The 3-connected stabilizer conjecture for universal partial fields

Let $N$ be a 3-connected matroid. A matroid is ${\mathbb{P}}_N$-representable when it has a representation over the universal partial field ${\mathbb{P}}_N$. The matroid $N$ is a ${\mathbb{P}}_N$-stabilizer for a class of matroids when its representations determine representations of the matroids in that class up to the relevant equivalence. 3-connected stabilizer conjecture. If $N$ is 3-connected, then $N$ is a ${\mathbb{P}}_N$-stabilizer for the class of ${\mathbb{P}}_N$-representable matroids.

The conjecture is presented as related to uniqueness of representation and as having important implications, including an immediate consequence of a theorem attributed to Geelen, Gerards, and Whittle. The source does not state that it has been resolved.