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.

Ample rank-two bundles on the quadric surface without Griffiths-positive metrics.