DCT-DM-01 · DCT cluster

Dark-matter Avrami crystallization and the radial-acceleration relation

in Dimensional Coherence Theory

Nolan G. Parrott ORCID 0009-0009-8794-2589 Reserved DOI: 10.5281/zenodo.20032821 arXiv (primary): astro-ph.CO

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In one sentence: How DCT recovers the radial-acceleration relation. Avrami condensation of the tie field on the 600-cell graph predicts the SPARC galaxy fits and an M_lens/M_dyn turnover at z~1.5 falsifiable by Euclid 2027–2029.

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Abstract

The Allen–Cahn condensation of the Brans–Dicke amplitude \(P\) on the 600-cell graph yields the Avrami profile \(P(g) = 1 - \exp(-\sqrt{g/g_\dagger})\) as the static solution to the gravitationally-driven phase-ordering equation. The conformal physical metric \(\tilde g_{\mu\nu} = P g_{\mu\nu}\) then produces an effective gravitational acceleration \(g_{\rm obs} = g_{\rm bar}/P(g_{\rm bar})\) that reproduces the observed radial-acceleration relation (RAR) of disk galaxies without dark matter particles. The MOND scale \(g_\dagger\) is derived from the Brans–Dicke field mass \(m\) as \(g_\dagger = c^2 m^2 / (4\omega_0)\), evaluating to \(1.130\times 10^{-10}\,\mathrm{m/s^2}\) in the Einstein frame and \(1.224\times 10^{-10}\,\mathrm{m/s^2}\) in the Jordan frame. The Einstein-frame value matches Milgrom’s measurement at 2.4%; the Jordan-frame value matches at \(0.81\sigma\). SPARC galaxy fits with the Einstein-frame value give per-galaxy \(\chi^2/\mathrm{dof}\approx 2.4\) comparable to MOND on the real Lelli–McGaugh–Schombert 2016 dataset; an earlier synthetic 175-galaxy benchmark gave \(\chi^2/\mathrm{dof} = 1.141\), a difference we document and acknowledge honestly. The smoking-gun observable distinguishing DCT from \(\Lambda\)CDM and MOND is the cluster \(M_{\rm lens}/M_{\rm dyn}\) ratio: in DCT this peaks at \(1.30\) at \(z\sim 1.5\), while \(\Lambda\)CDM gives unity and MOND gives a different profile shape. Euclid 2027–2029 resolves the smoking gun. Direct dark-matter detection in DCT is exactly zero (\(\sigma_{\rm SI} = 0\)); current null results are consistent with this prediction. The dark-matter density parameter receives an order-of-magnitude DCT contribution \(\Omega_{\rm DM} \sim (1 - P_0) = 0.149\), giving \(\Omega_{\rm DM} h^2 \sim 0.068\) (factor \(\sim 2\) of the measured \(\Omega_{\rm DM} h^2 = 0.120\)); a precision derivation requires the full BEC-density-time analysis described alongside the BEC reality cross-domain check in DCT-FND-V2 / the published Foundation deposit. The paper supplies the dark-matter content of the corpus master scorecard that draws on the canonical DCT_03 line within that deposit.

Keywords

dark matterAvramiradial-acceleration relationSPARCMONDBrans-DickeM_lens/M_dyn turnoverEuclidDimensional Coherence Theory

Cite

APA

Parrott, N. G. (2026). Dark-matter Avrami crystallization and the radial-acceleration relation. Zenodo. https://doi.org/10.5281/zenodo.20032821

BibTeX 
@misc{parrott_dct_dm_01_2026, author = {Parrott, Nolan G.}, title = {Dark-matter Avrami crystallization and the radial-acceleration relation}, year = {2026}, publisher = {Zenodo}, doi = {10.5281/zenodo.20032821}, url = {https://doi.org/10.5281/zenodo.20032821}, note = {DCT-DM-01, DCT paper cluster}
}
RIS 
TY - GEN
AU - Parrott, Nolan G.
PY - 2026
TI - Dark-matter Avrami crystallization and the radial-acceleration relation
PB - Zenodo
DO - 10.5281/zenodo.20032821
UR - https://doi.org/10.5281/zenodo.20032821
ER -

This page is part of the public archive at dctheory.org. The PDF and .tex source above are byte-identical to the Zenodo deposit at 10.5281/zenodo.20032821.