Try setting an alarm in the morning (make sure Alarm is set up as the default alarm app in PC Settings). If you could wake up, then CS was active the whole time.Well, I can only tell you what does get recorded in the sleepstudy. Mine doesn't pass 4 hours while on battery.
Or try sending yourself an email after the SP3 went for 4 hours in CS. If the mail is there when you wake it up, then CS was active the whole time as well.
I know it stays in CS because of that