Two certificates Cert_k,a and Cert_k,b are said to be conflicting if both are valid with respect to the previous certificate Cert_k-1 but the operations associated with the two certificates do not have a legal sequential history. In other words, when taking the output state of Cert_k,a (resp. Cert_k,b) and passing it as input to Cert_k,b’s (resp. Cert_k,a) zk-STARK, the verification will fail.