We show the exact solution of the self-dual ϕ4-model on the 4-dimensional Moyal space. Using the results explained in Raimar's talk, an implicitly defined function converges to a Fredholm integral, which is solved, for any coupling constant λ more than −1π, in terms of a hypergeometric function. We prove that the interacting model has spectral dimension 4−2arcsin(λπ)π for |λ| less than 1π. It is this dimension drop which for λ more than 0 avoids the triviality problem of the ϕ44 model on the Moyal space.