**(a)** Animation 6a corresponds to

Fig. 2a of

Friedman+2013 for the case α = 180 degrees where the redshift of event A is fixed to z

_{A}=0.5 and the redshift of event B is allowed to vary in the range 0.5 < z

_{B} < 71.91. For z

_{B} <

**z**_{B} ~ 50, events A and B have intersecting past lightcones and a shared causal past. For z

_{B} >

**z**_{B} ~ 50, the events do not have a shared causal past. This corresponds to fixing z

_{A} and α = 180 degrees and increasing z

_{B} until the point (z

_{A}, z

_{B}) lies in the light gray region in

Fig 3b of

Friedman+2013. For z

_{A} <= z

_{B} <= 3.65, events A and B both have shared causal pasts with Earth's worldline, whereas event B does not when z

_{B} > 3.65. The critical redshift

**z**_{B} is computed from Eq. 30 of

Friedman+2013 (substituting labels A <--> B), and using Eq. 12 of

Friedman+2013 to determine redshift for a given comoving distance.

**(b)** Animation 6b corresponds to

Fig. 2a of

Friedman+2013 for the case α = 180 degrees with symmetric redshifts z

_{A}=z

_{B}, where both redshifts are increased in the range 1 <= z

_{A}=z

_{B} <= 24.47. The symmetric case illustrates the role of the causal independence redshift z

_{ind}=3.65. For z

_{A}=z

_{B} <= z

_{ind}=3.65, events A and B have intersecting past lightcones and shared causal pasts with each other and Earth's worldline. For z

_{A}=z

_{B} > z

_{ind}=3.65, events A and B have no shared causal past with each other or our worldline. The finite redshift resolution of the movie shows a frame with z

_{A}=z

_{B}=3.62 where the past lightcones of A and B clearly intersect (green circles), while the next frame with z

_{A}=z

_{B}=3.67 clearly shows that the past lightcones of the events no longer intersect.