The Sea of Paradigms: From Grothendieck to the Dissolution of Hard Problems in a New Geometric Framework Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract Grothendieck once likened his mathematical method to a "rising tide": instead of ...
DOG Discrete Order Geometry and Hilbert Space: Bidirectional Isomorphism, Limit Correspondence, and Paradigm Bridging Theory
Author: Zhang Suhang, Luoyang
Abstract
Traditional discrete combinatorial geometry and continuous functional a...
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)—...
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 ...
Paradigm Incorporation of the Hodge Conjecture – Natural Dissolution within the MOC‑DOG‑ECS Framework
Author: Zhang Suhang Address: Luoyang, Henan
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The Hodge conjecture is one of the seven Millennium Prize Problems. Tradi...
The Foundational Paradigm of Probability-Geometry Isomorphism: From Gaussian Distribution to General Measure CorrespondenceAuthor: Zhang Suhang, Luoyang, HenanAbstractThe probability density function of Gaussian distribution p(x)=\frac{1}{\sqrt{2\...
--- A Study of Fractal Order and Chaos Emergence Mechanisms Based on Finite-Level Continued Fraction Sequences Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract Fractal geometry and continued fractions belong respectively to the two ma...
Discrete Order Geometry (DOG) Framework for the Geometric Origin of Weak Interactions: From Discrete Chiral Lattice Points to the V–A Current Author: Zhang Suhang(Luoyang, Independent Researcher) Abstract: Based on the four‑dimensional discre...
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 9: The Riemann–Roch Theorem under UPGS — A Geometric Proof Based on the Étale Heat Kernel, MIE Variational Principle, and ECS Conservation Laws
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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...
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...
--- Native Derivation of Yang-Mills Equations within the DOG Framework (Under the Unified Four-Force Paradigm) Author: Zhang SuhangAffiliation: Independent Researcher, Luoyang, Henan --- Abstract Traditional Yang-Mills theory is a field-theor...
DOG Discrete Lattice Unified Four-Force System: Completeness Conclusion for Quantitative Computation
Core Conclusion
The unified four-force mathematical-physical system based on Discrete Order Geome...
DOG Discrete Order Geometry: A Minimal Mathematical Paradigm for Unifying the Four Fundamental Interactions
I. Fundamental Unified Substrate
Let the set of all discrete spacetime lattice points in t...
Discrete Order Geometry (DOG) First‑Principles Derivation of the Dirac Equation: Spinor Order and Relativistic Discrete Evolution
Author: Zhang Suhang (Luoyang, Independent Researcher)
Abstract – Based on the unified discrete evolution p...
Complete Self‑Consistency of Spatial, Evolutionary, and Constraint Triple Curvatures Author: Zhang Suhang(Independent Researcher, Luoyang) System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical‑Physical ParadigmSeries Number: Thirteenth Paper ...
--- Structural Defects of Single‑Origin Complex Analysis and a Proof of Incompatibility with the Riemann Hypothesis Author: Zhang Suhang (Bosley Zhang / Bi Sulin)Research Affiliation: Luoyang Independent ResearcherSystem Affiliation: MOC‑MIE‑ECS...
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...
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...
Unified Theory of the Four Fundamental Interactions under the Discrete Lattice Paradigm of the DOG Universe Author: Zhang Suhang, Luoyang, Henan --- Core Synopsis The entirety of spacetime is fundamentally a giant discrete DOG cosmic lattice. ...
MOC Axiomatic Construction of Multi-Origin Higher-Dimensional Space
Author: Zhang Suhang (Bosley Zhang / Bi Sulin) Research Affiliation: Luoyang Independent Researcher System Affiliation: MOC‑MIE‑ECS‑UCE Unified Mathematical‑Physical Paradigm...
Under the MOC paradigm, the complete analytical equations for the gravitational three-body problem of the Earth, Moon, and Sun. Author: Zhang Suhang (followed by the detailed sections I–IV as in your Chinese text) …Is this acceptable? My res...
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...
Proof of the P vs. NP Problem within the DOG/MOC/ECS/MIE Framework
The P vs. NP problem is a central open question in theoretical computer science, asking whether every prob...
DOG Discrete Order Geometry and Modular Forms: The Recursive Nature of Coefficient Sequences
Modular forms are central objects in number theory and algebraic geometry; their Fo...
Discrete Order Geometry (DOG): Primitive Inclusion and Paradigm Incorporation of Fiber Bundle Theory – A Unified Geometric Architecture with Discrete Connection as the Primordial Source and Smooth Connection as the Continuous Special Case ...
--- On the Essential Identity of Binary and the Law of Excluded Middle and Its Core Significance Abstract This paper aims to clarify the intrinsic relationship between binary (the binary numeral system) and the law of excluded middle (LEM). Bre...
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...