I really can't see a runner with a "real" 400 PR of 56 breaking 4 in the mile. I don't have any scientific evidence, but I'm thinking back on my high school track days and the team I ran on. Our team was pretty good (by Southeast US standards) and we all ran the 4 X 400 pretty much every small meet. Our top miler (4:20 or so) ran about 52-53 on a good day. I guess he could have gone a couple of seconds faster if he'd really concentrated on it. A couple of slightly slower milers could run about the same kind of 400 times as him. Nobody was blindingly fast, but every guy I thought of as fast (sub 4:40 or so) could at least run 55. Most of the scrubs such as myself (I ran about 5:10) could at least break 60. Actually, I was probably the slowest 400 guy on the team, usually running 61-63 if I was trying hard. My all time best split was like 60.7. And I know that sucks, but the point is, I was famously short on speed. People always made fun of it. Years later, by which time I had improved some overall, I got my 1500 time down to 4:12, but ran a couple of open 400s and still couldn't quite break 60. I was quite proud to be able to run even a 4:12 given my complete lack of basic speed, because it meant I could hold 67-68 pace despite not being able to break 60. I even thought to myself that I must be the slowest guy around to be able to run 4:12. Anyway, to sum up, almost every runner I've ever been around who trained regularly could break 60, and most of these guys had very little natural talent. Anybody who could break 5:00 seemed to be able to run at least 56-57. So when somebody suggests a sub 4 miler with a 56 400 PR, I think of one of my old HS teammates in Scrubland and try to think of them running a sub 4 mile, and I'm thinking, no way. I supposed it's possible that a sub-4 miler exists who never actually has broken 56, but only because he never ran a hard 400. Even that seems unlikely, though. Just based on my observations of all the runners I have personally encountered, I'd say about 52-53 would be the minimum speed needed for a sub 4.