The endless continuability conjecture for Borel-transformed WKB solutions

Let $\cQ$ be an $\hbar$-differential operator, lifted to an $\hbar$-connection after fixing a spin structure, and assume WKB-regularity. Let $L$ be the characteristic variety of $\cQ$, and let $x\in C$ lie outside the turning points. A formal WKB solution at $x$ has a Borel transform. The endless continuability conjecture. The Borel transformation is endlessly continuable.

This is the first conjectural step in the proposed higher-order spectral scattering construction. The paper explains that endless continuability means analytic continuation indefinitely with certain poles, referring to work of Kamimoto–Sauzin and Écalle; the supplied text does not state that the conjecture has been proved or refuted.