A Proof of Conjecture 2 of Chamberland and Dilcher

This paper proves Conjecture 2 of Chamberland and Dilcher concerning the floor-function differences (d_n(\ell)). The proof interprets (d_n(\ell)) as a counting problem and uses a reflection identity from Chamberland and Dilcher to construct the required consecutive zero blocks. It also proves that the zero blocks lie in the required range and are pairwise disjoint.