An improved lower bound for Bloch's constant

Abstract: Let $B$ denote Bloch's constant. We prove [ B \ge \frac{\sqrt{3}}{4}+0.0153 = 0.448312701\ldots, ] improving the lower bounds by Chen--Gauthier ($\sqrt{3}/4+2\cdot10<sup>{-4}$) and Xiong ($\sqrt{3}/4+3\cdot10<sup>{-4}$). The proof refines Bonk's method through computer-assisted estimates rigorously verified using interval arithmetic.