All-coupling frequency independence of Sturmian spectral dimensions

Let $d706>0$ and let $d6fc\in(0,1)\setminus\mathbb{Q}$ be an irrational frequency. Denote by $d6a9_{\lambda,\alpha}$ the phase-independent spectrum of the corresponding Sturmian Schrödinger operator. The paper proves that the Hausdorff and upper box-counting dimensions are almost everywhere constant in $d6fc$ when $d706\geq24$. Large-coupling conjecture. The assumption $d706\geq24$ can be dropped in the theorem, so the same almost-everywhere constancy holds for every $d706>0$. A proof is described as currently well out of reach because the methods rely essentially on large coupling.