# Almost-complex compatibility assumption map

Family 342: Donaldson's tamed-to-compatible conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Geometry researchers can distinguish tamed and compatible symplectic forms while preserving the almost complex structure.

## Applicability and commercial boundary

The cohomology class may change; the result does not give a numerical form solver or guarantee a prescribed class is retained.

## 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

Record this degree of freedom in a formal or computational geometry adapter.

## 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).

[Taming implies compatibility on four-manifolds](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Taming-implies-compatibility-on-four-manifolds-October-6-2026/paper.pdf).