String theory at order ??2 and the generalized Bergshoeff-de Roo identification

It has been shown by Marques and Nunez that the first $\alpha'$-correction to bosonic heterotic string can be captured in $O(D,D)$ covariant formalism of Double Field Theory via a certain two-parameter deformation double Lorentz transformations. This turn leads an infinite tower $\alpha'$-corrections it suggested they generalization Bergshoeff-de Roo identification between gauge degrees freedom extended DFT formalism. Here we provide strong evidence this indeed gives correct $\alpha'^2$-corrections showing cubic Riemann term for former but not latter, agreement with known structure these corrections including coefficient cubed.