On the four-arm exponent for 2D percolation at criticality

For two-dimensional percolation at criticality, we discuss the inequality α4 > 1 for the polychromatic four-arm exponent (and stronger versions, the strongest so far being α 4 ≥ 1 + α 2 2 , where α2 denotes the two-arm exponent). We first briefly discuss five proofs (some of them implicit and not self-contained) from the literature. Then we observe that, by combining two of them, one gets a completely self-contained (and yet quite short) proof