NOTE: The following essay owes a tremendous amount to my consultation with Stephen Delaney of the Araki-ryu gunyo-kogusoku. I take full responsibility, however, for everything – both history and speculation – within this essay.
Araki Buzaemon and his immediate successors
Two different martial traditions, Araki-ryu gunyo-kogusoku and Araki Shin-ryu, are associated with Araki Buzaemon Hisakatsu, a man otherwise unknown, but believed by these ryuha to be related to Araki Mujinsai (AKA Muninsai) Minamoto Hidetsuna, the founder of Araki-ryu torite-kogusoku.
These two schools are profoundly different, but both have the same anomaly in their lineage: after Araki Mujinsai, both Araki Shin-ryu and, until recently, Araki-ryu gunyo-kogusoku then listed the next two generations blank, followed by Araki Buzaemon in the fourth generation. Such blanks in the lineage are not unusual in Japanese ryuha. For example, Miura Yoshin-ryu has a gap between the alleged founder, Nakamura Sakyodayu Yoshikuni (Miura Yoshin) and the sixth, Abe Kanryu. Generally speaking, such a gap implies that the person after the gap, in this case Buzaemon, created a new ryu inspired somehow by Mujinsai, but separated by a few generations.