Bernoulli coordinate observable is not almost periodic ($\Vert U^{n}f-U^{m}f{\Vert }_2^2=2(n\ne m)$)

For independent fair signs on a two-sided Bernoulli shift, the coordinate observable $f(y)=y_0$ has unit norm and pairwise orthogonal orbit values. Their pairwise squared distance is two, excluding a finite small net in global $L^2$. Its pullback along a factor map can nevertheless be a relatively almost periodic observable, since it is fiber-constant and takes only two values.