Conjecture on the Courant contact model and the cubic model

Let the Courant contact model be the local $L_\infty$-algebra construction associated to the relevant Courant algebroid, and let the cubic model be the constrained-field model introduced by Ashmore. Conjecture. The Courant contact model should be quasi-isomorphic, as sheaves of $L_\infty$ algebras, to the cubic model of Ashmore. The conjecture compares an unconstrained BV-compatible Courant contact model with the cubic model known to reproduce minimal type I BCOV theory in the Calabi–Yau case; it remains open here.