Assuming I read that right, this is entirely dependent on the ability to set up that situation where a user is not able to edit their data, nor is a history kept. I don't see any way this could be done.
The next reasonable choice would be to have the certificates encrypted by the certificate creators
and given a copy to the wallet owners. This way they will have documents that vouch for their
wallets' states, and they will be unable to edit the certificates without corrupting them (if it is taken
for granted they will not be able to crack the encryption). A strong enough method of encryption
must be selected so this can be taken for granted. The certificates should include information on
how to contact the node which encrypted (and thus can decrypt) the information in the certificate.
Regardless of whether they can edit the certificates, nothing prevents them them from backing up and restoring them, or even just running many clients and using themselves as witnesses to make a full wallet, in which case they could spend infinitely, as no ledger is kept other than their own.
As people would be able to run multiple clients and use those as their witnesses, to validate the wallet you'd have to have a majority of the network validate each transaction, and therefore also know the size of the network. This could also cause issues if too many nodes are down, as not enough validates would be able to be done.