Splitting conjecture for tangent cones at infinity of manifolds with non-negative Ricci curvature

Let $M$ be a complete Riemannian manifold with $\operatorname{Ric} \ge 0$, and let $u$ be a non-constant solution of the minimal surface equation satisfying the one-sided linear growth condition

$$.$$

A tangent cone at infinity of $M$ is a pointed metric-measure limit obtained by rescaling $M$ along a sequence of scales tending to infinity.

Splitting conjecture. Every tangent cone at infinity $M_\infty$ splits isometrically as

$$M_\infty = N_\infty \times \mathbb{R}.$$

The conjecture concerns the geometric structure forced by a non-constant minimal graph with one-sided linear growth on a manifold with non-negative Ricci curvature. It was verified under the stronger assumption that $u$ is globally Lipschitz, while the stated version is resolved according to the supplied status information.