# Kähler uniformization provenance module

Family 338: Yau's uniformization conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Complex-geometry researchers can document when positive holomorphic bisectional curvature implies biholomorphism to complex affine space.

## Applicability and commercial boundary

Existence of a biholomorphism does not give efficient coordinates or a general numerical uniformization algorithm.

## 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 information and a restricted computable example.

## 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).

[Uniformization of complete Kähler manifolds with positive bisectional curvature](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/paper.pdf).