The torus-knot extension conjecture for Proposition 1.3

A torus knot is a knot $T(s,t)\subseteq S^3$ with $\gcd(s,t)=1$. Let Proposition 1.3 denote the proposition preceding this conjecture, which establishes the stated well-defined Laurent power series for the listed families of torus knots. Torus-knot extension conjecture. Proposition 1.3 holds for all torus knots $T(s,t)\subseteq S^3$ with $\gcd(s,t)=1$. The claim extends the preceding proposition from the explicitly treated torus-knot families to all torus knots; the source provides no resolution evidence.