The iterative surface-Hadamard conjecture for the semiclassical Yukawa model

Let $\chi$ be the classical scalar field, let $\omega_{\mathcal C}$ be an initial state on an initial surface $\mathcal C$, and consider the three 3-smeared initial two-point functions of the quantum field and its momentum. Yukawa iterative conjecture. At the $k$th stage, conditions on these initial two-point functions depend only on the values of $\chi$ and its derivatives through order $k-2$, determined at earlier stages, and determine the $(k+1)$st time derivative of $\chi$. This conjecture is the basis for defining surface Hadamard initial states through an infinite iterative process; the paper does not prove the asserted continuation of the process.