Examining how certificate chains are built and validated, it is important to note that a concrete certificate can be part of very different certificate chains (all of them valid). This is because several CA certificates can be generated for the same subject and public key, but be signed with different private keys (from different CAs or different private keys from the same CA). So, although a single X.509 certificate can have only one issuer and one CA signature, it can be validly linked to more than one certificate, building completely different certificate chains. This is crucial for cross-certification between PKIs and other applications.