The effective bounded negativity conjecture for blowups of the projective plane

Let $f:X_s\rightarrow\mathbb{P}^{2}$ be the blow-up of $\mathbb{P}^{2}$ at $s$ arbitrary points. Let $D\subset\mathbb{P}^{2}$ be a reduced divisor, and let $\widetilde{D}$ be the strict transform of $D$ under $f$.

Effective bounded negativity conjecture. One has

$$\widetilde{D}^{2}\geqslant -4\cdot s.$$

This is an effective version of bounded negativity for all blow-ups of $\mathbb{P}^{2}$, with a uniform bound depending only on the number of blown-up points. The paper presents the result as additional evidence for this conjecture; its status is not resolved in the supplied text.