We wish to report the following corrections to the manuscript [1]. In the second expression given in its equation (72) there is a sign error, since ζ1/2 should read -ζ1/2. The correct expression thus is, 2Δτt (q) = (-ζ1/2 + C φ(τkF→, q))2. This correction implies that for τ = t the exponent ζt(k) given in equation (71) of [1] is negative for k > 0 at any spin density m value, so that in the corresponding range k ∈ [kt, π] considered in that paper one has that kt = 0, including in equation (73) for m→1. Indeed, the sign error also affects the second expression of equation (75) of [1] valid for m→1, which should read, ζt(k) = -1/2 - 2φ(0, k - π)[1 - φ(0, k - π)]. This sign error propagates to the plots of the exponent ζt in figures 2 4 of [1]. The exponent ζt is called ζxx1 in [2], being plotted as a function of k/π for a set of spin density values in figure 6 of that reference. These plots correct those of the exponent ζt in figures 2 4 of [1]; the plots of the spectra and exponent ζt also shown in the latter figures remain correct. A physical consequence of the present sign correction is that there are lower threshold singularity cusps in the corresponding transverse spin dynamical structure factor for the whole momentum range k ∈ [0, π] and not only for k ∈ [kt, π], with kt finite and given in [1].