# Positive-characteristic threefold adjoint contract

Family 035: Log-canonical threefold abundance in numerical dimension one. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Track semiampleness for a nef log-canonical threefold divisor of numerical dimension one.

## Applicability and commercial boundary

Characteristic greater than three, projectivity and numerical dimension one are required. No general positive-characteristic optimizer is supplied.

## 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 a computable divisor example and the multiple or section construction.

## 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).

[Log abundance in numerical dimension one for threefolds in positive characteristic](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Log-abundance-in-numerical-dimension-one-for-threefolds-in-positive-characteristic-October-5-2026/paper.pdf).