  Multiple investigations support describing galaxy growth as a stochastic
process with correlations over a range of timescales governed by a parameter,
$H$, empirically and theoretically constrained to be near unity. Here, we show
that the distribution of UV-slopes, $\beta$, derived from an ensemble of
theoretical $H=1$ star formation histories (SFHs) is consistent with data at
all redshifts $z\le 16$. At $z=0$, the median value
$\langle\beta_{H=1}\rangle=-2.27$ agrees well with the canonical
$\beta_0=-2.23$ for local starbursts \citep{meurer1999}. At $4\lesssim
z\lesssim16$, JWST data span the model distribution's 2nd to 98th percentiles.
Values of $-2.8\le \beta \le -2.5$ should be common in early galaxies without
reference to exotic stellar populations -- arising solely from a null
hypothesis of $H=1$ for the underlying diversity of galaxy growth histories.
Future data should be interpreted with this fact in mind.
