Snaith's conjecture on the Kervaire problem in dimension 126

Let $n=126$. The Kervaire problem asks whether there exists a framed manifold of dimension $2^{n+1}-2$ with Kervaire invariant one. Snaith's conjecture. The Kervaire problem is negatively solved for $n=126$, meaning that no such manifold exists. The Kervaire problem is known to have positive solutions for $n=2,6,14,30,62$ and negative solutions for $n\geq 254$ by the Hill–Hopkins–Ravenel theorem; the case $n=126$ remains open.