The logarithmic exponent of the Ramsey number $r(4,t)$

We prove that $r(4,t)\ge \frac{t^3}{(\log t{)}^{2+o(1)}}$. This improves the lower bound of Mattheus and Verstraëte (Ann. of Math., 2024) by a factor of $(\log t{)}^{2-o(1)}$.