OpenAI reports the planar Schrödinger convergence endpoint

For initial data in H^(1/3)(R^2), the planar Schrödinger evolution converges almost everywhere to the data as positive time tends to zero, with the pointwise evolution defined by a Gaussian regularization limit first.

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Understanding the problem

Read the background

For initial data in H^(1/3)(R^2), the planar Schrödinger evolution converges almost everywhere to the data as positive time tends to zero, with the pointwise evolution defined by a Gaussian regularization limit first.

Why it matters

If correct, settles the sharp planar Sobolev endpoint of Carleson’s Schrödinger convergence problem.

What counts as progress

Does planar Schrödinger evolution recover every H^(1/3) initial datum almost everywhere as time tends to zero?

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