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.

Deforming hypersymplectic four-manifolds to hyperkähler triples.