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I am an Indian physics student who will apply for graduate school in the US around December this year. Along with a European professor I have been working with for one year, I am currently writing a paper that will soon be submitted to, say, Physical Review B. But before that, we will of course, upload it to ArXiv. I am the first author on the paper, and the professor will write me a recommendation letter for solely based on this yearlong project.

Will such a manuscript hold much value in my applications even if the paper is not accepted by December?

Physiker
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Under review = not reviewed yet. You being the first author and having a recommendation letter are certainly good additional points, but otherwise answers suggested by @Anyon apply to your case. A paper on ArXiv is not as valuable on a CV as a published paper, but is still a valuable accomplishment.

Camille Gontier
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Interested academics will probably just read your papers directly

As a general rule, the publication records of higher-degree research applicants are small enough that it is not too onerous to directly read all of their papers; this allows direct review of the present quality of their research and writing. When I am considering taking on a PhD student as a supervisor, I would read all of their existing published works, including pre-prints on ArXiv. (I would expect that other relevant members of a selection panel for higher-degree research applicants would probably also do this.) If these works vary highly in quality, I would typically focus on the best ones and also ask the applicant which papers they consider to be their best works. If papers were done with academic co-authors then I would also inquire into the contributions of the applicant and try to make an inference of what they are contributing to the papers at issue. I would make further inquiries about this when checking their references.

Since directly reading the papers is feasible in this case, it is usually possible to get a reasonable idea of the present research quality of the applicant directly from the quality of the works, without relying on secondary markers like acceptance at a journal. The latter may still be useful in showing that other expert reviewers have accepted the paper and also in showing that the applicant has been able to successfully navigate the peer-review and publication process (which is a useful skill in its own right). Nevertheless, when directly reading the works at issue to evaluate a prospective higher-degree research student, it is not especially important whether or not the paper has been published in a peer-reviewed journal or just a preprint repository.

Ben
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