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In dimension four, the differences between continuous and differential topology are vast but fundamentally unstable, disappearing when manifolds are enlarged in various ways. I will discuss Wall's stabilization problem and some of its variants, all of which aim to quantify this instability. In particular, I'll outline a simple "atomic" approach to these problems and, as a proof of concept, use it to produce exotic pairs of knotted surfaces (with boundary) in the 4-ball that remain exotic after one "internal stabilization". The key obstruction comes from the universal version of Khovanov homology. Time permitting, I will speculate on some potential connections to Floer homology.