DAEDALUS: A Constraint-Filtered Dimensional-Analysis Engine for Discovering Relations Among Fundamental Constants
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2026
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| _version_ | 1866902225016586240 |
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| author | Zhang, Qingchun |
| author_facet | Zhang, Qingchun |
| contents | <p>We describe DAEDALUS (Dimensional Analysis Engine for Discovering Algebraic Links<br>in Underlying Symmetries), a systematic computational tool for searching for polynomial relations<br>among fundamental physical constants. The engine enumerates all dimensionless combinations<br>of a given set of constants and tests them against a dictionary of target values. We identify a<br>fundamental obstacle — the saturation problem — in which naive dimensional analysis produces<br>hundreds of thousands of apparent “coincidences” that are statistically inevitable rather than<br>physically meaningful. To address this, we introduce a two-level filter: (1) a numerical filter<br>that restricts the search to physically privileged targets and limits the number of constants per<br>relation, and (2) a structural filter that requires surviving candidates to have integer exponents,<br>physical sign structure, and standard prefactors consistent with quantum field theory. Applied<br>to a 17-constant database spanning electromagnetism, gravity, and particle physics, the engine<br>produces 307,900 raw hits but only 0–3 privileged-target hits per 7-constant subset after filtering.<br>We report the engine’s track record: four published relations, six systematic null results, and<br>a clear map of where dimensional analysis succeeds and fails. We calibrate the methodology by<br>running an analogous (simpler) form-specific permutation test on two textbook-accepted dimensional<br>relations (the Rydberg constant R∞= α2mec/(4πℏ) and the Bohr radius a0 = ℏ/(αmec)), obtaining<br>form-specific recovery rates of 1.0% and 0.5% respectively — of comparable order to the 1% rate<br>found independently for the cosmological-constant formula, indicating that the form-specific rate is<br>a property of the procedure rather than a number tuned to a single sector. The structural filter is<br>specified algorithmically, but we emphasize that it encodes physical priors that are themselves choices<br>— different priors would yield different survivors. In v2 (May 2026), we extend the look-elsewhere<br>analysis from the single-relation case to the multi-relation case (Section 7), providing trial-space<br>cardinality estimates under three formula-grammar levels, an independence reduction of the broader<br>empirical body to∼5–6 statistically independent matches, three procedural safeguards that pre-register<br>the strict grammar, and Bayes-factor calculations. The audit refines the program’s headline claim<br>and converts the informal look-elsewhere narrative into a formal pre-registration mechanism.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20062462 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | DAEDALUS: A Constraint-Filtered Dimensional-Analysis Engine for Discovering Relations Among Fundamental Constants Zhang, Qingchun 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 <p>We describe DAEDALUS (Dimensional Analysis Engine for Discovering Algebraic Links<br>in Underlying Symmetries), a systematic computational tool for searching for polynomial relations<br>among fundamental physical constants. The engine enumerates all dimensionless combinations<br>of a given set of constants and tests them against a dictionary of target values. We identify a<br>fundamental obstacle — the saturation problem — in which naive dimensional analysis produces<br>hundreds of thousands of apparent “coincidences” that are statistically inevitable rather than<br>physically meaningful. To address this, we introduce a two-level filter: (1) a numerical filter<br>that restricts the search to physically privileged targets and limits the number of constants per<br>relation, and (2) a structural filter that requires surviving candidates to have integer exponents,<br>physical sign structure, and standard prefactors consistent with quantum field theory. Applied<br>to a 17-constant database spanning electromagnetism, gravity, and particle physics, the engine<br>produces 307,900 raw hits but only 0–3 privileged-target hits per 7-constant subset after filtering.<br>We report the engine’s track record: four published relations, six systematic null results, and<br>a clear map of where dimensional analysis succeeds and fails. We calibrate the methodology by<br>running an analogous (simpler) form-specific permutation test on two textbook-accepted dimensional<br>relations (the Rydberg constant R∞= α2mec/(4πℏ) and the Bohr radius a0 = ℏ/(αmec)), obtaining<br>form-specific recovery rates of 1.0% and 0.5% respectively — of comparable order to the 1% rate<br>found independently for the cosmological-constant formula, indicating that the form-specific rate is<br>a property of the procedure rather than a number tuned to a single sector. The structural filter is<br>specified algorithmically, but we emphasize that it encodes physical priors that are themselves choices<br>— different priors would yield different survivors. In v2 (May 2026), we extend the look-elsewhere<br>analysis from the single-relation case to the multi-relation case (Section 7), providing trial-space<br>cardinality estimates under three formula-grammar levels, an independence reduction of the broader<br>empirical body to∼5–6 statistically independent matches, three procedural safeguards that pre-register<br>the strict grammar, and Bayes-factor calculations. The audit refines the program’s headline claim<br>and converts the informal look-elsewhere narrative into a formal pre-registration mechanism.</p> |
| title | DAEDALUS: A Constraint-Filtered Dimensional-Analysis Engine for Discovering Relations Among Fundamental Constants |
| topic | 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 |
| url | https://doi.org/10.5281/zenodo.20062462 |