The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond

We construct via forcing a model for the level by level equivalence between strong compactness and supercompactness in which both $V = {\rm HOD}$ and the Ground Axiom (GA) are true. In our model, various versions of the combinatorial principles $\square $ and $\diamondsuit $ hold. In the model constructed, there are no restrictions on the class of supercompact cardinals.