When Motion Logs Go Missing: Selective Visual Recovery for Persistent GUI State Tracking

Persistent GUI state trackers propagate spatial memory using both rendered screens and recorded actions, implicitly assuming that the action stream is complete. When a motion record is explicitly missing, the tracker applies an incorrect zero update and the resulting coordinate error can persist across subsequent observations. We study this failure mode and formulate recovery as selective substitution: observed actions remain unchanged, while only known motion erasures may be replaced using visual evidence. Our method estimates translation-like motion from consecutive screenshots with linear phase correlation and substitutes the estimate only on missing-action transitions, preserving exact behavior on complete logs. Across five independently trained checkpoints, visual recovery reduces hidden-state and recovery-state error on three frozen stress sets, with all six predeclared comparisons remaining significant after Holm correction. The benefit grows with missing-action severity and remains positive under fixed-budget bursts of one to six consecutive erasures. On held-out GUI-Odyssey trajectories with artificially erased motion logs, linear phase recovery reduces cumulative trajectory-log error from $0.157$ to $0.116$ and endpoint error from $0.260$ to $0.188$ at 20% erasure, with positive improvements from 5% through 40% erasure. Under the same trajectory protocol, RAFT-Small provides smaller gains, while a missing-only true-action oracle reveals substantial remaining headroom. On Android-in-the-Wild, linear phase yields the largest gesture-referenced displacement-error reduction among the evaluated estimators. These results show that repairing missing motion inputs can improve persistent GUI state without altering valid action logs. The method targets explicit translation-like motion erasures and does not address arbitrary nonzero action errors or end-to-end GUI-agent control.