# Bundle positivity assumption audit

Family 050: A counterexample to Griffiths’ positivity conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Record that ampleness of a rank-two bundle need not supply a Griffiths-positive Hermitian metric.

## Applicability and commercial boundary

The specified bundle on the product of two projective lines does not contradict all positive-curvature results or produce a mesh solver.

## 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 bundle and curvature obstructions with coefficient and base conditions.

## 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).

[Ample rank-two bundles on the quadric surface without Griffiths-positive metrics](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/ample-rank-two-bundles-on-the-quadric-surface-without-griffiths-positive-metrics-September-24-2026/paper.pdf).