A lifting defect for oriented t₃ and t₆ moves

We study oriented t₃- and t₆-moves through the problem of lifting Fox $3$-colorings to colorings by a nine-element Alexander quandle. We define a nonnegative integer lifting defect $δ$ for oriented links and prove that it is invariant under these moves. For knots, the defect equals the rank of an alternating bilinear form obtained from a Seifert matrix, so it is even. We also prove that it is additive under connected sum. Let Kₛ be the connected sum of s≥ 1 copies of 9₄₆. Then δ(Kₛ)=2s, so these knots represent infinitely many distinct equivalence classes under the oriented moves, and none is equivalent to an unlink. After forgetting orientation, each Kₛ can be transformed into an unlink with $2s+1$ components by $3s$ ordinary $3$-moves.