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Today it is there a three main branches of Buddhism. Each of these branches are somtimes given a deographic description.
Vajrayāna - Northern Buddhism
Mahāyāna - Eastern Buddhism
Theravāda - Southern Buddhism
Have a fourth branch of what can be called 'western' Buddhism develop sometime after 500BC, and before 1500AD.
How would this branch be different from the other branches? What similarites would it share with the other branches? How would this branch be influenced by it's environment(Perhaps Abrahamic Faiths)?