When was the zone shut down?

Is there an easy way (or any way) to determine from a ksh script when a specific zone was shut down? I'm assuming the zone had been running and is now properly shut down in the 'installed' state. Is there a log entry or some other reliable way to find out when the zone had been shut down?

I would look to the last modified file timestamp in the zone file system, like utmpx or /var/adm/messages.