  The usual spinor construction from one fermion yields four irreducible
representations of the Virasoro algebra with central charge $c = 1/2$. The
Neveu-Schwarz (NS) sector is the direct sum of an $h = 0$ and an $h = 1/2$
module, and the Ramond (R) sector is the direct sum of two copies of an $h =
1/16$ module. In addition to the fundamental fermions, which represent a
Clifford algebra, and the Virasoro operators, there are infinitely many other
vertex operators, in one-to-one correspondence with the vectors (states) in the
NS sector. These give the NS sector the structure of a Vertex Operator
SuperAlgebra, and the R sector the structure of a ${\bold Z}_2$-twisted module
for that VOSA. Keeping both copies of the $h = 1/16$ modules in the R sector,
we can define intertwining operators in one-to-one correspondence with the
states in the R sector such that the usual Ising fusion rules for just three
modules are replaced by a rule given by the group ${\bold Z}_4$. The main
objective is to find a generalization of the VOSA Jacobi-Cauchy identity which
is satisfied by these intertwining operators. There are several novel features
of this new ``Matrix'' Jacobi-Cauchy Identity (MJCI), most of which come from
the fact that correlation functions made from two intertwiners are
hypergeometric functions. In order to relate and rationalize the correlation
functions we use the Kummer quadratic transformation formulas, lifting the
functions to a four-sheeted covering, branched over the usual three poles,
where the Cauchy residue theorem can be applied. The six possible poles on the
cover give six terms in the MJCI. Furthermore, we organize those functions into
$2\times 4$ matrices and find the $2\times 2$ (fusion and braiding) matrices
which relate them at the six poles. These results for intertwiners
