{\red\bf A faster program,} in which the Feynman diagrams are ``pre-computed'' (see theta.nb at \web{ap}):

\noindent\nbpdfInput{Snips/theta/1.pdf}

\noindent\nbpdfInput{Snips/theta/2.pdf}

\noindent\nbpdfInput{Snips/theta/3.pdf}

\noindent\nbpdfInput{Snips/theta/4.pdf}

\noindent\nbpdfInput{Snips/theta/5.pdf}

\noindent\nbpdfInput{Snips/theta/6.pdf}

\noindent\nbpdfInput{Snips/theta/7.pdf}

We call the invariant computed $\theta$:

\noindent\nbpdfInput{Snips/theta/8.pdf}

\needspace{15mm}
{\bf\red Some Knots.}

\noindent\nbpdfInput{Snips/theta/9.pdf}

\noindent\nbpdfMessage{Snips/theta/10.pdf}

\noindent\nbpdfOutput{Snips/theta/11.pdf}

\noindent\nbpdfInput{Snips/theta/12.pdf}

\noindent\nbpdfInput{Snips/theta/13.pdf}

\noindent\nbpdfMessage{Snips/theta/14.pdf}

\noindent\nbpdfMessage{Snips/theta/15.pdf}

\noindent\nbpdfOutput{Snips/theta/16.pdf}

So $\theta$ detects knot mutation and separates the Conway knot from the Kinoshita-Terasaka knot!

%\needspace{50mm}
The 48-crossing Gompf-Scharlemann-Thompson knot \cite{GompfScharlemannThompson:Counterexample} is significant because it may be a counterexample to the slice-ribbon conjecture:

\[ \resizebox{\linewidth}{!}{\import{../Waco-2203/}{GST48-Marked.pdf_t}} \]

\noindent\nbpdfInput{Snips/theta/17.pdf}

\noindent\nbpdfOutput{Snips/theta/18.pdf}

