Simple $5$-dimensional right alternative superalgebras with trivial even part

We study the simple right alternative superalgebras whose even part is trivial; i.e., the even part has zero product. A simple right alternative superalgebra with the trivial even part is singular. The first example of a singular superalgebra was given in [1]. The least dimension of a singular superalgebra is $5$. We prove that the singular $5$-dimensional superalgebras are isomorphic if and only if suitable quadratic forms are equivalent. In particular, there exists a unique singular $5$-dimensional superalgebra up to isomorphism over an algebraically closed field.