On graphs of total projective functions

It is well known that the graph of a total ${\mathbf{\Sigma }}_n^1$-function is ${\mathbf{\Pi }}_n^1$. We prove the consistency of the dual assertion at the third projective level: there is a model of $\text{ZFC}$ in which the graph of every total ${\mathbf{\Pi }}_3^1$-function is ${\mathbf{\Sigma }}_3^1$. This principle is incompatible with ${\mathbf{\Pi }}_3^1$-uniformization and hence with the usual projective-determinacy picture. The construction also repairs the final step of the failure-of-uniformization argument from~\cite{HOFFELNER2023103292}.