Conjecture on the Courant contact model and the extended BPS complex

Let $\mathcal E_{\mathrm{twist}}$ be the Courant algebroid associated to the twist, and let the extended BPS complex be the complex for $G=U(5)\times SO(10+k)$ associated to the corresponding involutive subbundle. Conjecture. The complex underlying the Courant contact model should be quasi-isomorphic to the extended BPS complex for $G=U(5)\times SO(10+k)$. This proposes a comparison between two complexes arising from generalized $G$-structures and twisted supergravity; it remains conjectural in the paper.