Solution (source code)

= Solution

The <causal past> follows from the same covering-space argument with reversed endpoints:
$$
\boxed{J^-(0)=\{(t,\bar x):-ct\ge d(\bar x,0)\}.}
$$
For $t\le-\pi R/c$, the whole spatial circle can send a causal signal to the origin. The lower-left <spacetime diagram> in part <1/c> is therefore completely orange sufficiently far below the origin.