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Example：10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502
We define the stabilizing number $sn ( K )$ of a knot $K ⊂ S 3$ as the minimal number $n$ of $S 2 × S 2$ connected summands required for $K$ to bound a null‐homologous locally flat disk in $D 4 # n S 2 × S 2$. This quantity is defined when the Arf invariant of $K$ is zero. We show that $sn ( K )$ is bounded below by signatures and Casson–Gordon invariants and bounded above by the topological 4‐genus $g 4 top ( K )$. We provide an infinite family of examples with $sn ( K ) < g 4 top ( K )$.