= Finite-box comparison for percolation parameters
{title2=$\mathbb P_q(A)-\mathbb P_p(A)\leq m(q-p)$}
If an <increasing event> $A$ depends on $m$ sites or <edges>, the uniform-label <monotone coupling of Bernoulli percolation> and the <union bound> give $0\leq\mathbb P_q(A)-\mathbb P_p(A)\leq m(q-p)$ for $p\leq q$. A change of the event requires a coordinate with label in $(p,q]$. For <bond percolation> from the origin to the boundary of $[-n,n]^2$, first-hit <graph paths> use the $4n(2n+1)$ internal <edges>, so the same count bounds the parameter sensitivity.
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