Small cap decoupling for the parabola with logarithmic constant

We note that the subpolynomial factor for the ${\mathrm{\ell }}^q{L}^p$ small cap decoupling constants for the truncated parabola ${\mathbb{P}}^1=\{(t,t^2):\mathrm{\mid }t\mathrm{\mid }\le 1\}$ may be controlled by a suitable power of $\log R$. This is achieved by considering a suitable amplitude-dependent wave envelope estimate, as was introduced in a recent paper of Guth and Maldague to demonstrate a small cap decoupling for the $(2+1)$ cone; we demonstrate that the version for ${\mathbb{P}}^1$ may be taken with a loss controlled by a power of $\log R$ as well.