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Given two schemas, automated migration discovery now builds a cost function network and minimizes its integer cost. The result includes a certificate stating whether optimality was proved and which solver ran.

The network has one variable per source vertex. Its domain contains kind-compatible target vertices plus ⊥, which means the vertex is omitted from the span. Each choice has an integer cost. The solver returns the minimum-cost complete assignment without enumerating every candidate.

Four solvers are available: bucket elimination in the (min, plus) semiring; hybrid best-first search with EDAC*; the same search with a counting Hall propagator for injective maps; and weighted partitioning for maximum common induced sub-schemas.

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