# Perfect-completeness reduction benchmark library

Family 105: Perfect completeness for 2-to-1 games. First review, 8 October 2026.

## Problem and potential new use

Solver researchers can test whether exact satisfiable cases and low-value gap cases expose weaknesses in approximation pipelines.

## Applicability and commercial boundary

An NP-hardness theorem is not a new efficient label-assignment solver. Fixed-gap alphabets and reductions must be reconstructed rather than invented.

## Initial business decision

Research infrastructure. Buyer demand and profitability remain hypotheses. This first pass does not establish a validated commercial market.

## Next verification action

Read the reduction and identify small concrete instances suitable for reproducible stress fixtures.

## Evidence scope

Catalog statement reviewed; inspect linked opportunity dossier for any deeper source review. This record alone does not establish full manuscript or proof verification.

Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json) for the exact manuscripts and available scope notes.