# Adjoint linear-system generation contract

Family 038: Fujita’s freeness conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Provide a research reference for global generation of the specified adjoint line bundle on a smooth complex projective variety.

## Applicability and commercial boundary

An existence theorem for generating sections does not construct a basis cheaply; dimension and ampleness are required.

## 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

Compare explicit section computations with an existing algebraic-geometry workflow.

## 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).

[Fujita's freeness conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Fujitas-freeness-conjecture-September-23-2026/Fujitas-freeness-conjecture-September-23-2026.pdf).