Consider two participants (a.k.a. "material points%22), $P$ and $Q$, who had been coincident ("meeting, in passing") at exactly and only one event, $\varepsilon_{P Q}$.
Further, for all events in which $P$ had taken part, i.e. the (ordered) set of events $\{ ... \, \varepsilon_{B P} \, ... \, \varepsilon_{K P} \, ... \, \varepsilon_{P Q} \, ... \, \varepsilon_{P V} \, ... \, \varepsilon_{P Y} \, ... \}$, along with all events in which $Q$ had taken part, i.e. the (ordered) set of events $\{ ... \, \varepsilon_{A Q} \, ... \, \varepsilon_{J Q} \, ... \, \varepsilon_{P Q} \, ... \, \varepsilon_{U Q} \, ... \, \varepsilon_{X Q} \, ... \}$, the values of Lorentzian distance $\ell$ between any pairs of events shall be given.
Under exactly which condition, expressed in terms of the given values $\ell$, are participants $P$ and $Q$ said to have been "momentarily co-moving" at event $\varepsilon_{P Q}$ ?
A note concerning terminology:
While in 2015 the notion of Lorentzian distance $\ell$ was denounced as "a mathematical function that isn't used in physics", its use in physics appears suitably reputable since 2016.