{\bf\red Implementation} (sources: \url{http://drorbn.net/icerm23/ap}). I like it most when the implementation matches the math perfectly. We failed here.

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\par{\bf\red Utilities.} The step function, algebraic numbers, canonical forms.

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\needspace{32mm}
\par{\bf\red Pretty-Printing.}

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\par{\bf\red The Face-Centric Core.}

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\par GT for Gap Touch: \hfill \input{figs/GT.pdf_t}

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\par\vskip 1mm\par\Cordon

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\par\needspace{20mm}
{\bf\red Strand Operations.} c for contract, mc for magnetic contract:

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\par{\bf\red The Crossings} (and empty strands).

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\par{\bf\red Evaluation on Tangles and Knots.}

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\par\needspace{20mm}
\parpic[r]{\input{figs/R3.pdf_t}}
{\bf\red Reidemeister 3.}

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\needspace{15mm}

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\par
\parpic[r]{\input{figs/R2.pdf_t}}
{\bf\red Reidemeister 2.}

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\par
\parpic[r]{\input{figs/R1.pdf_t}}
{\bf\red Reidemeister 1.}

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\par
\parpic[r]{\includegraphics[width=1in]{8_5.png}}
{\bf\red A Knot.}

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\par\picskip{0}{
  \def\nbpdfInput#1{\vskip 1mm\par\noindent\includegraphics{#1}}
  \def\nbpdfOutput#1{\hfill\includegraphics[width=0.4\linewidth,valign=t]{#1}}

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}

\needspace{30mm}
\par\parpic[r]{\includegraphics[width=1.88in]{figs/CKT.pdf}}
{\bf\red The  Conway-Kinoshita-Terasaka Tangles.}

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\par\needspace{10mm}

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\parpic[r]{\includegraphics[width=1.88in]{figs/B1B2.pdf}}
{\bf\red Examples with non-trivial codimension.}

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\par\needspace{10mm}

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