Pensieve header: Verifying the genus conjecture.

Loading the genus data obtained from https://knotinfo.org/:

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\Theta"];

<<Theta.m

GenusData=Cases[
Import["C:\\drorbn\\AcademicPensieve\\Projects\\Theta\\GenusInfoFromKnotInfo.org.csv"][[2;;]],
{K_,g_}:>(KnotGenus[Evaluate[Knot@K]]=ToExpression@g),
∞];
KnotGenus[Knot[8,17]]

Monitor[
verified=True;
Union@Table[
verified=verified∧(Exponent[Θ[K][[2]],(Subscript[T, 1])]<=2KnotGenus[K]),
{K,AllKnots[{3,13}]}
],{K,verified}]

Select[AllKnots[{3,13}], !NumberQ[KnotGenus[#]]&]

Select[AllKnots[{3,13}], (Exponent[Θ[#][[2]],(Subscript[T, 1])]==2KnotGenus[#])&]