GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s51> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s50> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s48> GLYPH<s49>GLYPH<s48> GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s50> GLYPH<s49>GLYPH<s48> GLYPH<s51> GLYPH<s48>GLYPH<s44> GLYPH<s48>GLYPH<s48> GLYPH<s48>GLYPH<s44> GLYPH<s48>GLYPH<s52> GLYPH<s48>GLYPH<s44> GLYPH<s48>GLYPH<s56> GLYPH<s48>GLYPH<s44> GLYPH<s49>GLYPH<s50> GLYPH<s48>GLYPH<s44> GLYPH<s49>GLYPH<s54> GLYPH<s48>GLYPH<s44> GLYPH<s50>GLYPH<s48> GLYPH<s48>GLYPH<s44> GLYPH<s50>GLYPH<s52> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s51> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s50> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s48> GLYPH<s49>GLYPH<s48> GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s53> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s52> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s51> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s50> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s49> GLYPH<s124> GLYPH<s51>GLYPH<s44>GLYPH<s116>GLYPH<s114>GLYPH<s105>GLYPH<s118>GLYPH<s105>GLYPH<s97>GLYPH<s108> GLYPH<s40> GLYPH<s44> GLYPH<s84>GLYPH<s32> GLYPH<s41>GLYPH<s124> GLYPH<s32>GLYPH<s107> GLYPH<s66> GLYPH<s84>GLYPH<s32> GLYPH<s47> GLYPH<s32>GLYPH<s91> GLYPH<s48> GLYPH<s40> GLYPH<s49> GLYPH<s41> GLYPH<s50> GLYPH<s97> GLYPH<s51> GLYPH<s93> GLYPH<s102> GLYPH<s32>GLYPH<s47>GLYPH<s32> GLYPH<s102> GLYPH<s68> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s32> Fig. S 1: The quantity | X$_{trivial}$ | = | χ 3 $_{,trivial}$( ω ) k$_{B}$T ϵ 0 (Δ χ 1 ) $^{2}$a3 | is plotted as a function of the ratio f/f$_{D}$ . Inset: same graph in log-log plot showing that X$_{trivial}$ decreases as f − 3 when f ≫ f$_{D}$ . The last term in the rhs of the latter equation depends only on f/f$_{D}$ , i.e. f/f$_{α}$ . Thus, the latter equation and Eq. (1) of the letter are formally similar: The quantity X$_{trivial}$ = χ 3 $_{,trivial}$( ω ) k$_{B}$T ϵ 0 (Δ χ 1 ) $^{2}$a3 plays, for the ‘no glassy correlations’ case, the same role as X = χ 3 ( ω ) k$_{B}$T ϵ 0 (Δ χ 1 ) $^{2}$a3 in the main letter. The behavior of X$_{trivial}$ is shown on Figs S1-S2. Three main features are noticeable: (i) On Fig. S1, one sees that | X$_{trivial}$ | has no peak in frequency, at variance with what is observed on Figs (1),(2),(4) of the main letter. This strongly support that, as claimed in the letter, the peak in frequency of | X | is directly linked to the effect of glassy correlations. (ii) From Eqs. (8)-(10), one sees that the magnitude of | X$_{trivial}$ | does not depend on the temperature T . The T dependence of X$_{trivial}$ is only through τ$_{D}$ ( T ), since we have set f$_{D}$ = f$_{α}$ . This absence of temperature dependence of | X$_{trivial}$ | strongly supports our claim that the increase of the maximum value of | X | seen on Figs (1),(3) of the letter comes from the variation of the correlation volume when the temperature is decreased towards T$_{g}$ . (iii) On Fig. S1, one sees that | X$_{trivial}$ | is maximum for ω = 0. The trivial part of χ$_{3}$ thus 15