  The concordance crosscap number $\gamma_c(K)$ of a knot $K$ is the smallest
crosscap number $\gamma_3(K')$ of any knot $K'$ concordant to $K$ (and with
$\gamma_3(K')$ defined as the least first Betti number of any nonorientable
surface $\Sigma$ embedded in $S^3$ with boundary $K'$). This invariant has been
introduced and studied by Zhang using knot determinants and signatures, and has
further been studied by Livingston using the Alexander polynomial. We show in
this work that the rational Witt class of a knot can be used to obtain a lower
bound on the concordance crosscap number, by means of a new integer-valued
invariant we call the Witt span of the knot.
