From editor or global species database
Type species Lumbricus cirratus O. F. Müller 1776 as in Fauchald, 1977:29. Lamarck appears to rename Lumbricus cirratus [he credits Fabricius's Fauna Groenland with the authorship] as Cirratulus borealis, but this is not valid unless Müller's species name required replacing. C. borealis Lamarck, 1818 is an unnecessary replacement name and thus an objective synonym of Cirratulus cirratus.
As a side issue if Lamarck's specimens could be relocated this matter of C. borealis sensu Lamarck may need revisting. A note in Blake 1996:347 indicates Mary Petersen had determined “C. borealis Lamarck 1818 is distinct from Lumbricus cirratus …”, and earlier Petersen (1991:abstract only) had stated that "Cirratulus borealis Lamarck is considered distinct; it differs from C. cirratus (0. F. Muller) in having two branchiae per segment throughout rather than just anterior." However, it is unknown what relevant material was used for this observation. It would need to be associated with Lamarck, but there is no 'borealis' type at the MNHN according to Solis-Weiss et al's (2004) catalogue [details]