Existence of a non-trivial intertwining from the infinite Ehrenfest process to the Ornstein–Uhlenbeck process

Let $D_{\infty}$ denote the infinite Ehrenfest process and let $L$ be the Ornstein–Uhlenbeck operator. An intertwining existence conjecture. There exists a non-trivial intertwining from $D_{\infty}$ to $L$. The conjecture is motivated by an abstract group-theoretical approach, although the previously claimed intertwining in Biane's work does not hold. Its status is unresolved in the supplied source.