[CobrastanJorji]

Theorems 1 and 2 are a little weak. For theorem 1, once a mustard watch reaches a sufficiently enormous size, material weaknesses become relevant problems to overcome, and it is not clearly shown that adding a few more grains will in fact allow the watch to still operate. And theorem 2 doesn't discuss how much time is needed to measure the current time. I'm not entirely sure this has been peer reviewed. No notes on theorem 4, though.

[SyzygyRhythm]

You can prove it easily by induction. If Wm(n) is a mustard watch containing n micrograms of mustard, then it suffices to show that Wm(0) exists, and that if Wm(n) exists then Wm(n+1) must exist. Obviously a single additional microgram of mustard could not overload the structure of a watch. Therefore, Wm(10^100) or any other size must exist.

[dosinga]

material weaknesses would be more of a problem for ketchup watches. dijon mustard is strong enough so you don't require that much for it to become an issue