# Termination-versus-runtime solver contract

Family 056: Termination of projective and Kähler fourfold minimal model programs. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Use generalized log-canonical flip termination to distinguish a permitted four-dimensional MMP sequence from a solver with bounded work.

## Applicability and commercial boundary

Existing sequences, rational Q-factorial data, nef b-data and projective small diagrams are required. Termination alone supplies no usable iteration bound.

## 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

Inspect effectiveness, step construction and explicit bounds before a symbolic pipeline.

## 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).

[Termination of generalized log canonical flips on compact Kähler fourfolds](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Termination-of-generalized-log-canonical-flips-on-compact-Kahler-fourfolds-October-7-2026/termination-generalized-lc-kahler-fourfolds.pdf).