But the cutoff is obviously not "continent"/"not continent", but rather "takes up more than half the world" versus "doesn't take up more than half the world" - possibly with an additional constraint of a sufficiently simple shoreline...

This is answer is about as informative as answering "Why do aeroplanes fly?" with "Calculus. Differential equations with forces.".

If you are talking about continents larger than half the world, then DanArmak has already pointed it out and much more politely. However, as dlthomas points out the distinction is not based on it being a continent or not, but on it covering more than half the word.

Also, everything we call a continent on Earth takes up less than half of it, and for such things there is a minimum perimeter that increases as the area increases. (The minimum perimeter is something a little bit like 2*sqrt(pi*Area) (except different because the Earth is a sphere rather than a plane).)

Were you trying to point out that the shoreline's length varies as the square root of the size of the island?