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

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