We prove that the moduli stacks of marked and labelled Hodgespecial Gushel–Mukai fourfolds are isomorphic. As an application, we construct rational maps from stack Hodge-special discriminant d to space (twisted) degree-d polarized K3 surfaces. use these results a counting formula for number fourdimensional fibers Fourier–Mukai partners very general with associated surface, lower bound this in c...