Thanks. I think you nailed just about every one of my concerns about this paper. I've only read the introduction, but if the rest of the paper can deliver what the first 16 pages promise, it looks like a winner to me. I suspect that if there's some problem hidden somewhere, it's a case of showing that some property or another of k-SAT holds almost always in the limit, but not being able to show that any specific instance of k-SAT has that property. And, if that's the case, it's probably a symptom of relying on one of those physics "theorems" you've mentioned. Color me cautiously optimistic, here.