The Latest on the "Split" of Katy and Russell

I hope they work out! They're so sweet!!

Katy Perry and Russell Brand have not decided to end their marriage ... this according to multiple sources directly connected to the couple.

We are told, however, that they are having problems, but our sources say it has nothing to do with reports of a big, blowout argument ... because we're told no such argument ever occurred.

Russell was spotted out in London today ... again without his wedding ring. He wasn't wearing it yesterday either.

As for Katy not wearing her ring, we're told it's no big deal. As one source notes, she doesn't wear the ring when she performs ... and it has nothing to do with Russell or her marriage.

One of our sources says it's clear Katy and Russell are "dealing with something," but divorce court is not the end game ... at least not yet.