Chromatic redshift for rigid symmetric monoidal stable categories

Determine the conditions under which a rigid symmetric monoidal stable category, viewed as a rigid Sp-algebra, satisfies chromatic redshift for continuous algebraic K-theory.

Background

For a rigid symmetric monoidal stable category, the paper establishes that continuous K-theory either preserves chromatic height (noshift) or raises it by one (redshift). It gives examples of both behaviors, including T(n)-complete rigid Sp-algebras satisfying noshift, but does not characterize which rigid Sp-algebras exhibit redshift. The authors therefore state the conditions for chromatic redshift as an explicit open question.