# Varifold regularity class audit

Family 346: Sharp singular-set bounds for stationary integral varifolds. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Geometric solver researchers can record what singular-set size is permitted for stationary integral varifolds in Euclidean or spherical settings.

## Applicability and commercial boundary

Stationarity and integral-varifold status require evidence. A dimension bound does not identify singular points or certify a finite numerical surface.

## 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

Pair the source with a separate discretization and stationarity-error analysis.

## 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).

[A Codimension-One Bound for the Singular Set of a Stationary Integral Varifold](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Codimension-One-Bound-for-the-Singular-Set-of-a-Stationary-Integral-Varifold-October-5-2026/varifold-singular-dimension.pdf).