The Monasson et al. mixed 2- and 3-SAT threshold conjecture

Let $F_{2,3}(n,m_1,m_2)$ be the conjunction of independent random $2$-SAT and $3$-SAT formulas with the indicated numbers of clauses. Set $m_1=\alpha_2 n$, $m_2=\alpha_3 n$, let $p=\alpha_3/(\alpha_2+\alpha_3)$, and write $\alpha=\alpha_2+\alpha_3$.

Monasson et al.'s mixed-SAT conjecture. For every $p\in[0,1]$ there exists a value $\alpha_\mathrm{sat}(2+p)>0$ such that, whenever $\alpha_2,\alpha_3>0$ satisfy $\alpha_3/(\alpha_2+\alpha_3)=p$,

$$\lim_{n\to\infty}\mathbb P(F_{2,3}(n,\alpha_2 n,\alpha_3 n)\text{ is satisfiable})=\begin{cases}1,&\text{if }\alpha<\alpha_\mathrm{sat}(2+p),\\\\0,&\text{if }\alpha>\alpha_\mathrm{sat}(2+p). \end{cases}$$

Furthermore, for $p<0.413\dots$ one has $\alpha_\mathrm{sat}(2+p)=\alpha_\mathrm{sat}(2)/(1-p)$, whereas this equality does not hold for $p\geq0.413\dots$. The conjecture extends the proposed sharp threshold picture to mixed clause models; the source reports the stated threshold relation as part of the conjectural claim.