Can a student be a provider of letter of recommendation for research based MS - USA I belong to an environment where gaining a valuable/ meaningful Letter of Recommendation (LoR) is difficult. There exist various reasons, from they themselves not being researchers to fake letters; but that is not the region of interest for this question.

I have been working in the industry for couple of years, where I had the opportunity to work with a Masters student. I mentored her, worked on a project, and we have proposed a new algorithm. That is pending a review, but we have put a pre-print on arXiv. A notable thing is, there was no other project guide. I, and my student, we both believe and agree to the fact that I led the project and saw it to the succession, be it the underlying mathematics or drafting a paper. 

I am applying to US universities for MS degree in Computer Science. As mentioned above, running out of quality recommendations. 

So the question is: will it be considered a quality letter if my student writes it? The thought of doing so occurred to me while reading that, in the application, review committee looks out for the direct proofs that persons is capable of conducting a quality research. I felt that this project is my biggest evident proof.

I already agree that from person to person, the scenario would differ. But objectively, are there solid reasons? Have you witnessed such a case in the past? If yes, did it have a positive impact?
There's nothing to stop you from submitting a LOR written by your former student but it's very difficult to see how such a letter could help you (in either business or academia).  If you can't get someone who has supervised your work to write your letter, you should at least try to find a peer who could do it.