Top panel: Correlation between the three rotational invariants of protohaloes: energy overdensity ϵ, the traceless energy shear q, and μ (see equation 4). The colour displays the value of μ. The dashed lines show ϵ = nq for n = {1, 4/3, 5/3, 2} (from bottom to top), corresponding to the minimum value of ϵ for μ = {1, 0.815, 0.185, −1} whenever the energy shear tensor is positive definite – as shown by equation (10). Bottom panel: Expected distribution of ϵ − q and μ if protohaloes where centred on random locations constrained to have the measured values of ϵ (typically ϵ ≳ 2).