DCT-SPI-01 · DCT cluster

Spectral and structural identities on the 600-cell

A Bayes-factor test of polytope-derived constants of nature

Nolan G. Parrott ORCID 0009-0009-8794-2589 Reserved DOI: 10.5281/zenodo.20032750 arXiv (primary): math-ph

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In one sentence: Twelve exact algebraic identities on the 600-cell match measured Standard Model constants. A Bayes-factor test rules out ‘numerical coincidence’ at >\(10^{9}\):1.

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Abstract

Twelve algebraic identities connect topological invariants of the 600-cell—the unique convex regular four-polytope with 120 vertices, 720 edges, and binary-icosahedral symmetry 2I—to measured fundamental constants of the Standard Model. Each identity is an exact theorem on the 600-cell or on its McKay-extended Lie algebra \(E_{8}\); matched to data, the residuals range from \(9 \times 1\)0^{-8} (proton-to-electron mass ratio) to 14% (\(\sin\theta_{13}\)). The joint chance probability under independence, computed by enumerating, for each identity, the search space of comparable algebraic expressions, is \(3.34 \times 1\)0^{-28}, corresponding to a Bayes factor of log_10(BF) = +27.5 in favor of the polytope hypothesis over the numerology null. A conservative bound, assuming the identities are perfectly correlated through the 600-cell, gives 3.9\(\sigma\) from the single most stringent identity alone. After a 10^{6} look-elsewhere correction on the implicit prior search space of theoretical proposals, the corrected significance remains greater than 9\(\sigma\). Two structural results underlie the analysis: the cancellation of √5 in the Lee-Huang-Yang geometric factor \(G_{ LHY}\) = 3701/6300 (with 3701 prime), and two exact integer Casimir spectral identities, 31 = \(f_v\) + z - 1 and 154 = 2· 7· 11. The analysis is post-dictive—the polytope was selected with knowledge of the measured constants—and we acknowledge this explicitly through a pre-registered extension protocol and a public Python implementation that allows independent replication. The 12-identity test is the strongest existing-data argument the corpus of Dimensional Coherence Theory can muster; we present it here as a standalone analysis whose mathematical content can be evaluated independently of the broader DCT framework.

Keywords

600-cellbinary icosahedral groupMcKay correspondencespectral graph theoryBayes factornumerical coincidencesfundamental constantsBrans-DickeDimensional Coherence Theory

Cite

APA

Parrott, N. G. (2026). Spectral and structural identities on the 600-cell. Zenodo. https://doi.org/10.5281/zenodo.20032750

BibTeX 
@misc{parrott_dct_spi_01_2026, author = {Parrott, Nolan G.}, title = {Spectral and structural identities on the 600-cell}, year = {2026}, publisher = {Zenodo}, doi = {10.5281/zenodo.20032750}, url = {https://doi.org/10.5281/zenodo.20032750}, note = {DCT-SPI-01, DCT paper cluster}
}
RIS 
TY - GEN
AU - Parrott, Nolan G.
PY - 2026
TI - Spectral and structural identities on the 600-cell
PB - Zenodo
DO - 10.5281/zenodo.20032750
UR - https://doi.org/10.5281/zenodo.20032750
ER -

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