Cellularity of Chromatic Synthetic Spectra

We show that the $\mathrm{\infty }$-category of synthetic spectra based on Morava E-theory is generated by the bigraded spheres and identify it with the $\mathrm{\infty }$-category of modules over a filtered ring spectrum. The latter we show using a general method for constructing filtered deformations from t-structures on symmetric monoidal stable $\mathrm{\infty }$-categories.