Universality conjecture for arm-event exponents on isoradial graphs

Let $G$ be an isoradial graph with the bounded-angles property, let $k\in\mathbb{N}$, and let $\sigma\in\\{0,1\\}^k$. For a translated annulus $\mathcal{A}^u(N,n)$ centred at $u$, let $A_{\sigma}^u(N,n)$ be the event that there are $k$ vertex-disjoint crossings of the annulus whose colours, in anticlockwise order, are given by $\sigma$. Arm-exponent universality conjecture. There exists $\rho(\sigma,G)>0$ such that

$$\mathbb{P}_G[A_{\sigma}^u(N,n)]\approx n^{-\rho(\sigma,G)}$$

as $n\to\infty$, uniformly in $u\in\mathbb{R}^2$, and the exponent $\rho(\sigma,G)$ does not depend on the choice of $G\in\mathcal{G}$. The conjecture asserts the existence and graph-independence of all colour-sequence arm exponents, extending the expected asymptotic power laws for one-arm and alternating-arm events. Establishing these exponents uniformly across isoradial graphs is part of the broader criticality and universality problem for percolation.