Logarithmic–Trigonometric Unicity Principle (Caraccioli): Methodology and Exploratory Results

Objective: To empirically test whether precise mathematical re- lationships exist between dimensionless physical constants using a logarithmic–trigonometric scheme. Methodology: We develop a systematic procedure to test identities among fundamental constants, based on CODATA 2022 values. Results: We identify interesting numerical correlations (mean error 2.00 × 10−1 %) for specific combinations. Conclusion: The observed patterns deserve independent scrutiny but do not constitute evidence of an underlying physical law. The study is offered as a starting point for critical discussion.