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Learn about Julia's revolutionary new package version resolver in this 34-minute conference talk from JuliaCon Global 2025. Discover how the Julia programming language has transitioned from a heuristic belief propagation-based solver to a more robust SAT-based approach for resolving package versions, addressing the inherent NP-hard nature of this computational problem. Explore the limitations of the previous system, including its inability to guarantee solution discovery, lack of optimality assurance, and rigid assumptions about semantic versioning that prevented proper handling of build and prerelease tags. Understand how the new SAT-based resolver overcomes these constraints by providing guaranteed solution finding when solutions exist, optimal result generation, and flexible version preference ordering that allows for different strategies such as preferring oldest versions or current versions. Gain insights into the technical architecture and implementation details of this significant improvement to Julia's package management system, presented by Stefan Karpinski, and learn how this advancement enhances the reliability and flexibility of dependency resolution in Julia projects.