Given a domain $R$ in $N^{*}_{\mathbb{R}}/\sigma\times N_{\mathbb{R}}/\tau\cong\mathbb{R}^{n}\times\mathbb{R}^{l}$ a $(\sigma,\tau)$-type singular solution to the split Monge-Ampère equation in $R$ is a pair of matrix functions $V^{ij},W^{pq}$ which are local Monge-Ampère solutions in $R\setminus(\Pi(\tau)\times\Pi(\sigma))$ with asymptotics at the discriminant locus governed by the distributional equation