I am a PhD student in theoretical computer science. It is my understanding that if I work on a paper without my PhD advisor (which is common in my research area) and without any lab resources then that work is my own, and I can submit the paper where I choose. In particular, my advisor cannot force me to add them as a co-author if they have not contributed to the paper either intellectually or in the form of resources. Is this the most widely held view among scientists? What if the PhD student is an RA for 20 hours a week?
If your advisor hasn’t contributed anything to the paper intellectually then they can’t ethically put their name on a paper they didn’t contribute to. That has nothing to do with funding or RAships.
That said, what I described above is the ideal. Students are often under pressure to do what advisors say. Authorship is best discussed directly and if you have any issues you should speak with your advisor and establish standards in your group.
Is this the most widely held view among scientists?
In principle, yes; in practice, perhaps not. But that's not the question you want to ask.
Is this the most widely held view among theoretical computer scientists?
Yes, it is.
The most widely held view in theoretical computer science is that authorship requires a significant intellectual contribution to the paper. Thus, if your advisor truly did not make a significant intellectual contribution to the paper, they cannot be a coauthor. The fact that they are your advisor is utterly irrelevant. The fact that they are giving you an RAship is utterly irrelevant. The fact that they may be going up for tenure is utterly irrelevant. No intellectual contribution, no coauthorship, period.
But let's be very clear here: "most widely held" does not mean "universally agreed, without exception". Even theoretical computer science has its (thankfully small) share of unethical advisors.
You need to have a direct, face-to-face conversation with your advisor about their expectations, both for authorship and for how you spend your research time, well before you have to worry about how they might respond to your submitting a paper without them. The best time to have this conversation is before you accept the RAship or sign an advisor agreement. (And yes, that might be before you accept the admission offer.)
Ideally, you should be comfortable telling your advisor about your independent results, asking for their suggestions for where to submit them, and even asking for their feedback on the results and presentation, without worrying about authorship issues. Ideally, they should either encourage you to submit without them or ask if they can work with you on further extending the results. But not everyone follows these ideals, which is why you must ask about their expectations well in advance.
(I am assuming here that you are meeting the requirements of your RAship, and your independent research is in addition to, not instead of, the research you are being paid to do. Skimping on your job is not going to make your boss happy.)
Unless you have signed some sort of agreement that states that any research you produce is the property of your advisor or university, papers you have written as an individual would be your own work to do what you please with it.
It might not be too hard for your advisor/university to establish a contribution of resources that would warrant authorship/acknowledgements. Especially in super computing. (Unless you have your own super computer).
Keep in mind that the large majority of university professors do not advise students because they love mentoring students absent of any publications. Your advisor is your advisor because he/she wants to put his/her name on research produced by you. I know of no professor who advises students solely because they love teaching students. They want credit for your work, whether they contributed significantly to it or not.
With these thoughts on authorship in mind, it is feasible to believe that your advisor may not be super happy to allow you to independently publish research you produced. They will have significant leverage on your degree progress and funding. Act accordingly.