Symmetry correspondence conjecture for effective physical models and correlation geometries

Let an effective physical model be a model featuring an isometry, and let all fields be invariant under this isometry. Suppose the model is mapped by a reference system $S$ satisfying an equation invariant under the same isometry. A correlation geometry consists of a fundamental physical model $(\mathcal{H},\mathcal{F}^{p,q},\rho)$, and a unitary transformation $U$ is a symmetry when

$$\rho(\Omega)=\rho(U\Omega U^{-1})$$

for every measurable set $\Omega\subset\mathcal{F}^{p,q}$. Symmetry correspondence conjecture. Every such effective physical model gives rise to a correlation geometry with a related symmetry in this sense. This conjecture proposes a general link between isometries of effective physical models and unitary symmetries of the associated correlation geometries. The supplied text does not state whether the conjecture has been proved or disproved.