9F13

Last Online Application Transaction Counter Register is the card's memory of what its own ATC (9F36) was the last time it successfully completed an online authorization - a single reference point the issuer's risk logic uses to measure how far offline the card has since drifted. Compare the two: if the current ATC has only advanced by a small, plausible amount since 9F13 was last updated, the card's offline activity looks normal; if it's jumped by far more transactions than the card's own velocity limits should allow, that gap is one of the stronger cloning or replay signals available, precisely because both numbers come from the card itself rather than from anything the terminal reports. It's the direct counterpart to the PIN Try Counter (9F17) in the card's own risk-state bookkeeping - one tracks transaction velocity since the last online contact, the other tracks verification attempts - and together they're much of what an issuer's offline risk-management logic actually evaluates before deciding whether to let a given card keep transacting offline at all. See EMV 4.4 Book 3.