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Bibliographic Details
Main Author:	Zhang, Qingchun
Format:	Recurso digital
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Published:	Zenodo 2026
Subjects:	dimensional analysis, fundamental constants, numerology, saturation problem, structural filter, look-elsewhere effect, permutation test, false-positive rate, fine-structure constant, cosmological constant, gravitational coupling, baryon-to-photon ratio, electron Yukawa, computational tools, Bayesian model comparison, pre-registration, multi-relation audit
Online Access:	https://doi.org/10.5281/zenodo.20062462
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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. 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. We calibrate the methodology by running an analogous (simpler) form-specific permutation test on two textbook-accepted dimensional relations (the Rydberg constant R∞= α2mec/(4πℏ) and the Bohr radius a0 = ℏ/(αmec)), 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. 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&sim;5–6 statistically independent matches, three procedural safeguards that pre-register the strict grammar, and Bayes-factor calculations. The audit refines the program’s headline claim and converts the informal look-elsewhere narrative into a formal pre-registration mechanism.

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