  The state spaces of machines admit the structure of time. A homotopy theory
respecting this additional structure can detect machine behavior unseen by
classical homotopy theory. In an attempt to bootstrap classical tools into the
world of abstract spacetime, we identify criteria for classically homotopic,
monotone maps of pospaces to future homotope, or homotope along homotopies
monotone in both coordinates, to a common map. We show that consequently, a
hypercontinuous lattice equipped with its Lawson topology is future
contractible, or contractible along a future homotopy, if its underlying space
has connected CW type.
