@ Pix3m: No doubt about it, yours is superior. You wouldn't by chance have a link or two lying about that explain mathematically correct AA would you? How did you do yours? Thank you for your edit
Oh funny. I was playing around by comparing two functionally identical images except the pixels are subtley different, as if pixel artists were so weird to be nitpicky over incredibly small, meaningless details no layman would care about.
But honestly, I don't completely understand the math to be able to do much of it personally, but what I do is teach myself what perfect AA looks like so I can recognize subpar AA when it shows up.
A little story though: I have attempted twice a couple of stuff that requires a ton of heavy AA but I have gotten feedback from people who aren't even pixel artists that my AA was off and my edges were jaggy. Different monitor qualities were by far the reason why I can't achieve smoothness on everyone else's monitors, and my monitor is definitely suboptimal. As a result, I learned about what gamma correction is and wondered if I could take advantage of that to avoid bad AA.
However, from what I understand, first take this tutorial by ptoing:
It's pretty straight forward and gives you everything you need to know, but there is a pretty subtle mistake. It's only noticable if you try rendering edges that are almost aligned with the pixel grid but not quite, like the Black Knight's sword. Pretty much, the resulting values used for AA assumes a gamma of 1. 50% black and white isn't a 50 on a scale of 0-100 on a HSL color space; the real number is 73 if we're dealing with what should be ideal for a PC. The human eye does not interpret increase in light linearly and is more sensitive to higher values.
Pretty much what I did was construct some edges very similarly to ptoing does in his tutorial. The edge labelled one assumes a gamma of 1 and created values exactly as done in the tutorial. This edge is also a difficult edge to AA since it is so close to being aligned with the grid but not quite. Bad AA technique would be more glaring with this sort of edge, but easier edges, it's hardly noticable.
Then what, I did was take graphicsgale's color adjustment tool and took a shortcut to to fix the colors for me. Middle one was adjusted to a gamma of 2.2 which in theory should be what is standard to PC's, and is more-or-less what this monitor is set to. However, sliding it around got me an optimal gamma of 1.9 (not sure why), which is the absolute best I can achieve on my particular monitor. Yours is probably different.
I told this to a friend and he said that my AA colors are too bright (and amusingly I took my gamma-cheating device and set it to what would appear to be the right gamma for him and he says it's perfect). With that in mind, I also noticed that edges (for some reason) require a lower gamma at 2x scale where 1x scale requires a higher gamma. I have no idea why, but at this point I'm just gonna say that 'mathematically correct' should exist in paper but not in practice.
I'd say take that top edge and play around with gamma-correction tools to try to get it as perfectly straight as possible. Show yourself what perfect AA looks like so you can recognize bad AA when it shows up. Besides, who's gonna take the time to bust out their calucator to do art?