Exact Algorithm Decides When an Agent Runtime Can Safely Checkpoint, Fork, Restore, or Merge an Execution

arXiv 2608.22928·medium signalXBlueskyLinkedInCopy link

Agent runtimes increasingly expose execution edits (checkpoint, fork, restore, merge) so a task can branch or rewind without restarting, but an edit cannot undo an authorization already granted or a tool request already sent. The paper shows an unsafe edit can authorize the same tool action twice, discard a result the task still requires, or conflict with a call that began before the edit, and that existing systems ship these operations without deriving what each edit must preserve. Their algorithm decides exactly whether an edit is safe, returning all safe continuations or a checkable proof that none exists.