Why doesn't \mathord work to turn an Acc atom into Ord?

Question

Writing ${\dot X^a}^b$ produces a very cryptic "double superscript" error: this has been explained here on this forum: the reason is that {\dot X}^a generates an Acc atom and that, for a reason that only Knuth must know, putting braces around a single Acc atom does not work to turn it into an Ord nucleus like it does for any other math list (see page 291, ¶5, of the TeXbook, quoted in the aforementioned thread).

What I'd like to know, now, is why $\mathord{\dot X^a}^b$ (or, for that matter, ${\mathord{\dot X}^a}^b$) doesn't work any better: unlike simple grouping, \mathord is not supposed to have any weird exception for single Acc atoms, at least if I believe the TeXbook (just two paragraphs below).

It's simple enough to work around ($\mathord{{}\dot X^a}^b$ works, or simply ${{}\dot X^a}^b$), and of course one shouldn't be writing this sort of thing anyway, but what I'd like to know is: does this count as a bug in TeX? Do I win a $327.68 check from Knuth ;-), or is there some fine print somewhere in the TeXbook or elsewhere that explains how \mathord is supposed to work?

Answer 1

I'm afraid you have discovered that \mathord{<math>} is exactly the same as {<math>}. See also module 1186 in tex.web where the "brace removing" around an Acc atom is described:

1186 Now at last we’re ready to see what happens when a right brace occurs in a math formula. Two special cases are simplified here: Braces are effectively removed when they surround a single Ord without sub/superscripts, or when they surround an accent that is the nucleus of an Ord atom.