Nix
I've used Nix, a software project I was taking a look at used Nix for reproducible builds (ultimately building firmware images to load onto a device.) I think some packages (edit: excuse me, closures*) had prebuilt binaries (with the option to build from source, but the binaries had checksums etc. to ensure they were identical to what the build would produce anyway.) The source builds, it has some tools that strip out whatever variant information (dates & times I suppose) that the compiler or linker throw into the binaries so it can directly check the result of the build is identical to what it should be.
I found it rather difficult to use; but, it put's everything in /nix/, there's subdirectories under there with the inscrutable hashes as alluded to by TFA. Each app has the ldconfig, path, etc. set so they're not expecting anything in the traditional /bin, /sbin, /usr etc. (your home directory does stay in /home, at least running Nix on a normal system it does.) It has a vaguely FreeBSD Ports or Gentoo portage style set of directories with available "packages" (I don't know if that's what Nix calls it) in there.
But, if you have multiple programs that are built on top of the same set of libraries, you do in fact have only 1 copy of those libs taking up space. But I don't know in practice how this works out; if you wanted to "update", say, gtk or libc, you either have to update a large number of packages with updated dependency (and compile them, either on their end or yours...), or alternatively the packages "drift" in what versions of libs they want and you do end up with multiple library verisons building up.
*re: closures. That was one issue with Nix, I found the terminology confusing as hell. Nix has done a mathetmatical proof that the builds are complete and reproducible -- among my comp sci. classes, I took an algorithms class that was heavy on the mathematics of proving if a bit of code was O(n), O(n^2), etc., and still found the terminology rather difficult just for the section on how you're supposed to use the darn thing let alone the proof.