How smooth can Nash–Kuiper embeddings be? Recent progress identifies a strict threshold at \(C^{1,1/2}\)

New popularized and high-level survey on _Quanta_:

Nash embedding theorem (here, in the form that all 2d surfaces have non-smooth embeddings in 3d preserving distances along surface curves):

For the notions of fractional smoothness considered here, left unexplained by the _Quanta_ article, see:

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