This is a meta-lemma, and so it could only be true if it would be more specific about the type of statement which is supposed to remain true. To see this, note that the proposed algorithm works if the maximum cell size is less than 2, but it doesn't follow from that statement that the proposed algorithm will also work if the maximum cell size is bigger.

Neither theorem 4.2 nor corollary 4.3 make any effort to ensure that application of lemma 4.1 is really appropriate. The proof of theorem 4.2 assumes a maximum cell size of 1, and applies lemma 4.1 to cover larger cell sizes. The proof of corollary 4.3 assumes maximum cell size 2, and also applies lemma 4.1 to cover the general case.

What I found interesting is the approach of the author towards notation. For example, he writes $G(\mathbf \nu, \mathbf \xi)$ for a bipartite graph. The implicit convention is that $\mathbf \nu$ and $\mathbf \xi$ denote the two different sets of nodes.

He does this, because he wants to have explicit names for these two sets. Or for "3.3 Input Pattern Generation," he writes $\mathbf {p_1}=\eta(\nu_i,\mathbf A)\in \mathbb R^M$ to indicate that $\mathbf {p_1}$ depends on $\nu_i$ and $\mathbf A$, and then later writes $\mathbf {p_1}(i)=\beta$, where this $i$ references to the now suppressed $i$ from $\nu_i$, but simulataneously also to the $i$-th coordinate of $\mathbb R^M$. In general, I think his approach to notation works well for this paper.

Reading the paper was easy, since the author tries his best to communicate his ideas. He doesn't include any defeat-devices in his algorithm to make harder to disprove it, he just beliefs in his ideas, has implemented them and compared the performance against Nauty. He openly admits that Nauty is orders of magnitude faster. He also cites appropriate literature, even so it is clear that he hasn't read or understood all of it. Otherwise he would have known that his approach cannot work.

As a final remark: I have not tried to contact the author in this case.