I published a paper called "A Proof of Liabilities Scheme for Ecash Mints" that we will implement for Cashu.
It allows ecash wallets to keep mints in check if they fractional reserve their Bitcoin, sth. still impossible with classical custodianship.
https://gist.github.com/callebtc/ed5228d1d8cbaade0104db5d1cf63939