This name is a synonym of Linum sulcatum var. harperi (Small) C.M. Rogers.
The record derives from Tropicos
(data supplied on 2012-04-18)
which reports it as a synonym (record 50120615) with original publication details: Fl. S.E. U.S. 663 1903.
Full publication details for this name can be found in IPNI: http://ipni.org/urn:lsid:ipni.org:names:140839-2.
This name was in version 1 of The Plant List, record tro-50120615.