It's not obvious how to set the 'composer' and 'arranger' relations for the Gurdjieff / de Hartmann oevre.
All of Gurdjieff's extant compositions are collaborations with Thomas de Hartmann, who transcribed and arranged for piano the melodies that he heard from Gurdjieff. But de Hartmann was a participant in the compositional process: Gurdjieff would usually give him fragments, hints and outlines which de Hartmann would interpret, fill out and notate, in 'real time' and drawing on his own training in the Russian school. So he could well be regarded as joint composer.
Then again, at least in many cases, Gurdjieff could be regarded as an arranger, since the melodies were often drawn from sacred and folk music that he had collected on his travels.
Setting Gurdjieff as composer and de Hartmann as arranger for these works seems a reasonable first approximation, but isn't entirely satisfactory.
See: Thomas and Olga de Hartmann, Our Life with Mr Gurdjieff (Penguin Arkana, 1992).