The D-progressive trajectory conjecture for scalar electrons

Let $\hat{x}(\circ,\bullet)$ be a D-progressive four-dimensional stochastic process as defined by the forward and backward stochastic differential equations, with diffusion parameter $\lambda>0$. Let $m_{0}$ denote the scalar electron's mass and let $\hbar$ denote the reduced Planck constant. D-progressive trajectory conjecture. When

$$\lambda=\sqrt{\hbar/m_{0}},$$

a D-progressive $\hat{x}(\circ,\bullet)$ is a trajectory of a scalar electron satisfying the Klein–Gordon equation. The conjecture proposes a stochastic-kinematic interpretation of scalar-electron trajectories whose dynamics reproduce the relativistic Klein–Gordon equation; its resolution is not established in the supplied text.