The unrestricted classification conjecture for periodic Golay pair compressions

Let $(A,B)$ be the $(v/2)$-decomposition of a periodic Golay pair $\operatorname{PG}(v)$ with row sums $a$ and $b$. Equivalence is taken in the sense used for these decompositions. Classification conjecture. Then $(A,B)$ is equivalent to either

$$([0,a],[0,b])$$

or

$$\bigl([\frac{a+b}{2},\frac{a-b}{2}],[\frac{a+b}{2},\frac{b-a}{2}]\bigr).$$

The preceding theorem proves this classification under a restriction on the prime factorization of $v/2$; the conjecture is that the same conclusion remains valid without that restriction. In particular, the case $v=50$ motivates the conjecture because exhaustive search found no compression of the additional form suggested by the multiple representations of $v/2$ as a sum of two squares.