= Polynomial critical one-arm upper bound
{title2=$g_n(1/2)\leq Cn^{-\alpha}$}
At $p=1/2$ for independent <bond percolation> on the <square lattice>, there exist $C<\infty$ and $\alpha>0$ with $\mathbb P_{1/2}(0\leftrightarrow\partial[-n,n]^2)\leq Cn^{-\alpha}$. The <Russo-Seymour-Welsh theorem> and the <Harris-FKG inequality> give a uniform positive <probability> of a closed dual <graph cycle> around each geometrically spaced square ring. The <independent annular barriers for percolation> give the polynomial bound and imply zero critical <percolation probability>. This does not determine the exact critical exponent.
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