Abstract
We describe DAEDALUS (Dimensional Analysis Engine for Discovering Algebraic Links in Underlying Symmetries), a systematic computational tool for searching for polynomial relations among fundamental physical constants. The engine enumerates all dimensionless combinations of a given set of constants and tests them against a dictionary of target values. We identify a fundamental obstacle — the saturation problem — in which naive dimensional analysis produces hundreds of thousands of apparent “coincidences” that are statistically inevitable rather than physically meaningful. To address this, we introduce a two-level filter: (1) a numerical filter that restricts the search to physically privileged targets and limits the number of constants per relation, and (2) a structural filter that requires surviving candidates to have integer exponents, physical sign structure, and standard prefactors consistent with quantum field theory. Applied to a 17-constant database spanning electromagnetism, gravity, and particle physics, the engine produces 307,900 raw hits but only 0–3 privileged-target hits per 7-constant subset after filtering.
A Monte Carlo permutation test (100 trials with scrambled values) yields a 27% false-positive rate for any structural survivor but only 1% for the specific QFT-coherent form of the published cosmological-constant formula. We calibrate the methodology by running an analogous form-specific permutation test on two textbook-accepted dimensional relations — the Rydberg constant and the Bohr radius — obtaining form-specific recovery rates of 1.0% and 0.5% respectively, of comparable order to the 1% rate found independently for the cosmological-constant formula, indicating that the form-specific rate is a property of the procedure rather than a number tuned to a single sector.
We report the engine’s track record: four published relations, six systematic null results, and a clear map of where dimensional analysis succeeds and fails. The structural filter is specified algorithmically, but we emphasize that it encodes physical priors that are themselves choices — different priors would yield different survivors.
In v2 (May 2026), we extend the look-elsewhere analysis from the single-relation case to the multi-relation case (Section 7), providing trial-space cardinality estimates under three formula-grammar levels, an independence reduction of the broader empirical body to ~5–6 statistically independent matches, three procedural safeguards that pre-register the strict grammar, and Bayes-factor calculations giving to in favor of the framework being non-trivial. The audit refines the program’s headline claim and converts the informal look-elsewhere narrative into a formal pre-registration mechanism.