  We present a lower bound on the radius of the universe today $a_0$ and a
monotonicity constraint on the Hubble diagram. Our theoretical input is
Einstein's kinematics and maximally symmetric universes. Present supernova data
yield $a_0 > 1.2\cdot 10^{26}$ m. A first attempt to quantify the monotonicity
constraint is described. We do not see any indication of non-monotonicity.
