This name is a synonym of Linum prostratum var. parvum (I.M. Johnst.) Mildner.
The record derives from Tropicos
(data supplied on 2012-04-18)
which reports it as a synonym (record 18700131) with original publication details: Contr. Gray Herb. 85: 172 1929.
Full publication details for this name can be found in IPNI: http://ipni.org/urn:lsid:ipni.org:names:140900-2.
This name was in version 1 of The Plant List, record tro-18700131, and has not been changed.