Database Theory Papers

A collection of research papers exploring advanced topics in database theory, including:

• Topos Theory applied to database design
• Functional query programming languages
• Cross-paradigm integration for key/value, relational, vector, and graph storage
• Insights from the Langlands program in database architecture
• Universal algebra and its implications for data models and query optimization

Table of Contents

• Overview
• Purpose
• Research Topics
• Contributing
• Acknowledgments
• License

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Overview

This repository serves as a hub for groundbreaking research in database theory. By combining mathematical rigor with practical applications, these papers aim to push the boundaries of how databases are designed, queried, and integrated across various paradigms.

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Purpose

The goal of this repository is to:

• Provide a centralized collection of detailed, peer-reviewed papers.
• Encourage collaboration and open discussions in database research.
• Explore interdisciplinary approaches, leveraging advanced mathematics such as Topos Theory, category theory, and automorphic forms.

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Research Topics

1. Topos Theory in Database Design

   • Universal abstractions for schema and query models.
   • Sheaf-theoretic representations for multi-model data integration.

2. Functional Query Programming Languages

   • Category-theoretic formulations for composable and type-safe queries.
   • Natural transformations for optimization and schema evolution.

3. Cross-Model Data Bridges

   • A universal layer connecting key/value, vector, relational, and graph databases.
   • Adjunctions and functorial mappings for seamless interoperability.

4. Langlands Program and Database Architecture

   • Schema transformations as Galois actions.
   • Query invariants inspired by automorphic forms.

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Contributing

We welcome contributions from mathematicians, engineers, and database researchers. Please follow these steps to contribute:

1. Fork this repository.
2. Clone the repository to your local machine.
3. Create a new branch for your paper or edits.
4. Commit your changes and push them to your branch.
5. Open a pull request with a detailed description.

For detailed contribution guidelines, see the CONTRIBUTING.md file.

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Acknowledgments

Special thanks to the contributors and reviewers who help advance the field of database theory. This project draws inspiration from foundational works in category theory, functional programming, and algebraic geometry.

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License

This repository is licensed under the MIT License. See the LICENSE file for more details.