Could somebody explains or points out a ressource explaining how GNU Taler solves the double-spending problem ? Or what the design is ? In the traditional mode

Could somebody explains or points out a ressource explaining how GNU Taler solves the double-spending problem ? Or what the design is ? In the traditional model (banks/credit cards), you simply sign a transaction that the receiver bank will then later handle to your bank. You let bank figure out how to transfer the money. Banks are basically a huge excel sheet with all the balances of customers. To avoid banks artificially adding numbers in the excel sheet, we rely on regulations (the fact that it works or not is besides the discussion here) In the cryptocurrency, you share that huge excel sheet and each transaction is a modification that should be approved by the majority of users. Unlike banks, it is now proved that it works and you cannot manipulate the excel sheet, meaning you don’t need regulation anymore (whether this is a good thing or not is besides the discussion here. Just stating facts). So my question: with GNU Taller, who maintain that huge excel sheet?