Simpler expression for the limiting constant

Derive a simpler expression for the constant c_\mathcal{R}=\int_0^1\mathbb{E}\left|\sum_{m\in\mathbb{Z}}Y_m\,\operatorname{sinc}(\pi(t-m))\right|\,dt, where the Y_m are independent Steinhaus random variables.

Background

The paper’s main construction produces the constant c_\mathcal{R}=0.953\ldots as an integral of the expected absolute value of a random sinc interpolation series. This constant determines the asymptotic lower bound obtained for the Wiener norms of the constructed integer sets.

Although the paper explains how to approximate the value numerically by truncation and sampling, it explicitly notes that no simpler expression for the right-hand side is known. The unresolved issue is therefore to obtain a more elementary or closed-form representation of this limiting constant.