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Re: three digital signature models ... for x9.59

model 2 ... has receiver of the transaction forwarding
the digital signature to the account-authority along
with possibly other transaction information for transaction
approval (including verification of the digital signature).
this looks similar to credit-card model with
the digital signature substituted in place of AVS.

model 3 ... has the receiver of the transaction sending
the account number to the account-authority, and getting
back a signed public key for that account (much more
like online status request). the receiver of the transaction
does the digital signature verification rather than the
account authority

both are online operations. model 3 does require the
receiver to have public key processing capability.
model 2 doesn't (itself) have the receiver doing any
public key operations or to have any public key
software or hardware (although other operations in x9.59