  Causal set theory is perhaps the most minimalistic approach to quantum
gravity, in the sense that it makes next to zero assumptions about the
structure of spacetime below the Planck scale. Yet even with this minimalism,
the continuum limit is still a major challenge in causal sets. One aspect of
this challenge is the measurement of distances in causal sets. While the
definition and estimation of time-like distances is relatively straightforward,
dealing with space-like distances is much more problematic. Here we introduce
an approach to measure distances between space-like separated events based on
their causal overlap. We show that the distance estimation errors in this
approach vanish in the continuum limit even for smallest distances of the order
of the Planck length. These results are expected to inform the causal set
geometrogenesis in general, and in particular the development of evolving
causal set models in which space emerges from causal dynamics.
