# Hypersymplectic deformation research toolkit

Family 341: Donaldson's hypersymplectic deformation conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Geometry researchers can organize cohomology-preserving paths from positive closed triples to hyperkähler triples.

## Applicability and commercial boundary

Existence of a deformation is not a stable discretized flow or an efficient metric optimizer; positivity and closed four-manifold hypotheses matter.

## 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 quantitative flow estimates and an explicit initial triple.

## 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).

[Deforming hypersymplectic four-manifolds to hyperkähler triples](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-October-7-2026/paper.pdf).