  We study the Adams-Novikov spectral sequence in $\mathbb{F}_p$-synthetic
spectra, computing the synthetic analogs of $\mathrm{BP}$ and its cooperations
to identify the synthetic Adams-Novikov $\mathrm{E}_2$-page, computed in a
range with a synthetic algebraic Novikov spectral sequence. We then identify
deformations associated to the Cartan-Eilenberg and algebraic Novikov spectral
sequences in terms of stable comodule categories, categorifying an algebraic
Novikov spectral sequence result of Gheorghe-Wang-Xu. We then apply
Isaksen-Wang-Xu methods in $\mathbb{F}_p$-synthetic spectra to deduce
differentials in the synthetic Adams-Novikov for the sphere, producing almost
entirely algebraic computations through the 45-stem.
