Counting is O(n) but sort at best O(n log(n))

Herr LanX! I believe you to be mistaken! I have it on the good authority of a 30-year veteran for whom the impossible is easy—and the legendary is been there done that—that sorting is, in point of factual experiences in those trenches of yore, actually and exactly more-or-less O(logn). I have no idea who you think you are to disagree with the wisdom of the ages! Harrumph!! Bully!!!1!