Nearest-neighbor critical-radius conjecture for the square-lattice disc model

Let $R_c^{\texttt{NN}}(p)$ denote the critical radius for the nearest-neighbor model with parameter $p$, and let $R_c^{\texttt{dec}}$ denote the critical radius of the decorrelated model. Critical-radius conjecture.

$$R_c^{\texttt{NN}}(\infty)=R_c^{\texttt{dec}}=1.$$

Numerical simulations suggest this equality. At $R=1$, the nearest-neighbor model has edge density $1/2$, matching the critical probability for Bernoulli percolation on the square lattice, while the decorrelated model has a symmetry around $R=1$. The exact critical radii remain to be determined.