# Complement-index boundedness contract

Family 066: Bounded klt complements for Fano contractions. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Organize uniform bounded complement indices under fixed dimension, coefficient, epsilon and Fano-type assumptions.

## Applicability and commercial boundary

Bounded existence is distinct from constructing a complement; relative and absolute regimes need separate inputs.

## 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 an explicit bound and construction cost before a CAS component.

## 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).

[Bounded klt complements for Fano contractions](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Bounded-klt-complements-for-Fano-contractions-September-25-2026/Bounded-klt-complements-for-Fano-contractions-September-25-2026.pdf).