  There is a well-known construction of a Jordan algebra via a sharped cubic
form. We introduce a generalized sharped cubic form and prove that the split
spin factor algebra is induced by this construction and satisfies the identity
$((a,b,c),d,b) + ((c,b,d),a,b) + ((d,b,a),c,b) = 0$. The split spin factor
algebras have recently appeared in the classification of 2-generated axial
algebras of Monster type fulfilled by T. Yabe; their properties were studied by
J. McInroy and S. Shpectorov.
