Standard block lexicographic order for products involving powers of the Petersen graph

Let $C_m$ be the cycle graph on $m$ vertices, $K_2$ and $C_3$ the indicated factors, and let $G$ be the Petersen graph. For nonnegative exponents, the displayed Cartesian products are formed using $\square$; the standard block lexicographic order is the order obtained by the paper's block-lexicographic construction. Petersen-product conjecture. If $d_1,d_2,d_3,d_4d_5\geq 0$, $n\geq 6$, and $G$ is the Petersen graph, then the standard block lexicographic order is optimal for

$$C_5^{d_1}\square G^{d_2}\square C_4^{d_3}\square K_2^{d_4}\square C_3^{d_5}$$

and

$$C_n\square C_5^{d_1}\square G^{d_2}\square C_4^{d_3}\square K_2^{d_4}\square C_3^{d_5}.$$

The source notes that the corresponding optimal order for the product of two Petersen graphs was established computationally, while general methods for products of two graphs remain an open direction. The exponent condition is reproduced exactly as stated in the source.