Mandel's extension conjecture for oriented matroids

An oriented matroid is a combinatorial abstraction of a vector or hyperplane configuration, and an extension $\mathcal{O}\cup g$ adds a new ground-set element $g$; the extension is in general position when $g$ is not a coloop and satisfies the usual general-position condition. For elements $f$ of $\mathcal{O}$ that are neither loops nor coloops, $(\mathcal{O}\cup g,g,f)$ denotes the corresponding oriented matroid program.

Mandel's conjecture. Every oriented matroid $\mathcal{O}$ has an extension $g$ in general position (not a coloop) such that $(\mathcal{O}\cup g,g,f)$ is a Euclidean oriented matroid program for all elements $f$ of $\mathcal{O}$ that are not loops or coloops.

This conjecture is the source of the paper's definition of Mandel oriented matroids. The supplied text gives no resolution status or general theorem establishing the claim.