The chromatic height red-shift conjecture for algebraic K-theory

Let $R$ be a ring spectrum of height $n$, meaning that $K(n)_*R\neq 0$ and $K(m)_*R=0$ for every $m>n$, where $K(m)$ denotes Morava K-theory. Height red-shift conjecture. The algebraic K-theory spectrum $\operatorname{K}(R)$ is of height $n+1$. This is a height-theoretic form of the red-shift principle, asserting that algebraic K-theory increases chromatic height by one; the supplied text does not give a resolution of the conjecture in this generality.