<human>: OK a bit of background. We have been together for nearly 6 years now and we have had issues with trust in the past. Mostly my issue because when we started dating I was not very open about my past because I was in a bad spot prior to dating him. It all came out in the open and we have worked past all those issues and are continuing to work on things as well.

Lets shoot forward to today; I work at 5am so I'm up at 4 every morning to get ready and go. I get a message on FB 3 hours after being at work asking if I went out at 2 am because the cell phone was outside the wifi zone. I didn't get the message for 45 mins because I am training currently so I didnt have a chance to look at them; he called to ask me (he was pissy) I told him not that I remember unless I did so in my sleep but its -40 outside so I think I would remember getting dressed and going outside.  He swears he heard the door open...

He went on to say well the same thing happened again at 430 (i was already in the car letting it warm up). I again reiterated that I didn't go out and I'm not sure why the wifi would drop. Now he is barley talking to me and thinks that I'm lying to him.
How do I handle this situation? I'm not lying; I didn't go out at 2 or 430!

Can you give me the gist of the text in a nutshell?
<bot>: BF has trust issues; believes I went out at 2am in middle of winter and will not believe that I didn't.