# Numerical semiampleness model contract

Family 036: Numerical semiampleness and generalized minimal models. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Distinguish numerical equivalence conclusions for adjoint divisors from actual section-based semiampleness.

## Applicability and commercial boundary

Klt, rational divisor, characteristic-zero and Kähler Bott–Chern regimes have different data. Generalized-pair conclusions require nef b-data.

## 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

Map exact equivalence relations and construction effectiveness in each manuscript.

## 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).

[Numerical semiampleness of nef adjoint classes on compact Kähler manifolds](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Numerical-semiampleness-of-nef-adjoint-classes-on-compact-Kahler-manifolds-October-6-2026/numerical-generalized-abundance.pdf).