Chain-map conjecture for cubical homology of digital images

Let $X\subset \mathbb{Z}^n$ and $Y\subset \mathbb{Z}^m$ be digital images with $c_1$-adjacency, and let $f:X\to Y$ be continuous. Chain-map conjecture. The induced homomorphism

$$f_\#: C_q(X)\to C_q(Y)$$

is a chain map. The preceding result establishes this when $n\leq 4$ by computer enumeration; a human-readable proof in arbitrary dimension remains open.