Origin Curvature (SMOC) Geometry **Author:** Zhang Suhang *Independent Researcher* **Abstract:** Based on the Multi-Origin Curvature (MOC) spacetime framework, this paper constructs the...
Pure MOC Multi-Origin Framework: A Complete Explanation of Mercury’s Perihelion Precession I. First, pinpoint the common flaw in Newtonian mechanics and general relativity 1. Newtonian systemAssumes the solar system has only the Sun as a single ...
Numerical Validation of the Extremum-Conservation-Symmetry System and a Case Study on Symmetry Group Extension
Author: Suhang Zhang Affiliation: Luoyang, Independent Researcher
This paper systematically conducts numerical...
The Homologous Generation Theory of Mathematical Objects
Author: Zhang Suhang, Luoyang
This paper proposes and systematically establishes the Homologous Generation Theory of Mathematical Objects, revealing the unified essence of ...
The Planckian Homunculus – A Different Kind of Observation If we could shrink ourselves down to the Planck scale – that extreme microscopic world where space is as small as 10^{-35} meters and time as short as 10^{-43} seconds – and become, so to...
URFE Calculates the Hohmann Window
Author: Zhang Suhang
The following directly uses URFE → Newtonian gravity + Keplerian orbits to calculate, without extraneous detail, the launch time and orbital parameters for minimum fuel c...
Proof of the ABC Conjecture within the DOG/MOC/ECS/MIE Framework
The ABC conjecture is a central problem in number theory. Shinichi Mochizuki attempted to prove it using his...
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...
Paper 2-2: Dual Rotation Structure: Π Transformation Rules for TorusAuthor: Suhang Zhang (Heluo Mathematical School)AbstractA torus is a 3D solid formed by rotating a circle (generatrix circle) of radius a around a coplanar non-intersecting axi...
Derivation of the Four Fundamental Interactions from the Unified Recursive Field Equation (URFE)
Abstract: Based on the Unified Recursive Field Equation (URFE), parameter partitioning, group subspace projection, and b...
MOC Embedding Theorem: Embedding Representation of Complex Projective Algebraic Varieties in Multi-Origin Curvature Geometry Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract Traditional complex projective algebraic varieties are built ...
--- Reconstructed Axioms of Set Theory under the MOC Multi-Origin High-Dimensional Framework Within the MOC multi-origin high-dimensional framework, we first establish the top-level paradigmatic axiomatic outline of set theory. The following fiv...
Information Ecological Topology and the MIE Principle: A Reconstruction and Unification of the Foundations of Classical Statistics
Independent Researcher in Mathematics and Theoretical Physics
Core The...
Continuous Extension of the Multi-Origin Curvature Symmetry Group in ECS Theory
Author: Suhang Zhang Affiliation: Luoyang, Independent Private Researcher
This paper establishes the rigorous continuous extension of the dis...
--- Derivation of the Weak Interaction from the MOC Unified Curvature Equation（UCE） Author: Zhang Suhang (Bosley Zhang), Luoyang --- 1. Basic Form of the MOC Unified Curvature Equation (UCE) The starting point of MOC is an action extremal pri...
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...
Newton’s Bucket Experiment The Newton’s bucket experiment is a classic thought experiment described by Isaac Newton in 1689. By observing the shape of the rotating water surface, Newton argued for the existence of absolute space. This experim...
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 ...
--- Mapping–Number Theory Bottom-Layer Unified Explanation Based on Projection, Dynamic Slope, and MOC Curvature Geometry
Author: Zhang Suhang Founder of the Heluo Mathematical School
In traditional mathematics, mapping ...
--- Part Two A Rigorous Global Proof of the Kakeya Conjecture via DOG-MOC Author: Zhang Suhang (Bosley Zhang) Location: Luoyang, Henan, China Date: May 2026 Abstract This paper, based on the self-developed Discrete Order Geometry (DOG) cov...
First-Principles Derivation of the Schrödinger Equation via Discrete Order Geometry (DOG): From Discrete Recursion to Continuous Wave Mechanics Author: Zhang Suhang Independent Researcher, Luoyang Abstract Based on the matrix evolu...
Theorem of the Optimal Dynamic Path of Zero Motion Author: Zhang Suhang (Independent Researcher, Luoyang)System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical‑Physical ParadigmSeries Number: Paper No. 6 --- Abstract Based on the previously ...
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...
Dynamics and Multi-Origin High-Dimensional Geometry Classical dynamics, based on a single-origin flat coordinate system, describes motion with all forces, displacements, and rotations normalized to a single coordinate reference. Motion evolution ...
The Time Perspective of the Planck Tiny ManThe Planck Tiny Man is tiny not only in spatial scale but also in temporal scale, operating at 10⁻⁴³ seconds. At this scale, “quantum superposition” vanishes from its view: an electron does not pass throu...
Paper 2-3: Periodic Micro-element Channel: Operator Implementation of Helical Curves and Helical Surfaces Author: Suhang Zhang (Heluo Mathematical School) Abstract Helical structures are among the most ubiquitous periodic forms in n...
--- Transcendental Continued Fraction Embedding and Multi-Origin Completion: The Grand Unified Framework of FCFG Fractal-Continued-Fraction Geometry Author: Zhang Suhang (Bosley Zhang) System Affiliation: FCFG Fractal-Continued-Fraction Geometr...