# Geometric Langlands correspondence provenance

Family 069: Global quantum geometric Langlands at irrational level. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Represent the claimed global unramified de Rham quantum geometric Langlands equivalence at irrational level.

## Applicability and commercial boundary

Quantum here describes a categorical deformation, not a quantum-computing circuit or hardware compiler. Irrational-level and category assumptions matter.

## 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

Map categories, functors and computable research examples rather than propose a consumer app.

## 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).

[Global quantum geometric Langlands at irrational level](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-quantum-geometric-Langlands-at-irrational-level-October-4-2026/quantum-langlands.pdf).