Exact Record Omission in Delta Attention: A Transport Criterion, Its Cost, and a Replay Certificate

Abstract

When a user asks an assistant to forget a record, the test is whether the memory now matches the state it would hold if the record had never been stored. Independently encoded rows can be removed directly; a recurrent memory folds records into an evolving state. One hope is a receipt: save the difference the record made when it arrived, carry it forward through later updates, and subtract it, so that deletion costs one fixed-size edit no matter how long the conversation runs. We show that a transported receipt reaches exact omission if and only if the changes the record induces in later updates cancel out on net, and we measure whether they do on the released 48B Kimi Linear hybrid. They do not: after 4,096 further tokens the record still leaves an imprint of about 4.5% of the state norm that none of the tested receipt classes removes, recomputing half the suffix closes less than half the gap, and the per-token log a receipt needs costs more than a full checkpoint after 88 tokens. The same write-rule classification held on Mamba-2, Falcon-H1, and RWKV-7 with predictions recorded before the runs. Restoring a checkpoint from before the record and replaying the surviving suffix matches the never-stored state exactly on every array we check. In the hybrid suffix sweep, masking the record's attention rows brings sampled recovery close to the never-stored floor even though the recurrent imprint remains, and an auditor who rebuilds the reference can still detect it. Among the evaluated methods, checkpoint replay achieves exact omission, with work proportional to the replayed suffix.