Open r-spin theory II: The analogue of Witten’s conjecture for r-spin disks

We conclude the construction of r-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define open r-spin intersection numbers, and we prove that their generating function is closely related to the wave function of the rth Gelfand-Dickey integrable hierarchy. This provides an analogue of Witten's r-spin conjecture in the open setting and a first step toward the construction of an open version of Fan-Jarvis-Ruan-Witten theory. As an unexpected consequence, we establish a mysterious relationship between open r-spin theory and an extension of Witten's closed theory.