Okay, now that that is done...
It is six years ago now that The Sopranos aired the final episode and it was brilliant.
There was an immediate out-pouring of confusion and anger at the ambiguous ending, but it was that ambiguity that was part of the brilliance.
David Chase gave the audience an ending that, if the demand for more Sopranos - an additional season, a movie, you name it - was great enough that it could be taken out of mothballs and the cast's demands could be met (all of which was unlikely, but was discussed publicly) the story could be taken up, with the interpretation of the end being something to the effect of the tension & paranoia of that final scene is a reflection of how Tony will have to live the rest of his life. (Yawn... wasn't that paranoia why Tony was having panic attacks in the pilot episode? Chase is a better story teller than that.) However, if you were paying attention to the show - both that scene as well as the previous few seasons - it was fairly easy to deconstruct the true ending. And now that James Gandolfini is dead, that IS the real ending forever and ever amen.
Like Mr. Gandolfini, Tony has left us.
It is actually quite simple.
For seasons (without going back to re-watch and check, I'm going to say "three seasons") we were told several times some variation on "You never hear the bullet that gets you." And really, it doesn't take much more than that to parse the ending. However, if you must... break down the scene in the diner - we keep getting shots of the door from Tony's point of view, the ten seconds of black... that is Tony's POV too.
I expect that someone somewhere has detailed far more completely than I have - some people were really fanatic about that show, and would have taken that end apart like a forensic investigator. They could probably tell you which customer at the diner pulled the trigger. I don't know that that even matters.
One last point - this interpretation has been attacked (to my face) by the argument that "The show is called The Sopranos. It is about Tony Soprano. If he died, they would show it. They would HAVE to show it!" Uh... no. The show is called The Sopranos. It is about Tony Soprano. He is the main character. It is HIS story. When he is dead, the story ends - abruptly and with far more art than showing it would have had. If they had shown it, obviously we wouldn't still be having this debate. If they had shown it, it wouldn't have been an ending worth discussing.
Rest in Peace James.
Your greatest work will remain secure as it was intended to be.