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Earlier work with Robert Gompf and Abigail Thompson classified, via a naturalslope indexed by the rationals, all two-component links which contain thesquare knot and from which $(S^1 \times S^2) \# (S^1 \times S^2)$ can beobtained by surgery. It was argued that a certain family $L_n$ of such linksprobably contradict the Generalized Property R Conjecture. Left unresolved washow the family $L_n$ fits into the classification scheme. This question isresolved here, in part by giving varied perspectives and more detail on theconstruction of the $L_n$.

Proposed Property 2R counterexamples classified