= Independent oriented-percolation comparison for the contact process
{title2=$q=e^{-2\delta}(1-e^{-\lambda\delta})^2$}
For the one-dimensional <contact process> with recovery rate one and per-neighbour infection rate $\lambda$, use parity sites $(x,n)$ with $x+n$ even. Call a site good if $x$ has no recovery in $[(n-1)\delta,(n+1)\delta]$ and sends an arrow to each neighbour during $[n\delta,(n+1)\delta]$. The goodness indicators are independent: recovery intervals for successive parity sites at the same spatial point only touch at endpoints, and all outgoing-arrow intervals and clocks are disjoint. Their common probability is the displayed $q$. A path of good sites carries infection from each time layer to the next, because both its source and target avoid recovery during the transmitting interval. Taking $\delta=\lambda^{-1/2}$ makes $q\to1$. The <incoming-edge coupling of site and bond percolation> and $p_c^{\mathrm{bond}}<1$ imply $p_c^{\mathrm{site}}<1$, so this proves a finite critical infection rate.
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