This members-only tutorial provides the steps to register a custom condition using which elements can be output only if the current user is logged in, is an author and has at least 1 published entry of the selected Custom Post Type in Oxygen.
For a possible use case for this condition, see this Facebook post.
Step 1
Install and activate Code Snippets plugin.
Go to Snippets > Add New.
Title: Author has CPT entry
Code: