OpenAI reports a sharp stationary-varifold singular-set bound

For every stationary integral m-varifold in an open Euclidean set, in every positive dimension and codimension, the singular set has Hausdorff dimension at most m−1.

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Understanding the problem

Read the background

For every stationary integral m-varifold in an open Euclidean set, in every positive dimension and codimension, the singular set has Hausdorff dimension at most m−1.

Why it matters

If correct, proves the sharp Euclidean codimension-one singular-set conjecture without stability or minimizing assumptions.

What counts as progress

Is the singular set of every stationary integral varifold at most codimension one?

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