Said another way, is there a way to ensure that the commands/code executed by such a program are all and only the commands and code specified in a publicly disclosed repository?
The motivation for this question is the following: In an age of highly sophisticated hackers as well as pressures from government agencies for "backdoors" that allow them to snoop on private transactions and exchanges, can we ensure that an application has been neither been hacked nor had a backdoor added?
For example, consider a server running python code like PyBitMessage (Bitmessage/PyBitmessage on github) for secure messaging.
Or consider an open source-based nodejs application like lesspass (lesspass/lesspass on github) which is used to manage passwords and available for use here (https://lesspass.com/#/).
Or an alternative program for a similar purpose encryptr (SpiderOak/Encryptr on github) with its downloadable version (https://spideroak.com/solutions/encryptr).
Is there a way to ensure that the versions available on their sites to download/use/install are running exactly the same code as is presented in the open source code?
Even if we have 100% faith in the integrity of the the teams behind applications like these, how can we be sure they have not been coerced by anyone to alter the running/downloadable version of their program to create a backdoor for example?
Thank you for your help with this important issue.
Note: Since this question concerns interpreted programs, the conversation on deterministic or reproducible builds did not seem to apply and seemed worth a new question.