Timed periodic dependency models

This is the comparison with Fritz and Cheung VII-J Fritz,CheungVIIJ. A finite-time jump is not bounded by the asymptotic polytope alone.

For the cardinal model with velocities $\pm c{e}_i$,

A Euclidean unit direction $u$ has radial speed $c/\Vert u{\Vert }_1$: in two dimensions it is $c$ on axes but $c/\sqrt{2}$ on diagonals. Compare En03-A prop:directional and VII-E's directional comparison CheungEn03A,CheungVIIE.

A fixed finite periodic model therefore has its own non-Euclidean attainability obstruction. It is not identical to an arbitrary schedule's metric envelope. If quotient complexity grows, the finite-time offset must be controlled along with the polytope shape.