<human>: Can you succinctly summarize the text in 1-3 sentences?

The other week I decided on having an open relationship with my SO of 9 months, he said yes to the condition that he won't lie to me when he's with women and I can come join when I ask.

I've just been messaged by a girl to confirm that I'm his girlfriend, which I expect and am okay with. I then find out she's gone over to his house the other night and I even had my suspicions and brought up the open relationship thing again and asked if he had a girl over, he said no.

Hes continuously asked me if I was serious because it's very contrasting to my behaviour before then, but I realised it's not the sex with other women, it's losing him emotionally to another woman that would hurt me, which he confirmed wouldn't happen.

I think he won't tell me the truth because he doesn't believe mean it and thinks it's a ploy for something (I can't imagine a scenario where it is!).

I think it's dumb to break up with him because he lied about something I'm okay with, I'd rather find a way to convince him it's real. Has anyone else had trouble with convincing their partner that they're serious about an open relationship? How did you solve it?
<bot>: Bf and I are in an open relationship, he doesn't think I'm being serious, how do I convince him?