From my understanding, JavaScript code, because it is client-side, is not hidden to the client, and is hence de facto open source.
I am aware of “code obfuscation”, but according to Wikipedia, “At best, obfuscation merely makes it time-consuming, but not impossible, to reverse engineer a program.”
Is it possible to truly hide your JavaScript code, to keep it closed source?
Open-source doesn’t mean “I can see the source”. It means, loosely, “the licence allows me to re-distribute this source and do what I like with it [disclaimer: see licence terms]”. So your terminology is in error.
Ultimately, if you are delivering your Javascript to a web browser on your user’s PC, the user has as much access to it as does his PC. You can’t prohibit that. You can mitigate it slightly with obfuscation, but the Wikipedia quote is absolutely correct.
Just provide quality software and move on.