M-theory $R^4H^{4g-4}$ U-duality conjecture

Let M-theory be compactified on $T^{d+1}$ with $d\leq4$, let $H$ denote the resulting three-form field strengths, and let $M(\mathrm{string})$ be the mass matrix in the string representation of $E_{d+1(d+1)}$. M-theory $R^4H^{4g-4}$ conjecture. Up to a power of Newton's constant, the coupling between four gravitons and $4g-4$ three-form field strengths is

$$I=\frac{V_{d+1}}{l_M^9}\int d^{10-d}x\sqrt{-\gamma}\,\widehat{\sum_m}\delta(m\wedge m)\frac{R^4(m\cdot H)^{4g-4}}{(m\cdot M(\mathrm{string})\cdot m)^{3g-\frac32}}.$$

The claim is motivated by the decomposition of the string multiplet under T-duality and is presented as a proposed non-perturbative completion; the source gives no resolution evidence.