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As far as I searched, I couldn't find something valuable but is there any combinatorial (or computable) gadget for knots to guarantee them to be smoothly slice?

For example, by the virtue of the great article of Freedman, topologically slice knots have such gadget in the following fashion:

Theorem(Fre82): If $K$ has Alexander polynomial $1$, then $K$ is topologically slice.

But the converse of the theorem is not true due to the work of Hedden-Livingston-Ruberman in HLR12.

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Paolo Lisca showed that

Theorem(L07): If 2-bridge knot $K$ is ribbon, then $K$ is slice.

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