Infinitely many spectral eigenvalues for singular continuous spectral pairs

Let $(\mu,\Lambda)$ be a singular continuous spectral pair in $\mathbb{R}$. A real number $t\in\mathbb{R}$ is called a spectral eigenvalue of $(\mu,\Lambda)$ if $(\mu,t\Lambda)$ is also a spectral pair. Infinitely-many-eigenvalues conjecture. There are infinitely many spectral eigenvalues of a singular continuous spectral pair in $\mathbb{R}$. This is a folklore conjecture concerning the scaling behavior of singular continuous spectral measures and their spectra; its general validity remains open.