If you're my friend or a business, and you see my balance is deeply negative, maybe you don't give some service.

If your my friend or a business, and my credit is not too bad, you follow my repo and give me some service. You commit a change that says, (pubkey:ae32...) paid (pubkey:af41...) 10 US dollars and reference my repo and commit.

I don't think there could be double spending because the receiver of the money acknowledges the credit offer on record (the git repo that paid).

If there are identities and entries in my ledger that are questionable, maybe you don't count them. For example, you might say credit only counts from those identities that are willing to answer a two-factor sms challenge. Or, if my git repo is credited by a google account, that's something worthwhile that could count toward my balance.