Is Oracle Solaris officially declared UNIX? I want to know all the official UNIX presently available in the market (weather free or paid)

Please correct me if I am wrong: To the best of my knowledge, an operating system must satisfy all the terms and conditions as laid by the owners of "UNIX", The Open Group; to be coined as UNIX. Linux is an UNIX-like kernel almost resembling UNIX but still open-source and free to distribute.