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

Abstract

An assistant can stop repeating a deleted statement while its recurrent memory still carries that statement's influence. We examine this distinction by saving the state difference immediately after a record, carrying this saved difference, or receipt, through later updates, and comparing the corrected state with the state built from the same conversation with the record omitted. Unrolling the recurrence gives an exact criterion: transport reaches this never-stored state if and only if the additional differences created by later updates cancel after transport. We evaluate eleven conditions using 40 prospectively selected synthetic Kimi Linear contexts, with 40 separate calibration contexts and paired uncertainty estimates computed across complete records. Attention masking removed all 40 exact greedy target answers, yet a fixed three-query candidate-scoring attack with known candidate values and log-probability access attained AUC 0.740 (95% interval 0.695--0.809); the measured false-positive rate was 7.5%. Prompt-only forgetting still returned 33 of the 40 targets. Checkpoint replay matched the complete declared active state and audit logits in all 80 contexts, while preserving all 120 retained answers in the evaluation cohort. An independent Qwen cohort and matched original-bf16/8-bit Kimi controls confirmed native transport mismatch beyond the numerical error measured in matched controls. Replay also supported record replacement and successive deletions with a new record added between them. These results provide a practical audit of both the requested memory change and the assistant's remaining behavior, with replay work determined by the surviving suffix.