Double-circuit formulation of the X-replacement conjecture

Let $D$ be a double ${\mathcal R}_3$-circuit, and let $w$ be a technicolour vertex of degree $5$ in $D$. The principal partition of $D$ is the partition associated with its double-circuit structure. Double-circuit X-replacement conjecture. Every pair of non-adjacent edges between four vertices in the neighbourhood of $w$ belongs to different parts of the principal partition of $D$. This is stated as a reformulation of the Tay–Whiteley $X$-replacement conjecture and is therefore open in the source.