The square-grid error-correcting locating-dominating set density conjecture

Let $SQ$ denote the infinite square grid, and let ERR:LD$(SQ)$ denote its error-correcting locating-dominating set density. Square-grid density conjecture.

$$\textrm{ERR:LD}(SQ)=\frac{2}{3}.$$

The authors state that this value is strongly suggested by their examination, but that no proof is known; the conjecture concerns the tight density bound for the square grid.