The conjecture on the stable gap for sequential topological complexity of real projective spaces

Assume $m\equiv2^e-1\pmod{2^{e+1}}$ with $e\geq0$, so $e$ is the length of the block of consecutive ones ending the binary expansion of $m$. Let $G(m,s)=sm-\operatorname{zcl}_s(\operatorname{\mathbb{R}P}^m)$, and let $G(m)$ be the stable value of the non-increasing sequence $G(m,2)\geq G(m,3)\geq\cdots\geq0$. Stable-gap conjecture. In Theorem 3.3 of the source, the equality $G(m)=2^e-1$ holds without restriction on $e$. This gives the asserted exact stable value for the gap between the dimensional upper bound and the zero-divisor-cup-length lower bound for sequential topological complexity. The source states that this conjecture has recently been proved, so the claim is solved.