Atomic Ledger Batches

You maintain a ledger of account balances. initial maps account names to their starting balances, and batches is a list of batches to process in order. Each batch is a list of [account, delta] updates.

A batch is atomic: compute the effect of all of its updates together. If every account the batch touches would end with a balance >= 0, apply the whole batch. Otherwise reject it entirely, leaving every balance exactly as it was.

Details:

• An account that does not exist yet has balance 0. It is created when a batch that mentions it is accepted (even if its final balance is 0); an account mentioned only in rejected batches never exists.
• The same account may appear several times in one batch. Only its balance after the whole batch is checked, not intermediate values.
• An empty batch is accepted and changes nothing.

Return the final ledger as a list of [account, balance] pairs sorted by account name (normal string order).