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The TLA+ Formal Specification skill enables Claude to design, document, and verify high-stakes software systems using mathematical precision. It provides specialized guidance for creating TLA+ modules and PlusCal algorithms, focusing on safety and liveness properties to eliminate race conditions and logic errors before implementation begins. By following a documentation-first approach based on Leslie Lamport's formal methods, this skill helps developers model everything from consensus protocols to intricate microservice workflows, ensuring system reliability through exhaustive state-space exploration and model checking principles.