S is very special and it is called the strong composition combinator, because when applied to two functions, let us say, f and g, as well as x, then the resulting term gx (fx) expresses the composition of g and f both applied to the same argument x.
Now we can define a metric tensor, g, on our manifold: The metric tensor assigns a metric, gx, to every point x in the manifold (such that it varies smoothly with x in the manifold).
Now, a metric at our point x is a function gx (Xx, Yx), which takes in the two tangent vectors Xx and Yx (at x), and outputs a real number.
Thus we arrive at a direct contradiction, since the state of S2 post-measurement cannot be both gx - and one of gy - or gy+.
And with the lack of diacritics available on most keyboards, it does not always even meet--in practice--the claim of "one letter, one sound"--eg., gx or gh.
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