# Complex-manifold Oka classification reference

Family 042: Oka classification for minimal compact complex surfaces: Kodaira dimension zero and class VII. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Support researchers comparing Oka properties of minimal compact complex surfaces of Kodaira dimension zero and specified class-VII surfaces.

## Applicability and commercial boundary

These geometric existence properties do not yield an automatic holomorphic interpolation solver or classify every complex manifold.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

## Next verification action

Extract one constructive interpolation example and distinguish the surface classes.

## Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Every complex K3 surface is Oka](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Every-complex-K3-surface-is-Oka-September-23-2026/paper.pdf).