The random-curve taut smoothing conjecture

A random curve means a curve sampled according to some sensible notion of randomness, for instance the notion considered by Aougab and Gaster. A taut smoothing is a smoothing with the tautness property defined in the paper.

Random-curve taut smoothing conjecture. A random curve has a taut smoothing.

This conjecture proposes that taut smoothings are generic in a probabilistic sense, but the paper does not specify a single notion of randomness or provide evidence resolving the claim.