$$\frac{1}{\mu(B)}\int_B \vert x \vert d\mu(x) = \frac{1}{p+1}$$

This formula holds for the unit ball in $\mathbb{Q_p}$. This formula also holds for $\mathbb{R}$ when $p=1$. Should one expect $$W_{1^{\infty}} $\mathrm{Frac}(W_{1^{\infty}} (\mathbb{F_1})=\mathbb{R}?$$ \mathbb{F_1}))=\mathbb{R}?$$ What (mathematical) criteria do people use to rule-out field with one element phenomena? What makes point counting formulas better (or worse)?

$$\frac{1}{\mu(B)}\int_B \vert f x \vert d\mu(x) = \frac{1}{p+1}$$

This formula holds for the unit ball in $\mathbb{Q_p}$. This formula also holds for $\mathbb{R}$ when $p=1$. Should one expect $$W_{1^{\infty}} (\mathbb{F_1})=\mathbb{R}?$$ What (mathematical) criteria do people use to rule-out field with one element phenomena? What makes point counting formulas better (or worse)?

$$\frac{1}{\mu(B)}\int_B \vert f \vert d\mu(x) = \frac{1}{p+1}$$

This formula holds for the unit ball in $\mathbb{Q_p}$. This formula also holds for $\mathbb{R}$ when $p=1$. Should one expect $$W_{1^{\infty}} (\mathbb{F_1})=\mathbb{R}?$$ What (mathematical) criteria do people use to rule-out field with one element phenomena? What makes point counting formulas better (or worse)?