Possible instant positions (small gray and colored dots) of a hypothetical and still undetected planet of mass 1 M_Jup on the sky plane, at the epoch labeled in the lower-left corner of each graph. We collected 10⁵ initial conditions. The bottom plot shows their distribution in the (a₀, e₀)–plane of canonical osculating elements at the initial epoch of 1998.830, similarly to Fig. 11. As in Fig. 10, the largest filled circles correspond to the positions of the planets HR 8799e and HR 8799d at the snapshot epoch (large filled circles) and the initial osculating epoch (shaded filled circles), respectively. Colors mark the lowest order MMR types, as labeled in the bottom plot. The light-gray curve marks the collision zone with HR 8799e, the thinner curve marks the stability zone for m₀ = 10⁻⁶ M_Jup (see Fig. 10), and the red curve is the image of the geometric collision curve shifted by Δa₀ ≃ 6 au toward the star.