Dimension greater than one for the attractors of a self-affine IFS

Let $0 < \lambda < \mu < 1$ with $\lambda + \mu > 1$, and define

$$T_0(x,y)=(\lambda x,\mu y),\qquad T_1(x,y)=(\mu x+1-\mu,\lambda y+1-\lambda).$$

Let $A_{\lambda,\mu}$ be the attractor of the iterated function system $\{T_0,T_1\}$.

Dimension conjecture. For all $0 < \lambda < \mu < 1$ with $\lambda + \mu > 1$, the set $A_{\lambda,\mu}$ has dimension strictly greater than $1$.

The paper proves the claim for a range of parameters occupying 91.8% of the parameter space, while the range satisfying both this result and the top-boundary theorem occupies 91.3%. The authors note that their technique may not extend arbitrarily close to all parameters, so the assertion remains open.