Aizenman's conformal invariance and Cardy formula conjecture for critical planar percolation

Let $\Omega$ be a simply connected open domain in the plane, and let $A,B,C,D$ be four boundary points of $\Omega$ in clockwise order. For critical percolation on the $1/n$-scaled hexagonal lattice, let ${\rm P}(\Omega,A,B,C,D,n)$ be the probability of a white crossing in $\Omega$ from the boundary arc between $A$ and $B$ to the boundary arc between $C$ and $D$. Aizenman's conformal invariance and Cardy formula conjecture. For all such $\Omega,A,B,C,D$, the limit

$${\rm P}(\Omega,A,B,C,D,\infty):=\lim_{n\to\infty}{\rm P}(\Omega,A,B,C,D,n)$$

exists and is conformally invariant: if $f$ is conformal, then

$${\rm P}(\Omega,A,B,C,D,\infty)={\rm P}(f(\Omega),f(A),f(B),f(C),f(D),\infty).$$

Moreover, when $\Omega$ is a rectangle and $A,B,C,D$ are its four corner points, this limit is given by an explicit formula called Cardy's formula. Since every such marked domain can be conformally mapped to a unique rectangle with the marked points sent to its corners, this determines the limit in general. This conjecture combines the conformal invariance conjecture attributed to Michael Aizenman with Cardy's conjecture. The scaling limit of critical planar percolation is a central problem linking discrete crossing probabilities with conformal geometry; the source does not state a resolution status for these claims.