Representability conjecture for single relaxations of K(r,t)

Let $K(r,t)$ be the non-representable matroid considered in the paper, with integers $r$ and $t$ satisfying

$$r \ge 4,\qquad t \ge 3,\qquad 2t+2 \ge r+4.$$

A relaxation of a circuit-hyperplane means replacing that circuit-hyperplane by a basis.

Representability conjecture for K(r,t). Every matroid obtained from $K(r,t)$ by relaxing a circuit-hyperplane into a basis is representable.

This conjecture formalizes the claim that $K(r,t)$ is close to representable despite itself being non-representable. The supplied text does not state whether it has been resolved.