Type IIA $R^4H^{4g-4}$ constrained-Eisenstein-series conjecture

Let type IIA string theory be compactified on $T^d$ with $d\leq 4$, let $\phi$ be the T-duality-invariant dilaton, let $H_{RR}$ denote the Ramond three-form field strengths, and let $M(\mathbf S)$ be the $SO(d,d)$ mass matrix in the spinor representation. Type IIA $R^4H^{4g-4}$ conjecture. The genus-$g$ coupling between four gravitons and $4g-4$ Ramond three-form field strengths is given by

$$I=\int d^{10-d}x\sqrt{-\gamma}\,\widehat{\sum_m}\delta(m\wedge m)e^{6(g-1)\phi}\frac{R^4(m\cdot H_{RR})^{4g-4}}{(m\cdot M(\mathbf S)\cdot m)^{3g-2}}.$$

The restriction $d\leq4$ is explained by dualization of the field strengths in lower dimensions; the source gives no resolution evidence.