What I understood then was that the local ledger of a given user of the coin would authorize and register the transactions done on/off the recorded balance and, when network available, would broadcast such transactions to the global ledger.
The global ledger was the total sum of transactions, not imperatively required to authorize transaction by transaction.
That requires a global ledger. Blockchain is an appallingly bad way to implement one.
What I understood then was that the local ledger of a given user of the coin would authorize and register the transactions done on/off the recorded balance and, when network available, would broadcast such transactions to the global ledger.
The global ledger was the total sum of transactions, not imperatively required to authorize transaction by transaction.