Non-existence conjecture for almost $m$-ary NPSs with two consecutive zero-symbols

An almost $m$-ary NPS is a nearly perfect sequence over an alphabet with $m$-th roots of unity, allowing two zero-symbols; its type is the pair $(\gamma_1,\gamma_2)$, and its period is $n+2$. The two zero-symbols are consecutive when they occur at adjacent positions, and the sequence is non-trivial when it is not an excluded trivial construction.

Non-existence conjecture. Let $m\geq 5$ be a prime, $\gamma_1,\gamma_2\in\mathbb Z$, and $n\in\mathbb Z^+$. There does not exist a non-trivial almost $m$-ary NPS of type $(\gamma_1,\gamma_2)$ and period $n+2$ with two consecutive zero-symbols.

The conjecture asserts a broad non-existence result extending the paper's preceding constructions and non-existence results for partial direct product difference sets and almost $m$-ary nearly perfect sequences. The supplied text gives no resolution, so its status remains open.