For a subring $R⊂ \mathbb Q$, a knot $K⊂S^3$ is called $R$**-slice** if there exists an embedded disk $D$ in an $R$-homology $4$-ball $B$ such that $∂(B,D) = (S^3,K)$, see [Definition 1.3, [KW16][1]]. We say $K$ is **rationally** (resp. **integrally**) slice if $R= \mathbb Q$ (resp. $= \mathbb Z$).

In terms of crossing, the minimal example of rationally slice knot seems (probably is) figure-eight knot $4_1$, see [Theorem 4.16, [Cha07][2]].

The classical definition of is that a knot $K ⊂ S^3$ is **slice** if it bounds a smoothly embedded disk $D^2$ in the $4$-ball $B^4$. Again in terms of crossing, the minimal example of slice knot is unknot $0_1$.

My question is that is there any minimal example of integrally slice knot?

  [1]: https://arxiv.org/pdf/1604.04870.pdf
  [2]: https://arxiv.org/pdf/math/0609408.pdf