Resolving this problem would unify persistent random walk theory with the broader literature on correlated random walks on lattices, with direct applications to the study of reinforced walks, directional diffusion limits, and transport processes in anisotropic media. It would also clarify the extent to which Bessel function universality, a hallmark of simple symmetric random walks, persists when spatial memory is introduced, potentially revealing a new class of special functions naturally associated with higher-dimensional persistent processes.