Sorting numbers in $O(1)$
This is similar to what is known as counting sort. Whether your method is more efficient than other methods depends on the model of computation, which you haven't specified. For example, what if the dynamic range of the numbers is really large, say they are integers from $0$ to $2^{100}$? You could use some adaptive approach ("scanning" from top to bottom, stopping each time a number is reached), but it really depends on what your computer is allowed to do, and in practice you probably won't be able to pull it off. Counting sort is a conventional algorithm which uses a very similar idea in situations in which the dynamic range is small, in which case the algorithm is highly effective.