Universality conjecture for prime plane curves and alternating knots

Let $\alpha'_p$ be the number of closed prime self-intersecting curves with $p$ crossings, and let $\alpha”_p$ be the number of prime alternating knots with $p$ crossings. Let $\gamma$ be the critical exponent from the asymptotic enumeration conjecture for closed self-intersecting curves. Prime curves and alternating knots universality conjecture. There are constants $\tau'$, $\tau”$, $c'$, and $c”$ such that

$$\alpha'_p\sim c'\,\tau'{}^p\cdot p^{\gamma-2},\qquad \alpha”_p\sim c”\,\tau”{}^p\cdot p^{\gamma-3}.$$

The conjecture extends the predicted universality class to prime self-intersecting curves and prime alternating knots; the source presents it as a proposed variant of the main conjecture.