The strictly upper triangular holonomy conjecture for a model manifold with density

Let $M^n$ carry the metric

$$g = e^{x_1}dx_1^2 + e^{2x_1+x_2}dx_2^2 + \cdots + e^{2x_1+\cdots+2x_{n-1}+x_n}dx_n^2$$

and density potential $\phi=x_1+x_2+\cdots+x_n$. Compute the holonomy Lie algebra at the origin $(0,0,\ldots,0)$. Strictly upper triangular holonomy conjecture. The holonomy Lie algebra is precisely the Lie algebra of strictly upper triangular matrices. This conjecture generalizes the explicitly verified two- and three-dimensional examples, where the holonomy is respectively the corresponding strictly upper triangular group; its status is not resolved in the supplied source.