Coupled onset parameter for origin percolation ($M=\inf \{p:I_p\}$)

In the uniform-label monotone coupling of Bernoulli percolation, let $I_p$ mean that the origin belongs to an infinite percolation cluster, and let $M=\inf \{p:I_p\}$. The occurrence parameters form an upper interval. Therefore $\{M<p\}={\bigcup }_{r<p,r\in \mathbb{Q}}{I}_r$ and $\theta (p-)=\mathbb{P}(M<p)$. Since $\{M<p\}\subseteq I_p\subseteq \{M\le p\}$, the jump is $\theta (p)-\theta (p-)=\mathbb{P}(I_p\cap \{M=p\})$. Occurrence at the infimum is not presumed.