After searching the docs, the forums and the issues on GitHub for a while I was not able to determine which version of osTicket supports which versions of PHP.
(The docs < PHP 5.6+, but various GitHub issues suggest that there is an upper bound for each version of osTicket.)
I am personally interested in whether osTicket 1.12 will run on PHP 7.2 without problems.
But regarding the broader issue I think there should be a detailed compatibility matrix available in the docs. If someone can provide the necessary information I could open a pull request for the docs on GitHub.
Cheers,
bmorg