Telescopic red-shift conjecture

Let $R$ be a commutative ring spectrum with telescopic complexity $n$, meaning that the thick subcategory determining its telescopic height is $\mathcal{T}_R=\mathfrak{C}_{n-1}$. Here $K(R)$ denotes the algebraic $K$-theory spectrum of $R$. Telescopic red-shift conjecture. The spectrum $K(R)$ is a commutative ring spectrum with telescopic complexity $n+1$. This is a formulation of the red-shift phenomenon, predicting that algebraic $K$-theory raises chromatic complexity by one. The source also mentions the Ausoni–Rognes formulation for suitably finite $K(n)$-local commutative ring spectra.