# Holomorphic splitting integrability contract

Family 052: Tangent splittings and product decompositions. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Distinguish an integrable tangent splitting and product universal cover from an arbitrary vector-bundle decomposition.

## Applicability and commercial boundary

Integrability is an explicit assumption except in the stated rationally connected setting; no cheap decomposition algorithm follows.

## 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

Read the integrability hypotheses and one explicit splitting example.

## 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).

[Universal-cover splitting for compact Kähler manifolds](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf).