Table 2 Criteria applied to distinguish phases in Figs. 5a and 4a

Phase	Local packing fraction, ϕ	Orientational order parameter, ψ₆	Mode speed, v_m
Cooled homogeneous	Unimodal Prob(ϕ) μ₃(ϕ) ≥ 0	No peak at ψ₆ ≥ 0.95	\({v}_{{{{\rm{m}}}}}\, < \,7{\tau }_{0}^{-1}\)
Heated homogeneous	Unimodal Prob(ϕ) μ₃(ϕ) ≥ 0	No peak at ψ₆ ≥ 0.95	\({v}_{{{{\rm{m}}}}}\ge 7{\tau }_{0}^{-1}\)
Cooled clustering	Unimodal Prob(ϕ) μ₃(ϕ) < 0	No peak at ψ₆ ≥ 0.95	\({v}_{{{{\rm{m}}}}}\, < \,7{\tau }_{0}^{-1}\)
Cooled solid	Unimodal Prob(ϕ) μ₃(ϕ) < 0	A peak at ψ₆ ≥ 0.95	\({v}_{{{{\rm{m}}}}}\, < \,7{\tau }_{0}^{-1}\)
Heated clustering	Unimodal Prob(ϕ) μ₃(ϕ) < 0	No peak at ψ₆ ≥ 0.95	\({v}_{{{{\rm{m}}}}}\ge 7{\tau }_{0}^{-1}\)
Mixed	Bimodal Prob(ϕ), with peaks at ϕ ≤ Φ and ϕ > Φ	Bimodal Prob(ψ₆), with peaks at ψ₆ ≤ 0.95 and ψ₆ > 0.95	Inside the cluster, \({v}_{{{{\rm{m}}}}} < \, 7{\tau }_{0}^{-1}\) Outside the cluster, \({v}_{{{{\rm{m}}}}}\ge 7{\tau }_{0}^{-1}\)

The skewness (third standardized moment) μ₃(ϕ) is defined as \({\mu }_{3}(\phi )=\frac{\int_{0}^{1}{({\phi }^{{\prime} }-\Phi )}^{3}\,{{{\rm{Prob}}}}({\phi }^{{\prime} })\,{{{\rm{d}}}}{\phi }^{{\prime} }}{{\left(\int_{0}^{1}{({\phi }^{{\prime} }-\Phi )}^{2}{{{\rm{Prob}}}}({\phi }^{{\prime} }){{{\rm{d}}}}{\phi }^{{\prime} }\right)}^{3/2}}\) and indicates, whether the mass of the distribution is concentrated on the right (negative skewness) or on the left (positive skewness).

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