Let x and y denote configurations. Let f(x) be a number (that depends on x). Its expectation is 𝔼ₓf(x). Let g(x,y) be a number. If x and y are independent, the expectation is 𝔼ₓ𝔼ᵧg(x,y). I suspect that the mysterious ² is analogous to the one that falls out here when we condition on x=y or the other terms cancel out.
Let x and y denote configurations. Let f(x) be a number (that depends on x). Its expectation is 𝔼ₓf(x). Let g(x,y) be a number. If x and y are independent, the expectation is 𝔼ₓ𝔼ᵧg(x,y). I suspect that the mysterious ² is analogous to the one that falls out here when we condition on x=y or the other terms cancel out.