The model class image-containment conjecture for secondary obstruction complexes

Let $(Y,T^*_{Y,-})$ be a $gt$-model. The secondary obstruction complex has differentials

$$\partial^{\{a,b\}}:{\bf H}^{a,b}_p(Y,T^*_{Y,-})\longrightarrow {\bf H}^{a-1,b+1}_{p+1}(Y,T^*_{Y,-}).$$

Let $\Theta(T^*_{Y,-})$ denote the model class and let $(\Theta(T^*_{Y,-}),-)^{\{a,b\}}_*$ be the induced map on the corresponding groups. Model class image-containment conjecture. For any $gt$-model $(Y,T^*_{Y,-})$ and any $a,b$,

$$\operatorname{im}\big(\Theta(T^*_{Y,-}),-\big)^{\{a,b\}}_*\subseteq \operatorname{im}\partial^{\{a,b\}}.$$

This conjecture predicts that the model class gives a map whose image is detected by the secondary obstruction complex, clarifying how the model class can obstruct families with refined splitting type. Its resolution status is not specified in the supplied text.