What's the way to align the brackets here rendered as markup paths with the
centre of the associated text, without hardcoding numbers. Is there a
self-alignment-y property or similar?

I may change the size of the font, and the length and shape of the
brackets, so I am after something generic.

Andrew

%===
\version "2.19.82"

leftBracketPath =
  #'((moveto 0 -1)
     (lineto 0 0)
     (lineto 2 0)
     )

rightBracketPath =
  #'((lineto 2 0)
     (lineto 2 -1)
     )

\markup {
  \path #0.25 #leftBracketPath "x3"
}

\markup {
  "x3"  \path #0.25 #rightBracketPath
}

%===
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