In Abstract geometrical computation for black hole computation (MCU '04, LNCS 3354), the author provides a setting based on rational numbers, abstract geometrical computation, with super-Turing capability: any recursively enumerable set can be decided in finite time. To achieve this, a Zeno-like construction is used to provide an accumulation similar in effect to the black holes of the black hole model. We prove here that forecasting an accumulation is $\Sigma_2^0$-complete (in the arithmetical hierarchy) even if only energy conserving signal machines are addressed (as in the cited paper). The $\Sigma_2^0$-hardness is achieved by reducing the problem of deciding whether a recursive function (represented by a 2-counter automaton) is strictly partial. The $\Sigma_2^0$-membership is proved with a logical characterization.