Conjecture on coincidences of ribbon stable Grothendieck polynomials

A ribbon is a connected skew Young diagram containing no $2\times2$ block. For a ribbon $\alpha$, let $G_\alpha$ denote its stable Grothendieck polynomial, and let $\alpha^*$ denote the associated dual ribbon. Ribbon Grothendieck coincidence conjecture. For ribbons $\alpha$ and $\beta$,

$$G_\alpha=G_\beta$$

if and only if $\beta=\alpha$ or $\beta=\alpha^*$. This conjecture proposes that the coincidences among ribbon stable Grothendieck polynomials are exactly those arising in the dual case; its resolution is not given here.