Not in asymtotic terms, at least. There exists a stable sorting algorithm that's O(1) axillary space, and O(n log n) worst-case time - wikisort. As both of tho

Not in asymtotic terms, at least. There exists a stable sorting algorithm that's O(1) axillary space, and O(n log n) worst-case time - wikisort. As both of those are provable lower bounds, this seems false.