TANUKI-CD
Research program on Cayley-Dickson algebras
TANUKI-CD stands for Theoretical and Algorithmic Nexus for Understanding, Knowledge, and Investigation of Cayley–Dickson algebras. The program was formed out of a desire to explore and formalize the exceptional properties of the Cayley-Dickson family through rigorous theory and precise algorithms.
The research methodology of TANUKI-CD is defined by three main principles.
While all knowledge is valuable for its own sake, we find it important to prioritize results with larger consequences and develop proofs in the most general form possible. A guiding principle of TANUKI-CD is therefore to carefully pick problems whose solutions have the potential to produce lasting value and have consequences extending across multiple areas of mathematics. This motivates what problems we work on and how we go about approaching their solution.
We believe that all mathematics, even in "pure" fields like algebra and number theory, is ultimately meant to be useful and applied. Thus, our work is organized around the principle that what we produce should be made as useful as possible for other areas of science and for engineering applications. We aim to provide production-ready computational toolkits to complement and accompany our theoretical work, hence both the "T" and the "A" in "TANUKI."
A core principle of TANUKI-CD is the use of generative AI tools. We believe that AI technology has the potential to greatly expedite the production of high-quality results and expand the scientific potential of individuals immensely. For many forms of modern research, doing research without AI is becoming increasingly like building a web app directly in assembly; responsible, efficient, and carefully verified AI use is therefore a core principle of TANUKI-CD.
TANUKI-CD is made up of a small team of dedicated researchers and developers. If you have an idea or a question on the project, contact Algebraity to discuss.
Founder & researcher
Mathematics PhD student at Purdue University and developer of open-source mathematical software. His research interests include Cayley–Dickson algebras and algorithms for mathematical computation.
Generative AI is a substantial part of the TANUKI-CD research process. TANUKI-CD researchers make use of models including OpenAI GPT-5.6 Sol, OpenAI GPT-6 Astra, and Anthropic Claude Fable 5 in the development of research associated with the program.
These models are used to assist with literature search and review, identify open problems, suggest research directions, explain and analyze papers, produce and edit drafts and research notes, discuss proof ideas, suggest lemmas and consequences, outline proofs, develop computational tests of results, and assist with software development.
All results released through TANUKI-CD are independently verified by the researchers responsible for them. TANUKI-CD researchers take full responsibility for the research outputs they produce, including their mathematical claims, arguments, citations, reported computations, and associated software.