Algorithmic Compressibility of Dimensionless Physical Constants Under Bounded Symbolic Grammars: A Negative Empirical Study

We investigate whether dimensionless physical constants exhibit statistically enhanced compressibility under bounded symbolic grammars, compared to random numbers and mathematical constants. We define a formal grammar G of free syntax trees over the set of constants {π, e, φ, √2, √3, √5}, rational coefficients bounded in [-50,50], standard arithmetic operations, and maximum depth d=3. For each target constant, we generate N=5,000,000 random expressions and measure the minimum symbolic complexity S_min of any expression matching within one experimental standard deviation. We test 15 dimensionless physical constants, 4 mathematical constants, and 40 random control numbers. A Mann-Whitney U test comparing S_min distributions between physical constants and random controls yields p=0.2754, failing to reject the null hypothesis at the 0.01 significance level. This negative result is presented as a reproducible benchmark for future studies employing deeper grammars or alternative complexity metrics. This deposit contains both the article (PDF) and the accompanying Python code used to generate the results. This deposit contains both the article (PDF) and the accompanying Python code used to generate the results. The code (compressibility_v2.py) implements the symbolic grammar study with fixed parameters:- Seed: 42- N: 5,000,000 trees per target- Depth: 3- S_INF: 1000.0- 15 physical constants, 4 mathematical constants, 40 random controls Requirements: numpy, scipy, matplotlib Results: Mann-Whitney U test p = 0.2754 (physical vs random), no significant difference found. The JSON file contains all raw data including S_min values, match counts, and statistical tests.