# Quaternionic and contact classification ledger

Family 062: Projective contact classification and the LeBrun–Salamon conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Link positive quaternionic Kähler manifolds of real dimension at least eight with the claimed Wolf-space classification and contact companions.

## Applicability and commercial boundary

Dimension, curvature and contact/Fano hypotheses cannot be inferred from an arbitrary finite point cloud.

## 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 concrete invariants and a computable example before any geometric software adapter.

## 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).

[Contact Fano manifolds and the LeBrun–Salamon conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Contact-Fano-manifolds-and-the-LeBrun-Salamon-conjecture-September-23-2026/paper.pdf).