Georgian hymn books of the tenth century carry chant signs, but nobody can say what they instruct. Comparison against Byzantine notation has not produced a reading and the Georgian signs do not map onto it cleanly. The consequence is severe for the tradition: no medieval Georgian melody can be recovered, and everything sung today descends from transcriptions made from living singers nine hundred years later. Nobody holds a rival decipherment; the question has simply been left where it was.
What would resolve this A Georgian manuscript giving the same chant in both neumes and a notation of known values, or a bilingual source setting Georgian signs beside Byzantine ones, would supply the external control the system lacks. Systematic comparison of the neume repertory across the surviving tenth century books may also isolate a small core of signs whose behaviour is regular enough to test.
OpenMusicology and Georgian palaeographyJohn A. Graham, The Transcription and Transmission of Georgian Liturgical Chant