# Injectivity-radius rigidity research reference

Family 344: The metric Blaschke conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Geometry researchers can recognize the exact classification triggered by equality of injectivity radius and diameter.

## Applicability and commercial boundary

Noisy numerical equality is not a rigidity certificate, and no stability or efficient classification algorithm is supplied.

## 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

Seek a quantitative near-equality theorem before proposing a finite-mesh shape diagnostic.

## 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).

[The metric Blaschke theorem](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-metric-Blaschke-theorem-September-23-2026/paper.pdf).