Figure 3: Force network and position overlaps in the fractal basin.

(a) Overlap between the force network edges f_ij=0, 1 that connect two particles i and j in two glass configurations a and b (at pressure p_f=10¹⁰), obtained by independent compression of the same initial configuration at initial pressure p_init (Supplementary Note 2). (b) Time-evolution of the mean-square displacement Δ(t) for glasses at p =10², 10³, 10⁴, 10⁵, 10⁶, 10⁷ and 10⁸ in d=4. The solid line indicates the ballistic dt² behaviour. The long-time value is the cage size dΔ_EA. (c) The pressure evolution of the cage size Δ_EA in various dimension closely follows a power-law ~p^−κ with the theoretical value κ =1.41575. (d) Analytical results for the order parameter Δ(y) at 2^d. Increasing the cutoff y_max~p indicates that the scaling regime Δ(y)~y^−κ extends to all y. (Supplementary Note 1)