  The stable Kauffman conjecture posits that a knot in $S^3$ is slice if and
only if it admits a slice derivative. We prove a related statement: A knot is
handle-ribbon (also called strongly homotopy-ribbon) in a homotopy 4-ball $B$
if and only if it admits an R-link derivative; i.e. an $n$-component derivative
$L$ with the property that zero-framed surgery on $L$ yields $\#^n(S^1\times
S^2)$. We also show that $K$ bounds a handle-ribbon disk $D \subset B$ if and
only if the 3-manifold obtained by zero-surgery on $K$ admits a singular
fibration that extends over handlebodies in $B \setminus D$, generalizing a
classical theorem of Casson and Gordon to the non-fibered case for
handle-ribbon knots.
