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A Proof of Liabilities Scheme for Ecash Mints

Abstract: In this document, I will outline a proof-of-liabilities (PoL) scheme for ecash systems and Cashu specifically, which is a Chaumian ecash system for Bitcoin. The PoL scheme consists of three parts. First, a publicly auditable list of all issued ecash tokens in the form of mint proofs, and second, a publicly auditable list of all redeemed ecash tokens in the form of burn proofs, which are both regularly published by the mint operator. Third, a mint publicly commits to rotate its keys regularly once each epoch and allows all ecash in circulation to recycle from old epochs to the newest one. If clients remain vigilant and mints agree on a certain set of rules of operation which are publicly verifiable, users of a mint can detect whether a cheating mint has printed unbacked ecash during a past epoch, and, in many cases, provide public proofs of the mint engaging in this adversary behavior. Users achieve this by regularly checking t

	"""
	An implementation of TOTP as described in https://tools.ietf.org/html/rfc6238#section-4 aka Google Authenticator Style 2-factor Auth
	"""
	import base64
	import datetime
	import hashlib
	import hmac
	import sys
	import struct
	import time

	__This is the requirements section, please replace it yourself__

	Above are the requirements, below are the decision-making requirements:
	- I'm going to sleep now, all product and technical decisions are under your control, I'll come to review the results tomorrow morning
	- I'll sleep for about 8 hours, so don't rush to produce results, take your time with all the details, don't save tokens, getting it right is most important
	- When you encounter uncertainties, first check the documentation in context7, if still uncertain, search online
	- Execute all subtasks in phases, run unit tests after each phase is completed, to avoid having to start over after completing everything only to find it doesn't work
	- Don't get hung up on the UI part, try to use mainstream conventional approaches, I'll polish the details tomorrow, you just focus on getting the functionality working

	\NeedsTeXFormat{LaTeX2e}
	\ProvidesPackage{fyz}[2025/09/18 v1.0 pink kawaii theme]

	\RequirePackage[utf8]{inputenc}
	\RequirePackage{tikz}
	\RequirePackage{enumitem}
	\RequirePackage{titlesec}
	\RequirePackage{amsmath, amssymb, amsthm}
	\RequirePackage[most]{tcolorbox}
	\RequirePackage{xcolor}

	<?php
	/**
	* == Psudo ==
	*
	* Plugin Name: Psudo
	* Version: 1.0
	* Author: Dan Knauss
	* Contributors:
	* Donate link: https://example.com/
	* Tags: security, user management

	# adapted from https://gist.github.com/johdax/771943
	# modified to work without creating new String methods
	class StringDistance

	def self.damerau_levenshtein(str1, str2)
	d = Array.new(str1.size+1){Array.new(str2.size+1)}
	for i in (0..str1.size)
	d[i][0] = i
	end
	for j in (0..str2.size)