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 for the exact manuscripts and available scope notes.