Equivariant irrationality of very general symmetric Verra fourfolds

We prove that a very general complex symmetric Verra fourfold is not $\text{ZZ}\mathrm{/}2$-birational to ${\text{PP}}^4$, using the \emph{theory of atoms} introduced by Katzarkov–Kontsevich–Pantev–Yu~\citep{Katzarkov2025BirationalIF} in the equivariant setting as in Cavenaghi–Katzarkov–Kontsevich~\citep{cavenaghi2026atomsmeetsymbols}.