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Citations in the personal and research statement

The NSF has rules about citations that apply to their normal grants.  For GRFP the rules are different, or in fact there are none other than to cite as your field typically does.  The specific response from NSF when asked is:
Thank you for your e-mail regarding the National Science Foundation (NSF) Graduate Research Fellowship Program (GRFP).
    The 2019 GRFP Program Solicitation (https://www.nsf.gov/pubs/2018/nsf18573/nsf18573.htm) contains application preparation instructions in Section V. The solicitation does not specify any particular standard for references and footnotes, beyond stating that they may be in 10-point Times New Roman font. Applicants may use their own discretion with regard to style and formatting of their citations, as long as they adhere to the guidelines regarding font size.
Please e-mail us at info@nsfgrfp.org or call us at (866) 673-4737 (toll-free from the US and Canada) or (202) 331-3542 (from international locations) if you have any further questions.

The citation using a footnote should be concise as it counts against the page limit.  It should also allow the reviewer to find it should they choose meaning that the citations should have a journal, volume and page number.  The minimum therefore is 1-3 authors, et al, year, journal, vol, page (starting and ending or just starting.  Be consistent for all.  You can also try to use a DOI.  Make sure you cite presentations if possible to again allow the reviewer to find them. 

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