Unsupported joists in attic?
In my mind, it comes down to what's under that beam and ceiling joists.  There should be a wall under the joists (looks like that may be the case 'cause you can see what looks to be the top plate of the wall under the joists), and a built up post of some sort under the edge of the beam.
If those conditions are met, than you should be OK to put down the plywood over the joists.