# Matching formulation complexity audit

Family 126: Exponential semidefinite complexity of perfect matching. First review, 8 October 2026.

## Problem and potential new use

Optimization researchers can review claims that exact general matching polytopes admit small semidefinite formulations.

## Applicability and commercial boundary

A lower bound on exact lifts does not establish slow matching algorithms; maximum matching remains a different computational task.

## 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 slack-matrix model and produce a precise formulation-versus-algorithm explanation.

## 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.