Rigorous analytical approximation of tritronquee solution to Painleve-1 and the first singularity

We use a recently developed method to determine approximate expression for tritronqu'{e}e solution for P-1: $y^{\mathrm{\prime }\mathrm{\prime }}+6y^2-x=0$ in a domain $D$ with rigorous bounds. In particular we rigorously confirm the location of the closest singularity from the origin to be at $x= - \frac{770766}{323285} = -2.3841687675\cdots$towithin$5 \times 10^{-6}$ accuracy, in agreement with previous numerical calculation.