Parity conjecture for epsilon-torsion in the 2-complete real motivic stable homotopy ring

Let $\alpha$ have degree $(s,w)$ in the $2$-complete $\mathbb{R}$-motivic stable homotopy ring.

Parity conjecture. If $(1-\epsilon)\alpha$ is non-zero, then $w$ is even.

This pattern was observed in a large-range inspection of the $2$-complete $\mathbb{R}$-motivic stable homotopy groups. The supplied context does not state whether the claim has been proved or disproved.