How may I protect this \godel command for section titles?

Question

In the first version of the answer to my question Gödel codes with rounded Cornes?, Sandy G offered the following solution:

\newcommand{\godel}[1]{{}\mathbin{\vcenter{\hbox{\tikz{
                    \node[inner ysep=-1pt, inner xsep=3pt](M){$#1\strut$};
                    \draw[rounded corners=.5mm]([xshift=-1mm]M.north east)--(M.north east)--++(0,-.1);
                    \draw[rounded corners=.5mm]([xshift=1mm]M.north west)--(M.north west)--++(0,-.1);
    }}}}{}}

The solution is quite satisfactory for my document, except that many errors are produced, so that the document does not compile, if I put $\godel{A}$ in the title of a section. I tried two ways to protect it, via. $\protect\godel{A}\protect$ and $\protect\godel[thick]{A}$.

Are there other ways to protect $\godel{A}$ in section titles which may help me out?

Answer 1

This works flawlessly:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\newcommand{\godel}{}% just to avoid redefining
\DeclareRobustCommand{\godel}[1]{%
  \mspace{1\medmuskip}%
  \vcenter{\hbox{%
    \begin{tikzpicture}
      \nodeinner ysep=-1pt, inner xsep=3pt{$#1\strut$};
      \draw[rounded corners=.5mm]([xshift=-1mm]M.north east)--(M.north east)--++(0,-.1);
      \draw[rounded corners=.5mm]([xshift=1mm]M.north west)--(M.north west)--++(0,-.1);
    \end{tikzpicture}%
  }}%
  \mspace{1\medmuskip}%
}
\begin{document}
\tableofcontents
\section{$x\godel{A}y$}
\end{document}

Note that I've changed how to space the construction: using {}\mathbin{...}{} introduces flexible space, that's obviously not wanted: if the formula turns out to need shrinking the space might disappear. Not with \mspace{1\medmuskip}, which is not flexible (and the same amount added by default around a \mathbin).

A better definition:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\DeclareRobustCommand{\godel}[1]{%
  \mspace{1\medmuskip}%
  \vphantom{#1}%
  \begin{tikzpicture}[baseline=(M.south)]
    \nodeinner ysep=0pt,inner xsep=3pt{\smash[b]{$#1\mathstrut$}};
    \draw[rounded corners=.5mm]([xshift=-1mm]M.north east)--(M.north east)--++(0,-.1);
    \draw[rounded corners=.5mm]([xshift=1mm]M.north west)--(M.north west)--++(0,-.1);
  \end{tikzpicture}%
  \mspace{1\medmuskip}%
}
\begin{document}
\tableofcontents
\section{$x\godel{A}y$}
a $\godel{f}$ b
\end{document}