The conjecture for the number of left braces of order $9p$

Let $b(n)$ denote the number of non-isomorphic left braces of size $n$, and let $p>3$ be a prime. The order-$9p$ counting conjecture.

$$b(9p)=\begin{cases} 14 & \text{if } p\equiv1\bmod9,\\ 4 & \text{if } p\equiv2,5\bmod9,\\ 11 & \text{if } p\equiv4,7\bmod9. \end{cases}$$

The conjecture is suggested by the table of computed values. The paper states that it was verified by computer calculations, together with the preceding order-$4p$ conjecture, for primes up to $997$; its general validity remains open in the supplied text.