Freidel does it: "BeeF, it's what's for dinner!" This looks like the Quantum Gravity+Matter breakthrough I've been expecting for a few years. The paper's arxiv number is easy to remember----just think of July 14 as Bastille Day and write this year's Quatorze Juillet holiday as 0607014 http://arxiv.org/gr-qc/0607014 [Broken] It is a paper by Laurent Freidel and two other gentlemen---a Pole and Russian, I believe---named Jerzy Kowalski-Glikman and Artem Starodubtsev. Jerzy K-G is at Wroclaw University, Artem S is in Renate Loll's group at Utrecht, and Laurent Freidel, as I guess everybody knows, is jointly at Perimeter and the Lyon Ecole Normale. The apparent breakthrough is not a sure thing. All I have to go on right now (besides some second-hand information) is a sense of confidence I get from reading the paper. It is an order of magnitude more on top of things than what I've met in the past. Let's explicate the paper: this thread can be devoted to doing that---and also to examining the followups. there are two or more other Freidel et al papers expected to follow this one.