# RCD local coordinate research toolkit

Family 357: Bi-Lipschitz coordinates at every regular RCD point. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Metric geometry researchers can document bi-Lipschitz neighborhood coordinates at points with all Euclidean tangents.

## Applicability and commercial boundary

The point-dependent constant and existence statement give no efficient chart algorithm or uniform global embedding of a sampled dataset.

## Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

## Next verification action

Inspect constructive coordinate methods and effective constants for a restricted model.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Bi-Lipschitz Coordinates at Regular Points of Noncollapsed RCD Spaces](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bi-Lipschitz-Coordinates-at-Regular-Points-of-Noncollapsed-RCD-Spaces-September-25-2026/paper.pdf).