Strong slicing conjecture (symmetric case) for convex bodies

Prove that for every centrally symmetric convex body K ⊂ ℝ^n (i.e., K = −K), the isotropic constant satisfies L_K ≤ L_{[-1,1]^n}.

Background

The strong slicing conjecture specifies the extremizer for isotropic constants in the symmetric setting: the hypercube [-1,1]^n. The authors present this as Conjecture 1, highlighting its central role and known partial results in low dimensions.

This conjecture is the symmetric analogue of the strong (non-symmetric) slicing conjecture that features the regular simplex as extremizer.