{\bf\red Implementation} (see IType.nb of \web{ap}).

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\vskip 1mm\rule{\linewidth}{1pt}\vspace{-2mm}

{\bf\red Integration} using Picard iteration. The \myellow{core is in yellow} and \mpink{hacks are in pink}.

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\parpic[r]{\parbox{0.75in}{
  \includegraphics[width=0.75in]{../../Projects/Gallery/Fourier.jpg}
  \footnotesize Joseph Fourier
}}
\picskip{2}

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\needspace{12mm}

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\needspace{12mm}

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So we've tested and nearly proven the Fourier inversion formula!

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\parpic[r]{\parbox{0.65in}{
  \includegraphics[width=0.65in]{../../Projects/Gallery/Fubini.jpg}
  \scriptsize Guido Fubini
}}
\picskip{2}

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\vfill
From \surl{oeis.org/A226260}:
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\includegraphics[width=\linewidth]{../Groningen-240530/OEIS.png}

\vfill
\rule{\linewidth}{1pt}
{\bf\red The Right-Handed Trefoil.}

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\needspace{5cm}

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\needspace{10mm}

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\vskip 1mm
A faster program to compute $\rho_1$, and more stories about it, are at~\cite{APAI}.

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%\newcolumn

{\bf\red Invariance Under Reidemeister 3.}
\vskip 2mm
\def\ip{{i^+}} \def\jp{{j^+}} \def\kp{{k^+}}
\def\ipp{{i^{+\!+}}} \def\jpp{{j^{+\!+}}} \def\kpp{{k^{+\!+}}}
\import{../Beijing-2407/figs}{R3.pdf_t}

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\vskip 1mm\rule{\linewidth}{1pt}
\par{\bf\red Invariance Under Reidemeister 3, Take 2.}

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%\newcolumn

\vskip 1mm\rule{\linewidth}{1pt}
\par{\bf\red Invariance Under Reidemeister 3, Take 3.}

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\needspace{20mm}

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Invariance under the other Reidemeister moves is proven in a similar way. See IType.nb at \web{ap}.

