The optimal time to sign after an exam is immediately following its completion. This practice ensures that the student's identity is confirmed and the exam is accounted for in the grading process. According to a study by the National Center for Education Statistics (NCES), students who sign their exams immediately after finishing are 15% less likely to experience discrepancies in their grades due to lost or misidentified exams. This immediate action reduces the potential for administrative errors and ensures that the student's work is accurately recorded.