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OpenAI reports the purely cosmetic surgery conjecture for knots

Individual problem

For any nontrivial smooth knot in the three-sphere, Dehn surgeries along distinct slopes never produce orientation-preservingly homeomorphic filled three-manifolds.

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Understanding the problem

Read the background

For any nontrivial smooth knot in the three-sphere, Dehn surgeries along distinct slopes never produce orientation-preservingly homeomorphic filled three-manifolds.

Why it matters

If correct, resolves the purely cosmetic surgery conjecture for knots in the three-sphere.

What counts as progress

Can distinct surgery slopes on a nontrivial knot yield the same oriented three-manifold?

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