Bi-Lipschitz coordinates at every regular RCD point

What OpenAI claims

Proves that every regular point of a noncollapsed RCD (K,n) space, for K ∈ ℝ and integer n ≥ 2, has an open neighborhood bi-Lipschitz to an open subset of ℝn. Regularity requires all pointed tangents to be Euclidean, the reference measure is exactly ℋⁿ, and the chart compares ambient distances with a point-dependent finite constant.

Paper

1. Bi-Lipschitz Coordinates at Regular Points of Noncollapsed RCD Spaces

   25 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract We resolve the regular-point bi-Lipschitz conjecture in the noncollapsed setting. For every integer n ≥ 2 and every real K, every regular point of a noncollapsed RCD(K,n) space has an open neighborhood bi-Lipschitz homeomorphic to an open subset of ℝn. The bi-Lipschitz constant depends only on n, and the neighborhood uses the restricted ambient distance.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.