(a) The php script should be named S_LOG.php and can be assumed to reside in the root of the server (i.e. its URL is just SERVER_URL/S_LOG.php).
(b) All the php script needs to do is create/verify a subfolder on the server (can be assumed to already exist) "/S_LOG/" and create an empty (0 length) file in that subdirectory in response to a request from the sample html file.
(c) No need for any error handling or any feedback from the php script. The result of the php is never displayed.
(d) The html file should just demonstrate with a single link that calls the S_LOG() function with a placeholder for me to replace with the server URL, and any sample filename.
2. The goal here is for a site developed and maintained using static html only to be able, in response to a link click for instance, to silently create an empty file on the server by submitting a hidden form (or any other method that either uses GET or is otherwise invisible to the user).
3. Use of JQuery is fine (you can assume the latest available version), any other GPL'ed or unlicenced scripts like mootools etc. are also fine provided there is no issue in using it on a live site.