3f+1 Replica Bound
To tolerate f Byzantine faults without synchrony, at least 3f+1 replicas are required: with fewer, the f faulty nodes plus f slow honest nodes leave the remainder unable to distinguish honest disagreement from lies. Equivalently, quorums of 2f+1 out of 3f+1 guarantee any two quorums intersect in at least one honest replica.
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To tolerate f Byzantine faults without synchrony, at least 3f+1 replicas are required: with fewer, the f faulty nodes plus f slow honest nodes leave the remainder unable to distinguish honest disagreement from lies. Equivalently, quorums of 2f+1 out of 3f+1 guarantee any two quorums intersect in at least one honest replica.
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