A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems

This is an arxiv preprint (not yet published) with zero signals of adoption, distribution, or public repository activity. The work presents a theoretical algorithmic contribution combining SDP relaxation hierarchies with spectral gap lower-bounding techniques for a specific quantum many-body problem class. The contribution is scientifically novel (hierarchical certificate approach to frustration-free systems) but highly specialized to theoretical quantum physics. No evidence of open-source release, package distribution, or user adoption. The paper appears to be pure theory/methods work without even a reference implementation repository linked. Defensibility is extremely low because: (1) zero replication cost—any competent quantum physics researcher can re-implement from the paper, (2) no network effects or data gravity, (3) purely algorithmic/theoretical, (4) no user base to create lock-in. Frontier risk is low because this solves a niche theoretical problem (rigorously certifying spectral gaps) that frontier labs do not prioritize; it's peripheral to their core products (LLMs, inference platforms, classical ML). The work is likely to remain in the academic literature without commercialization.