Almost-sure constancy of the dimension of uniformly random self-affine sets

A uniformly random self-affine set is obtained as the attractor of a random iterated function system of affine contractions, with the randomness specified by the model under consideration. Self-affine dimension conjecture. The Hausdorff dimension of a uniformly random self-affine set is a constant number almost surely. This would extend the almost-sure constancy result for uniformly random self-similar fractals to the self-affine setting; the source presents it as a direction for generalization, without stating a resolution.