Naked singularities can be stable — if you choose the right ruler

Christodoulou showed in the 1990s that certain self-similar naked singularities form in scalar-field collapse and are unstable to black hole formation — but only under rough perturbations. This work proves the opposite: perturb the same solutions with smooth enough initial data and the naked singularity persists, stable at the nonlinear level. The result turns on the choice of functional space, showing that cosmic censorship is not a binary truth but a statement that depends critically on what class of perturbations is allowed. The finding forces a more precise formulation of one of general relativity's central open conjectures.