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\title{A Fast, Strong, Topologically Meaningful, and Fun Knot Invariant}

\author{Dror~Bar-Natan}
\address{
  Department of Mathematics\\
  University of Toronto\\
  Toronto Ontario M5S 2E4\\
  Canada \ifpub{(corresponding author)}{}
}
\email{drorbn@math.toronto.edu}
\urladdr{http://www.math.toronto.edu/drorbn}

\author{Roland~van~der~Veen}
\address{
  University of Groningen, Bernoulli Institute\\
  P.O. Box 407\\
  9700 AK Groningen\\
  The Netherlands \ifpub{(corresponding author)}{}
}
\email{roland.mathematics@gmail.com}
\urladdr{http://www.rolandvdv.nl/}

\date{First edition September 22, 2025. This edition \today.}

\makeatletter
\@namedef{subjclassname@2020}{\textup{2020} Mathematics Subject Classification}
\makeatother
\subjclass[2020]{Primary 57K14, secondary 16T99}
\keywords{
  Alexander polynomial,
  loop expansion,
  solvable approximation,
  knot genus,
  fibered knots,
  ribbon knots,
  polynomial time computations,
  Feynman diagrams,
  perturbed Gaussian integration,
  Seifert formulas%
}

\thanks{This paper is available in electronic
form, along with source files and a demo {\sl Mathematica}
notebook at \url{http://drorbn.net/Theta} and at \arXiv{2509.18456}.}

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