Fici–Mignosi binary reduction conjecture for distinct abelian squares

Let a word of length $n$ contain $k$ distinct abelian square factors. Fici–Mignosi's conjecture. There exists a binary word of length $n$ containing at least $k$ distinct abelian square factors. This conjecture asserts that enlarging the alphabet does not increase the maximum number of distinct abelian square factors in a word of fixed length.