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Paper 4-1: Extension of the Π Operator to Four-Dimensional and Higher-Dimensional Euclidean Manifolds Author: Suhang Zhang (Heluo Mathematical School) Abstract A complete system of axioms, channels and algebraic structures for the Π...
--- MOC Coordinate System: Geometric Definition of Multi-Origin Hierarchical Nesting and Classical Coordinate Degeneration
Author: Zhang Suhang Founder of the Heluo Mathematical School
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Abstract
Based on the Multi-Origin Curvature...
DOG Discrete Order Geometry and Lattice Theory: Algebraic Representation of Order Structures Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract Lattice theory studies algebraic structures in which any two elements in a partially ordered ...
Discrete Order Geometry (DOG): A New View of Spacetime — Space as Matrix and Time as Fiber Bundle
Author: Zhang Suhang (Luoyang, Independent Researcher)
Abstract: Discrete Order Geometry (DOG) fundamentally reconstructs the picture of...
--- Part III: Subordination Relations, Nesting Rules, and Cross-Layer Mapping Systems for Hierarchical Sets Author: Zhang Suhang, Luoyang, Henan Abstract Building upon the establishment of the hierarchically nested set paradigm and the three-l...
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...
Discrete Order Geometry (DOG) and Classical Fractal Geometry: Paradigm Comparison and Pain Point Resolution
Author: Zhang Suhang Luoyang
Abstract: Classical fractal geometry, with its core assumptions of infinite self‑similarity and ...
Complete Exclusion of All Counterexample Paths at the Curvature Level Author: Zhang Suhang(Independent Researcher, Luoyang) System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical ParadigmSeries Number: Fifteenth Paper --- Abstract ...
A Topological Extremum Solving Method for the Navier-Stokes Equations Based on the boldsymbol{Pi} Projection Operator and the MOC-DOG-ECS-MlE Framework
Author: Zhang Suhang
1. Introduction The Navier-Stokes (NS) equations serve as the cor...
Paper 5-2: Historical Review on the Evolution of π Research: From Euler and Ramanujan to the Formulation of the Π Operator System Author: Suhang Zhang (Heluo School of Mathematics) Abstract The cognitive history of π consists of three ...
Paper E4-4: Generator Relations between Euler’s Formula and the Π-Operator Author: Suhang Zhang (Heluo School of Mathematics) Abstract Euler’s formula e^{i\theta}=\cos\theta+i\sin\theta intrinsically links complex exponentials to circu...
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)—...
Proof of the Twin Prime Conjecture within the DOG/MOC/ECS/MIE Framework
Author: Zhang Suhang Address: Luoyang, Henan
The twin prime conjecture is a century‑old core problem in analytic number theory. Its weak version, 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 Lattice Unified Four-Force System: Completeness Conclusion for Quantitative Computation
Author: Zhang Suhang, Luoyang
Core Conclusion
The unified four-force mathematical-physical system based on Discrete Order Geome...
--- Structural Shortcomings of Traditional Mathematical and Geometric Systems and the Systematic Complementation by the DOG Paradigm Author: Zhang SuhangLuoyang Abstract Modern mathematics, geometry, and celestial mechanics have, over centurie...
Proof that the Critical Line is the Principal Axis of Global Curvature Equilibration
Author: Zhang Suhang (Independent Researcher, Luoyang)
System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical Paradigm Series Number: Eleventh ...
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Paper 3-2: Composite Transformations and the Structure of Dimensional Transformation Group Author: Suhang Zhang (Heluo Mathematical School) Abstract The core function of the \Pi-operator is to perform mapping operations between spac...
Hierarchical Classification, Applicability Boundaries, and Value Analysis of Three Types of Flow Control Formulas under the Navier-Stokes System Author: Zhang Suhang AbstractRegarding the four core equations derived from the Multi-Origin Coordin...
Paper III: Global Unification of the Three Underlying Physical Systems of Mechanics, Geometry, and Energy via ECS Author: Zhang Suhang (Heluo School of Mathematics) AbstractBy integrating the complete set of derivations with newly established me...
Paper 2-1: Dual-Channel Transformation of the Π Operator for Cylindrical Bodies Author: Zhang Suhang (Heluo Mathematical School) Abstract A cylinder is the simplest non-spherical solid of revolution. Its formation intrinsically corr...
--- Part IV: Discrete Origin and Continuous Limit: The Unified Resolution of Binary Forms in the New Set Theory Author: Zhang Suhang, Luoyang, Henan Abstract The binary fragmentation between discrete and continuous is one of the longest-standi...
Paper II: Rigorous Derivation of Symplectic Structure Breakdown (Proof of the Degeneration of the Symplectic Form boldsymbol{omega}) Author: Zhang Suhang (Heluo School of Mathematics) Prerequisite KnowledgeFor a finite-dimensional Hamiltonian sy...
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Discrete Order Geometry (DOG) and Topology: A Preliminary Exploration of the Structured Description of Non‑Connected Spaces
The establishment of Discrete Order Geometry (DOG) removes spatial c...
MOC Higher-Dimensional Complex Space Reconstruction and the Intrinsic Geometric Definition of the Critical Strip Author: Zhang Suhang (Bosley Zhang / Bi Sulin)Research Affiliation: Luoyang Independent ResearcherSystem Affiliation: MOC‑MIE‑ECS‑UCE...
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...
Part Three: Fractal-Coefficient Coupled Evolution —— Synchronous Mapping from Numerical Parameters to Graphical Forms
Author: Zhang Suhang (Luoyang, Henan)
Abstract Based on the analogical framework and axiomatic system establish...
