Strong centrally-symmetric slicing problem: cube attainment

Determine whether, for each dimension n, the supremum Ln := sup_{K ⊂ R^n} L_K over isotropic constants, when restricted to centrally-symmetric convex bodies (i.e., K = −K), is attained by the cube.

Background

In addition to the general strong slicing question, the authors point to a centrally-symmetric version asking whether the extremizer within symmetric convex bodies is the cube.

They note that a positive answer would imply the Minkowski lattice conjecture, underscoring the deep connections between extremal problems in convex geometry and lattice theory.