This name is a synonym of Minuartia uniflora (Walter) Mattf..
The record derives from Tropicos
(data supplied on 2012-04-18)
which reports it as a synonym (record 50234393) with original publication details: Fl. Carol. 141 1788.
Full publication details for this name can be found in IPNI: http://ipni.org/urn:lsid:ipni.org:names:159513-1.
This name was in version 1 of The Plant List, record tro-50234393, and has not been changed.