Numerical Relations Between Fundamental Constants: An Information-Theoretic Approach

We explore numerical relationships between fundamental physical constants using an information-theoretic framework. Starting from the hypothesis that distinguishability may play a foundational role, we derive expressions for various quantities including the fine-structure constant, fermion mass ratios, and mixing matrix elements. The resulting values show close agreement with experimental data across multiple sectors. We present testable predictions for upcoming experiments (DESI, JUNO) that could support or refute this approach. This working paper documents the current state of an ongoing investigation.