Refined left Gog–GOGAm trapezoid equienumeration conjecture

For each $n,k$, consider left Gog and GOGAm trapezoids of shape $(n,k)$, and let $X_{1,1}=l$ denote their bottom entry. Refined left Gog–GOGAm conjecture. For each $n,k,l$, the $(n,k)$ left Gog and GOGAm trapezoids with bottom entry $X_{1,1}=l$ are equienumerated. This refines the unweighted left-trapezoid conjecture by requiring equienumeration separately at every fixed bottom-entry value; the source gives no resolution.