Comment by pistachiopro

Right, so for his nondeterministic path:

  r(t) = 0              ; t <= T
  r(t) = (1/144)(t-T)^4 ; t >= T

We can see that r''''(T) is either 0 or 1/6, depending on if we go with the top or bottom equation. That does look like some sort of hidden state change, there.

Interestingly, the spherical dome he mentioned (which doesn't yield to this non-determinism) forces all derivatives of r(t) to be continuous ...