Travkin's bimodule Kazhdan–Lusztig cell conjecture for microlocal cells

Let $RB$ be the set of colored permutations indexing the Kazhdan–Lusztig basis of the mirabolic bimodule, and let two-colored permutations define two-sided microlocal cells. The bimodule Kazhdan–Lusztig cells are the cells obtained from subbimodules spanned by subsets of the Kazhdan–Lusztig basis.

Bimodule–microlocal cell conjecture. The bimodule Kazhdan–Lusztig cells coincide with the two-sided microlocal cells.

This asserts equality between an algebraic cell decomposition and a geometric microlocal one. The source gives no resolution status or supporting result beyond the statement.