Bi-Lipschitz charts at every regular point of a noncollapsed RCD(K,n) space

Claims that for every integer $n\ge2$ there is $L_n\ge1$ such that every regular point of every noncollapsed $\mathrm{RCD}(K,n)$ space, $K\in\mathbb R$ , has an open neighborhood $L_n$ -bi-Lipschitz homeomorphic, with the ambient distance, to an open subset of $\mathbb R^n$ ; the neighborhood depends on the space and the point. Corollary: an open set of full $\mathcal H^n$ measure containing all regular points carries a countable bi-Lipschitz atlas with $L_n^2$ transition maps. It does NOT claim that the regular set is open, any collapsed or non-RCD statement, or regularity of the metric tensor in the charts.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 25, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Bi-Lipschitz charts at every regular point of a noncollapsed RCD(K,n) space · Bi-Lipschitz charts at RCD regular points

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
model · ai model contributor · OpenAI

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VibeMathed record: Bi-Lipschitz charts at every regular point of a noncollapsed RCD(K,n) space

specialist registry · passed

No independent mathematician has checked this yet. Theorem 1.1 was read against the conjecture as the manuscript states it; Honda-Zhang was not opened here. Scope limits the paper states: noncollapsed means the reference measure is exactly $\mathcal H^n$ ; regularity means every tangent at the point is Euclidean; the chart is an open neighborhood with the restricted ambient distance; no Holder control of the metric tensor and no bounded-Laplacian coordinates are claimed (Colding-Naber examples show the former can fail). Note the release's family summary says the constant is point dependent, but the manuscript's Theorem 1.1 and abstract say the constant $L_n$ depends only on $n$ . No Lean formalization exists for this family.

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Bi-Lipschitz charts at every regular point of a noncollapsed RCD(K,n) space

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Honda and Zhang (arXiv:2608.16021), Section 1.2, where the conjecture is recalled

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

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VibeMathed record: Bi-Lipschitz charts at every regular point of a noncollapsed RCD(K,n) space evidence for this event

Bi-Lipschitz charts at every regular point of a noncollapsed RCD(K,n) space evidence for this event

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Honda and Zhang (arXiv:2608.16021), Section 1.2, where the conjecture is recalled evidence for this event

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