If you plan to use your wrapper in a require_once you need to define stream_stat(). If you plan to allow any other tests like is_file()/is_dir(), you have to define url_stat().
stream_stat() must define the size of the file, or it will never be included. url_stat() must define mode, or is_file()/is_dir()/is_executable(), and any of those functions affected by clearstatcache() simply won't work.
It's not documented, but directories must be a mode like 040777 (octal), and files a mode like 0100666. If you wish the file to be executable, use 7s instead of 6s. The last 3 digits are exactly the same thing as what you pass to chmod. 040000 defines a directory, and 0100000 defines a file. It would be really helpful to add this to the official manual!