Motivic Telescope Conjecture in localization form

For each pair $(m,n)$, let $K(\leq\beta_{mn})$ be the wedge of the motivic Morava K-theories indexed by the set of $(i,j)$ with $d_{ij}>d_{mn}$, and define

$$L^f_{mn}:=L^f_{K(\leq\beta_{mn})},\qquad L_{mn}:=L_{K(\leq\beta_{mn})}.$$

Motivic Telescope Conjecture. The natural transformation

$$L^f_{mn}\to L_{mn}$$

is an equivalence. This is the localization formulation of the motivic Telescope Conjecture; its equivalence with the other formulations is not established in general.