The state of Minkowski spacetime up to Σ₀ is not responsible for the development of closed timelike curves, since Minkowski spacetime contains no closed timelike curves.

Thus, if the operation of a Thornian time machine is to be a live possibility, some condition weaker than causal determinism must be used to capture the sense in which the state on \(\Sigma_0\) can be deemed to be responsible for the subsequent development of CTCs. Given the failure of causal determinism, it seems the next best thing to demand that the region \(V\) is “adjacent” to the future domain of dependence \(D^+ (\Sigma_0)\). Here is an initial stab at such an adjacency condition.