# Six-dimensional Fano classification reference

Family 067: The Campana–Peternell conjecture in dimension six. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Track the claimed homogeneous-space conclusion for a six-dimensional Fano manifold with nef tangent bundle.

## Applicability and commercial boundary

The result is dimension six, not all dimensions; a nef tangent hypothesis is not a finite numeric observation.

## 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

Inspect computable invariants and classification witnesses.

## 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).

[The Campana–Peternell conjecture in dimension six](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Campana-Peternell-conjecture-in-dimension-six-September-25-2026/main.pdf).