The Johnson homomorphism formula for homologous bounding-pair maps

Let $\Sigma_g$ be a closed oriented surface of genus $g$, and let $\gamma,\gamma'$ be nonseparating simple curves that are homologous and disjoint from pairwise disjoint curves $\beta_1,\ldots,\beta_g$. Assume that the homology classes $[\beta_1],\ldots,[\beta_g]$ form a basis for a Lagrangian subspace of $\mathrm{H}_1(\Sigma_g,\mathbb{Z})$. Let $\alpha_1,\ldots,\alpha_g$ be curves such that $[\alpha_1],\ldots,[\alpha_g],[\beta_1],\ldots,[\beta_g]$ form a symplectic basis of $\mathrm{H}_1(\Sigma_g,\mathbb{Z})$. Define $\operatorname{sgn}_{\gamma,\gamma'}(\beta_i)\in\{0,\pm1\}$ according to whether $\beta_i$ is of type $LR$, $RL$, or neither, as specified by the regions determined by $\gamma$ and $\gamma'$ after cutting along the $\beta_i$. The Johnson homomorphism formula. The image of the Johnson homomorphism on the mapping class $T_{\gamma}T_{\gamma'}^{-1}$ is

$$\@ifnextchar_\@mysum\oldsum_{i=1}^{g}\operatorname{sgn}_{\gamma,\gamma'}(\beta_i)\,[\alpha_i]\wedge[\beta_i]\wedge[\gamma].$$

This is a conjectural formula for the Johnson homomorphism associated with a pair of homologous nonseparating curves; the supplied text gives no evidence resolving whether the formula is proved or remains open.