Geometric Recursive Conservation Chain System: Reframing and Extending Classical Group Symmetry Theory
Author: Zhang Suhang, Luoyang, Henan
Abstract
Classical physics established a binding paradigm of continuous symmetry group – Noethe...
So Mighty is the Pull: Reflections on Mechanics
So mighty is the pull, so vast its spirit. For millennia, humanity's quest to understand the forces of the universe has carried this indomitable resolve.
Starting from the sages who came before...
Geometric Progressive Conservation Law and the Complementary Architecture of Noether Theorem — Dual Paradigm Unification of Geometric Origin and Symmetric Origin
Author: Zhang Suhang Affiliation: Luoyang, Henan
---
In class...
--- Geometric Progressive Conservation Chain in Curved Spacetime: Spacetime Curvature and Conservation Transmission Mechanism
Classical general relativity establishes a...
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)...
--- Theoretical Support of Poisson Mechanics for the Geometric Progressive Conservation Law (GPCL)
Author: Zhang Suhang
Affiliation: Luoyang, Henan
Based on the core geometric axiom that "linear motion is equivalent to circul...
--- 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
Under the framework of Multi-Origin...
Paper 13: The Trinity of Frequency, Probability, and Geometric Measure — From Discrete Order Geometry to Étale Schemes
This paper achieves a seamless connection between ...
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
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
...
Paper 8: Étale Random Walks and Arithmetic‑Quantum Unification under the UPGS Framework — Geometric Origins of Prime Distribution, Zeta Functions, and Born’s Rule Author: Zhang SuhangAffiliation: Luoyang, HenanDate: May 25, 2026 --- Abstrac...
Paper 7: Flat Probabilistic Schemes — Migration from Geometric Measure Spaces to Étale Sites
Author: Suhang Zhang, Luoyang, Henan Abstract
Based on the axiomatic system of probability geometry established in previous papers (Paper 1 & P...
Paper 6: The Unification of Algebra, Probability and Geometry: The New UPG Paradigm — History, Framework and Applications Author: Zhang Suhang
This paper is a review and applications paper in...
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 probability-geometry isomorphism frame...
Paper 4: Geometric Reconstruction of Probability Axiom System: Kolmogorov Axioms Equivalent to Geometric Measure Axioms
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
Continuing the probabilistic-geometric isomorphism fr...
--- Paper 1: The Fundamental Paradigm of Probability-Geometry Isomorphism: From Gaussian Distributions to General Measure Correspondences
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...