The Prime Reduction Theorem: Toward an Axiomatic Framework Related to Hilbert's Sixth Problem

This work introduces the Prime Reduction Theorem and proposes a structured mathematical framework aimed at contributing to the axiomatization of physical theories, in the spirit of Hilbert’s Sixth Problem.

We develop a formal system that connects discrete mathematical structures with continuous physical models, with emphasis on reduction principles that relate complex systems to fundamental components. The theorem establishes conditions under which such reductions preserve structural and analytical properties.

The paper provides:
- A set of axioms defining the framework
- Formal statements and proofs of the Prime Reduction Theorem
- Conceptual connections to kinetic theory and continuum descriptions
- Discussion of implications for the mathematical foundations of physics

This work is intended as a theoretical contribution and does not claim a complete resolution of Hilbert’s Sixth Problem, but rather presents a direction for further formal development and validation.

All results are presented with full mathematical rigor and are open for verification, critique, and extension by the research community.