First-order statistics determine the complete modeling theory

Let $\mathbf A$ be a modeling, and for every first-order formula $\phi$ let $\langle\phi,\mathbf A\rangle$ denote its satisfaction probability in $\mathbf A$. Modeling-theory conjecture. Knowledge of all values $\langle\phi,\mathbf A\rangle$ for first-order formulas $\phi$ is sufficient to deduce the complete $\mathcal L(Q_m)$-theory of $\mathbf A$. The supplied text states this as a conjecture after discussing the preceding characterization; no proof or disproof is provided.