I'll explain my case as an example, but I think the problem applies to other web projects as well:
I have developed a Telegram bot in Python and made its source public. Then, I have deployed the bot on Heroku, where it is running now. The question is, how can I assure users that the bot runs on the shared code and not on a modified version?
I'm asking for web applications in general, but if there are specific tools or methods for Python or Heroku, I'll be happy to learn about them to use in this project.
EDIT: Judging by the comments and answers, I think the task is not possible as long as the server's contents cannot be reached by the users. I do not know if Heroku allows access to the app's files, but some tools for other kinds of projects exist. For example, a webpage repository on Github can be configured to be hosted in github.io, and the source on Github is guaranteed to be the same as the hosted site's source.
Please let me know if you know of a tool or method that applies to my case.