Researchers have formally verified Romanov's Triplet Logic (TLS), a mathematical theory for reasoning about compatible paths through layered structures. The verification was done using the Rocq proof assistant, which confirmed the correctness of TLS and its applications to Boolean satisfiability. A tool called VFR was also developed, providing a verified decision procedure for the sliding-window fragment and a sound one-sided filter for general 3-CNF. The research is significant because it establishes precise bounds on the performance of TLS-based filters. --- Why it matters: This work matters to AI researchers because it provides a formally verified foundation for reasoning about complex structures, which can be used in areas such as knowledge graph analysis and natural language processing. Source: https://arxiv.org/abs/2608.18445