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This skill provides Claude with a rigorous framework for bidirectional programming based on Jules Hedges' foundations of the 4-kind lattice. It allows developers to model complex systems where information flows in multiple temporal directions—forwards (covariant) and backwards (contravariant)—using GF(3) multiplication to govern tensor products. This is especially valuable for building mathematically sound CRDTs, compositional game theory models, and cybernetic systems. By defining specific scoping rules for bivariant and invariant types, the skill ensures that operational semantics for data synchronization and state updates remain consistent and predictable across distributed environments.
