A finite channel does not select its continuous-time completion

This is an elementary comparison, not the native incidence continuum limit. Extra spectral, refinement, calibration, or dynamical conditions might select one completion. They are not consequences of the common finite channel.

Likewise, a finite stencil need not be isotropic. Cardinal unit steps with waiting on ${\mathbb{Z}}^2$ reach exactly $\left|x_1\right|+\left|x_2\right|\le n$ after $n$ ticks. Rescaling by $n$ yields an ${\ell }^1$ ball, not a Euclidean disk. Periodic-graph velocity polytopes provide related context Fritz; that fixed-graph conclusion is not imported as a no-go for growing directional families such as those reported in En05-B.