 Harris theorem for square-lattice bond percolation

Uniform fixed-aspect rectangle crossing in bond percolation bounds at the self-dual parameter yield a positive lower bound for closed dual circuits in geometrically spaced disjoint annuli. The independent annular barriers for percolation imply that an origin-to-infinity open graph path has probability zero. Parameter monotonicity gives zero percolation probability for every $p\le 1/2$.