Topological slice genus subadditivity conjecture for satellite knots

Let $P$ be a pattern, meaning a knot in a solid torus, and let $K$ be a knot in $S^3$. Write $P(K)$ for the satellite knot and $P(U)$ for the satellite of the unknot, and let $g_4^{\mathrm{top}}$ denote the topological slice genus. Topological slice genus subadditivity conjecture. For any pattern $P$ and knot $K$,

$$g_4^{\mathrm{top}}(P(K))\leq g_4^{\mathrm{top}}(P(U))+g_4^{\mathrm{top}}(K).$$

The conjecture asserts that the winding number of the pattern does not contribute to this upper bound, unlike the corresponding general bound involving a pattern 4-genus. The paper presents evidence for the claim, but does not establish it in general.