Try slice/draw cutting the paper, instead of push-cutting. I prefer testing with a slicing/draw cut (heel to tip), because more of the edge will be involved in the cut. A push-cut may only indicate condition of a narrow portion of the edge. Do some slicing cuts in the phone book paper, using the full length of the edge, then make 2 or 3 hard draw cuts into a piece of firm/hard wood (cross-grain), then try the paper again. More often than not, if a wire edge is there, it won't hold up so well to the wood, and the results will be seen when attempting to slice the paper afterwards. The wood will likely fold it over, or perhaps break fragments of the wire away, in which case the paper will either slip over the edge without being cut (rolled wire, or simply dull), or snag on burrs/fragments of the wire. On the other hand, if the edge continues to slice cleanly through the paper without slipping or snagging, then your edge is likely in very good shape.
BTW, the wood cutting can also be helpful in removing some (but not all) burrs & wires, precisely because of the tendency of them to break off in the wood. Do a few draw cuts in the wood, then test cutting the paper, then strop the edge and test the paper-cutting again. When you get to a point where you can go back & forth between the wood-cutting and the paper slicing, with little or no degradation in cutting performance, you're edge is good to go.