The $mathbb{R}^{0|18}$ dust gravity model contains analogues to the particle spectrum and interactions of the Standard Model and gravity, but with only four tunable parameters. As the structure of this model is highly constrained, predictive relationships between its counterparts to the constants of the Standard Model may be obtained. In this paper, the model values for the masses of the tau, the $W$ and $Z$ bosons, and a Higgs-like scalar boson are calculated as functions of $alpha$, $m_e$, and $m_mu$, with no free fitting parameters. They are shown to be $1776.867(1)~mathrm{MeV}/c^2$, $80.3786(3)~mathrm{GeV}/c^2$, $91.1877(4)~mathrm{GeV}/c^2$, and $125.16(1)~mathrm{GeV}/c^2$ respectively, all within $0.5,sigma$ or better of the corresponding observed values of $1776.86(12)~mathrm{MeV}/c^2$, $80.379(12)~mathrm{GeV}/c^2$, $91.1876(21)~mathrm{GeV}/c^2$, and $125.10(14)~mathrm{GeV}/c^2$. This result suggests the existence of a unifying relationship between lepton generations and the electroweak mass scale, which is proposed to arise from preon interactions mediated by the strong nuclear force.
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