Minimum value of the semi-major axis above which particles initially sampled with q ∈ [40, 60] au spread beyond q = 80 au in 4.5 Gyrs, with respect to their initial ecliptic inclination. The horizontal bars show our twenty 0.1-width slices of cosI, connected in their centre by a full curve. The location of the four major resonances for the weakly perturbed planetary Hamiltonianare indicated by dotted black lines.