\backcite {Ohtsuki:TwoLoop}{{1}{(document)}{Doc-Start}} \backcite {Rozansky:Contribution, Rozansky:Burau, Rozansky:U1RCC, Kricker:Lines, GaroufalidisRozansky:LoopExpansion}{{1}{(document)}{Doc-Start}} \backcite {Klarreich:QRCode}{{2}{1}{section.1}} \backcite {Alexander:TopologicalInvariants}{{2}{1}{section.1}} \backcite {Lalani:ThetaSurvey}{{2}{1}{section.1}} \backcite {Self}{{4}{1.2}{figure.caption.3}} \backcite {Self}{{4}{1.3}{figure.caption.4}} \backcite {DHOEBL:Random}{{5}{1.4}{figure.caption.5}} \backcite {IType}{{6}{2}{equation.2.2}} \backcite {APAI, Toronto-241030}{{6}{2}{equation.2.2}} \backcite {APAI}{{7}{3}{theorem.3}} \backcite {APAI}{{7}{3}{theorem.3}} \backcite {IType}{{7}{4}{theorem.4}} \backcite {Wolfram:Mathematica}{{8}{3.1}{subsection.3.1}} \backcite {Self}{{8}{3.1}{subsection.3.1}} \backcite {Self}{{11}{3.2}{figure.caption.6}} \backcite {APAI}{{11}{4.1}{subsection.4.1}} \backcite {APAI}{{11}{4.1}{subsection.4.1}} \backcite {APAI}{{12}{4.1}{equation.4.7}} \backcite {APAI}{{14}{4.1}{theorem.8}} \backcite {APAI}{{14}{4.1}{theorem.8}} \backcite {APAI, Oaxaca-2210, Toronto-241030}{{14}{4.1}{figure.caption.7}} \backcite {Polyak:RMoves}{{15}{4.2}{figure.caption.8}} \backcite {APAI}{{15}{4.1}{figure.caption.7}} \backcite {BecerraVanHelden:RotationalReidemeister}{{17}{4.1}{figure.caption.9}} \backcite {Self}{{22}{4.2}{equation.4.19}} \backcite {Self}{{23}{5.1}{table.caption.11}} \backcite {Levine:KnotCobordism, Tristram:CobordismInvariants, Conway:SignaturesSurvey}{{23}{5.1}{table.caption.11}} \backcite {Geneva-231201}{{23}{5.1}{table.caption.11}} \backcite {CullerDunfieldGoernerWeeks:SnapPy}{{24}{5.1}{table.caption.11}} \backcite {Rozansky:Contribution, Rozansky:Burau, Rozansky:U1RCC, Overbay:Thesis}{{24}{5.1}{table.caption.11}} \backcite {APAI}{{24}{5.1}{table.caption.11}} \backcite {Oaxaca-2210}{{24}{5.1}{table.caption.11}} \backcite {GompfScharlemannThompson:Counterexample}{{25}{5.2}{figure.caption.13}} \backcite {GaroufalidisKashaev:Multivariable}{{25}{5.1}{figure.caption.12}} \backcite {GaroufalidisLi:Patterns}{{25}{5.1}{figure.caption.12}} \backcite {Genus}{{25}{5.2.1}{subsubsection.5.2.1}} \backcite {GompfScharlemannThompson:Counterexample}{{25}{5.2.1}{theorem.18}} \backcite {GompfScharlemannThompson:Counterexample}{{26}{5.2.1}{figure.caption.13}} \backcite {LopezNeumannVanDerVeen:FibredLinks}{{26}{5.2.2}{subsubsection.5.2.2}} \backcite {LivingstonMoore:KnotInfo}{{26}{5.2.2}{theorem.19}} \backcite {Self}{{26}{5.2.2}{theorem.19}} \backcite {Rolfsen:KnotsAndLinks}{{26}{5.2.2}{theorem.19}} \backcite {Kauffman:RotationalVirtualKnots}{{27}{6.1}{figure.caption.15}} \backcite {CrowellFox:KnotTheory}{{27}{6}{theorem.20}} \backcite {Lickorish:KnotTheory}{{27}{6}{theorem.20}} \backcite {Kauffman:VirtualKnotTheory}{{28}{6}{figure.caption.15}} \backcite {Murugesan:ThetaRecovers}{{28}{24}{theorem.24}} \backcite {Rozansky:Contribution, Rozansky:Burau, Rozansky:U1RCC, Overbay:Thesis}{{28}{24}{theorem.24}} \backcite {APAI}{{28}{24}{theorem.24}} \backcite {Ohtsuki:TwoLoop}{{28}{25}{theorem.25}} \backcite {GaroufalidisRozansky:LoopExpansion, Rozansky:Contribution, Rozansky:Burau, Rozansky:U1RCC, Kricker:Lines}{{28}{25}{theorem.25}} \backcite {Ohtsuki:TwoLoop}{{28}{26}{theorem.26}} \backcite {Garoufalidis:Whitehead}{{28}{26}{theorem.26}} \backcite {Ohtsuki:Cabling}{{28}{26}{theorem.26}} \backcite {DPG, PG}{{28}{6}{theorem.26}} \backcite {BDV:OU}{{28}{7}{figure.caption.15}} \backcite {Kauffman:RotationalVirtualKnots}{{28}{8}{figure.caption.15}} \backcite {DPG, PG}{{29}{27}{theorem.27}} \backcite {Lawrence:UniversalUsingQG, Ohtsuki:QuantumInvariants}{{29}{27}{theorem.27}} \backcite {APAI, PG, Oaxaca-2210}{{29}{27}{theorem.27}} \backcite {Schaveling:Thesis}{{29}{6}{theorem.27}} \backcite {Harper:Non-Abelian}{{29}{29}{theorem.29}} \backcite {Ohtsuki:Cabling}{{29}{31}{theorem.31}} \backcite {Drinfeld:QuantumGroups}{{29}{10}{theorem.27}} \backcite {Polyak:FeynmanDiagrams}{{30}{32}{theorem.32}} \backcite {Bar-NatanGaroufalidisRozanskyThurston:Aarhus}{{30}{32}{equation.6.21}} \backcite {IType}{{30}{33}{theorem.33}} \backcite {Ohtsuki:TwoLoop}{{31}{6}{theorem.35}} \backcite {Kauffman:OnKnots}{{31}{6}{theorem.36}} \backcite {Bai:Alexander}{{31}{6}{theorem.36}} \backcite {FoxMilnor:CobordismOfKnots}{{31}{37}{theorem.37}} \backcite {Self}{{31}{39}{theorem.39}} \backcite {Self}{{31}{39}{figure.caption.16}} \backcite {BurdeZieschang:Knots}{{31}{11}{figure.caption.16}} \backcite {Gassner:OnBraidGroups}{{32}{39}{figure.caption.16}} \backcite {Kawauchi:Srvery}{{32}{39}{figure.caption.16}} \backcite {Khovanov:Categorification, Bar-Natan:Categorification}{{32}{6}{figure.caption.16}} \backcite {OzsvathSzabo:IntroductionToHF, Manolescu:KnotFloerHomology, Juhasz:Survey}{{32}{6}{theorem.40}}