If you assume fully independent git nodes that interact, then there is no authoritative 'branch', 'repo', or anything. Every node will have it's own world view (repo and history) and to enforce a 'global consensus' you will need a BFT distributed consensus algorithm on top of your git scheme so all bank can agree on transactions and apply patches (accept transactions).
If you assume partial consensus -- only interacting banks of a transaction need to be in agreement -- then you still need a consensus for that smaller group to 'merge' their collective actions into a linear transitional narrative.
For most people using 'git', the "distributed transaction log via git" is owned and managed by GitHub, a central authority.
It's a generic distrubuted data structure in git, with identities and signature, and conflict merge. At the moment it's used to store bugs, more to come later.