--- Complete Proof of the Gilbert-Pollak Conjecture Based on the MOC-DOG-MIE-ECS Native Framework Author: Zhang Suhang, Luoyang, Henan --- Abstract The Gilbert-Pollak conjecture is a core classical problem in planar extremal geometry. Traditi...
--- 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...
Dynamical Substrate of FCFG: Continued-Fraction Expansions of Complex Exponentials and Spin-Fractal Recursive IsomorphismAuthor: Zhang SuhangCore Axiomatic Support: FCFG Recursive Isomorphism Axiom (r_n = S_n); Multi-Origin Curvature (MOC) Framewo...
On the Central Position of Geometry in Mathematics
For a long time, many people merely regard mathematics as a tool for calculation and problem-solving, which greatly narrows its true meaning. Mathematics is essentially an organic and vibran...
--- 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...
--- Part One Title: The Geometric Foundation and Model Transformation of the Kakeya Conjecture via DOG-MOC
Author: Zhang Suhang (Bosley Zhang) Location: Luoyang, Henan, China Date: May 2026
Abstract
Under the framework of Multi-Origin...
Frequency, Probability and Geometric Measure: A Trinity Author: Zhang SuhangAffiliation: Luoyang, HenanAbstractThis paper establishes the connection between Discrete Order Geometry and flat schemes, thereby bridging the logical and mathematica...
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, ...
Paper 11: Computation on UPGS — Algorithms, Complexity, and Numerical Implementation
Author: Zhang Suhang Affiliation: Luoyang, Henan Date: May 25, 2026
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UPGS (Étale Probability Schemes), as a unified theoretical frame...
Paper 10: The Weil Conjectures under UPGS — Étale Random Walks, Curvature Duality, and ECS Stability
Within the UPGS (Étale Probability Schemes) fram...
Paper 9: The Riemann–Roch Theorem under UPGS — A Geometric Proof Based on the Étale Heat Kernel, MIE Variational Principle, and ECS Conservation Laws
...
UPGS: A Preliminary FrameworkUPGS: Extending and Interfacing the UPG Framework with Scheme Theory Author: Zhang SuhangAffiliation: Luoyang, Henan --- Abstract This paper establishes an interface between UPG and scheme theory, embedding the pro...
Applications of the UPG Framework: Central Limit Theorem, Statistical Inference, Machine Learning and Quantum Physics Author: Zhang Suhang Affiliation: Luoyang, Henan Abstract This paper serves as an application article for the Unifie...
Paper 6: Dynamic Midpoint Extremum Theorem: The Dynamic Tripartite Unification of Probability–Geometry–Algebra (UPG) Author: Zhang Suhang Affiliation: Luoyang, Henan Abstract This paper establishes the Dynamic Midpoint Extremum Theore...
For the longest time, I honestly thought all volleyball nets were basically the same. As long as the ball could go over and the poles stayed upright, I figured that was enough. A few months ago, my friends and I started playing more regularly on ...
Paper 5: Stochastic Processes and Geometric Flows: From Random Walks to Brownian Motion and Quantum Probability Author: Zhang Suhang Affiliation: Luoyang, Henan Abstract This paper extends the tripartite unifying framework of probabil...
Paper 4: Geometric Reconstruction of Probability Axiom System: Kolmogorov Axioms Equivalent to Geometric Measure Axioms
Author: Zhang Suhang Affiliation: Luoyang, Henan
This paper accomplishes a landmark unification between pr...
Paper 3：Geometric Embedding of Multivariate Random Variables: A Unified Triple Operation of Joint Distribution, Marginalization, and Conditioning Author: Zhang Suhang Affiliation: Luoyang, Henan, China Abstract Building upon the algebraic-prob...
Paper 2: Geometric Realizations of One-Dimensional Probability Distributions: Bell Curve, Staircase, Lattice, and Fractal
Author: Zhang Suhang
Affiliation: Luoyang, Henan
Continuing the probabilistic-geometric isomorphism fr...
--- Paper 1: The Fundamental Paradigm of Probability-Geometry Isomorphism: From Gaussian Distributions to General Measure Correspondences
Author: Zhang Suhang, Luoyang, Henan
The probability density function of the Gaussian dist...
Scientific Implications of Frequency Difference Determining Probability: God Does Not Play Dice This conclusion settles the long-standing debate between Bohr and Einstein. If we follow Bohr’s standpoint, the universe would descend into chaos. ...
Frequency Difference Determines Probability: Geometric Proof of God Does Not Play Dice from the Perspective of Discrete Order Geometry Author: Zhang Suhang Address: Luoyang, Henan, China Abstract The intrinsic randomness of probabi...
Preliminary Exploration of the Fusion Configuration as a Concrete Prototype of Fiber Bundles Author: Zhang Suhang, Luoyang, Henan
--- Abstract Based on previous research results on spherical cap‑derived self‑similar geometry (SCD‑SG), thi...
Spherical-Cap Derived Self-Similar Geometry (SCD-SG): A New Natural Finite-Level Spherical Composite Solid Geometry Author: Zhang Suhang, Luoyang, Henan Abstract Nature abounds with three-dimensional composite configurations featuri...
Application Chapter —— Grounded Mapping of the Three‑Layer Number‑Theoretic Structure in Computing and Engineering
Author: Zhang Suhang (Luoyang, Henan)
Abstract Based on the three‑layer structure of “prime primitive – regular co...
Part Three: Fractal-Coefficient Coupled Evolution —— Synchronous Mapping from Numerical Parameters to Graphical Forms
Abstract Based on the analogical framework and axiomatic system establish...
Part Two: Axioms and Mathematical Formulas —— Formal Foundations of the Composite Number Construction System
Abstract Based on the analogical framework of “primes–composites” and “fractal pri...
Part One: Analogical Foundation in Number Theory —— The Fractal Generation Logic of Composite Numbers
Abstract Starting from the constructive processes of number theory and fractal geometry, this paper ...
Frequency Difference Determines Probability Distribution: Empirical Verification Based on Multi‑Country Academic Dissemination Data Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract The core proposition of Discrete Order Geometry (DOG)—...
Curvature-Driven Fluid Equation Verification via Discrete Order Geometry: A Numerical Case Study
Author: Zhang Suhang (Independent Researcher, Luoyang, Henan)
Within the Multi-Origin Curvature (MOC) framework, the stea...