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Why does the cosmic censorship conjecture hold so well?

Penrose proposed spacelike singularities and closed timelike curves are always hidden behind event horizons in general relativity. His conjecture appears to hold pretty well. But he only assumed some energy condition (null, weak, dominant) for it to hold, and some topological assumptions on the initial conditions? That makes it a mathematical conjecture? If so, why does it hold so well?

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