# Holomorphic coordinate limitation reference

Family 359: Negative Kähler curvature without bounded holomorphic coordinates. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Complex-geometry researchers can separate negative Kähler curvature from bounded-coordinate uniformization.

## Applicability and commercial boundary

The contractible complex-three-dimensional counterexample and unbounded-curvature companion do not forbid useful local coordinates or numerical approximations.

## 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

Preserve the two curvature regimes and extract a concrete domain representation.

## 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 negatively pinched Kähler threefold without bounded holomorphic coordinates](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-negatively-pinched-Kahler-threefold-without-bounded-holomorphic-coordinates-September-25-2026/paper.pdf).