You know the drill - If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one.
3. Open Threads should start on Monday, and end on Sunday.
4. Open Threads should be posted in Discussion, and not Main.
Hmm. To me it seemed intuitively clear that the function would be monotonic.
In retrospect, this monotonicity assumption may have been unjustified. I'll have to think more about what sort of curve this function follows.