What is Circuit soundness? Definition and why it matters
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A circuit is sound with respect to a specification if every witness that satisfies its constraints also satisfies the specification, so a malicious prover cannot produce an accepting proof of a false statement.

Detail: Soundness is the property that rules out underconstrained circuits, and it is what most ZK verification efforts prove first. Because the adversary chooses the witness, a soundness argument must consider every satisfying assignment, not only the ones an honest witness generator produces. Soundness alone is not enough: a circuit with no satisfying assignments is vacuously sound. That is why Clean and zk.golf require completeness alongside it, and why a soundness-only theorem should be read together with tests showing the circuit accepts honest inputs.

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Last reviewed: 2026-09-13