Asymptotic slope conjecture for the 2-adic valuations of Taylor coefficients

Let $a_m$ be the Taylor coefficients of $\Theta(z)=1/\Psi(1/z)$, let $m=2^n m_0$ with $m_0$ odd, and fix $n=\overline{n}$. Write $u= u_2$ for the 2-adic valuation. Asymptotic slope conjecture. The sequence $\{-\nu(a_m)\}_{n=\overline{n}}$ is asymptotically linear, with slope

$$\frac{2}{2^{\overline{n}+1}-1}.$$

This conjecture concerns the observed linear growth of denominator exponents along fixed 2-adic subsequences. The surrounding results establish related valuation bounds and exact formulas in special cases, but do not prove this asymptotic statement.