Throwing weak subliminals where the rapper's name isn't even called out isn't "Beef", it's just competition that's been going on damn near since Hip Hop's inception.
Jay has dissed Wayne subliminally and done songs with him in the same year. He was on Wayne's highest selling album and Wayne was on Jay's most critically acclaimed album since His retirement.
Fat Joe has stated on NUMEROUS occassions that he has no true beef with Jay, any last incidences are left in the past. Fat Joe isn't a big enough name nor any true type of competition for Jay himself to acknowledge.
There is no true beef between Good Music and YMCB, that shyt is all hype, fluff, and gimmick marketing.
Like the above posted said, TRUE rap beef died in 2002 with Nas/Jay-Z, almost all the rest are pomp and bullshyt
I do believe the 50/Fat Joe beef was real as well as the Papoose/Fat Joe beef.