Linked paper: https://arxiv.org/abs/2506.24088

“Unknotting number is not additive under connected sum” (2025 v1)

> We give the first examples of a pair of knots K1,K2 in the 3-sphere for which their unknotting numbers satisfy u(K1#K2)<u(K1)+u(K2) . This answers question 1.69(B) from Kirby's problem list, "Problems in low-dimensional topology", in the negative.