I've done it. The parts are available. Essex makes a mini frame. (smaller than Colt officers) you can use all the officers model top end parts, (I wouldn't go any shorter) and the Smaller sized Mini Detonics magazine, or if you use a mag well you could use a officers model mag, kinda defeats the purpose though. It will be small and It will all go together and work, but it is still heavy, and the frame is so small it is not designed for a grip safety, although you might be able to squeeze in an abbrieviated one by cutting one up. getting it to work may be a problem though. Still its more fun than watching tv.
I've worked on one, and I was not able to fix what ailed it. I did learn, though - I learned that these little pistols are a lot more unforgiving than their larger cousins. The 5" guns clunk right along. The little ones have to do things a lot quicker, and in less space.
I guess at my point in learning about building 1911s, I'm just to this point: I am comfortable building and working on full-sized gun. I am not comfortable, and will not be until I understand more, building little ones.
you can build one, there are two essex frames that are the detonics size on gunbroker right now. for what it will cost you to source parts, you can buy a complete functioning detonics. the mags, grips, sear spring, hammer strut and grip safety plate( no functioning gs usually, Nonte made one work in his book Pistolsmithing) are all different than GI and OACP parts like IronHawk said. . Detonics seems to come into and out of existance, parts for their guns may be hard to come by, if you get ahold to the frame. Brownells had some a while back, the essex chopped frame and they havent made any for quite a while. I think they supplied detonics for a while, but I am not sure