**(a)** Animation 5a corresponds to

Fig. 2a of

Friedman+2013 for the case in which the event redshifts are fixed to z

_{A}=5 and z

_{B}=3.65, while the angular separation α as seen from Earth is allowed to vary from 0 to 360 degrees (or, without loss of generality, 0 < α < 180 degrees by symmetry about the x-axis). As in

Animation 4, the green circles show the projection of the past lightcones on the hypersurface τ=τ

_{AB} when the lightcones first intersect; these are also shown as black circles projected onto the τ=0 plane. For these redshifts, events A and B have a shared causal past for angles below some critical value (α <=

**α**) but do not for angles greater than that value (α >

**α**), where

**α** is found from Eq.~31 of

Friedman+2013. The movie represents a point in the z

_{A} - z

_{B} plane which lies in the white box in the upper right region of

Fig 3b of

Friedman+2013, where event pairs do not have a shared causal past with each other as long as the angular separation α exceeds some critical angle

**α**. Since z

_{A} > 3.65 for any angle α, event A also does not have a shared causal past with our worldline along the τ-axis from the origin. Since z

_{B}=3.65, event B just barely has a shared past with our worldline for all angles α.