Finite-dimensionality conjecture for bounded biharmonic functions on manifolds with nonnegative Ricci curvature

Let $M$ be an open manifold with nonnegative Ricci curvature, and let $u$ be a bounded biharmonic function on $M$, meaning that $abla^4 u=0$ in the source's terminology via the biharmonic equation $Delta^2u=0$. Bounded biharmonic-function conjecture. Every bounded biharmonic function on $M$ is constant. The source presents this as a natural conjecture because bounded biharmonic functions can be nonconstant on some complete noncompact manifolds, while the resolution status is not specified.