Complete with the negative phrase formed from can and the adjective in brackets: The certificate claims to authenticate a Ming vase. The issuing authority's registry assigns its unique serial number to a washing machine and to no other object, so this certificate ___ for the vase. (authentic)

Erklärung

Cannot be authentic gives the confident negative conclusion because the certificate names the vase while its unique identifier is bound exclusively to another object. Must not be authentic would normally convey a prohibition rather than an evidence-based conclusion about its present status.