The improved Adams-filtration bound for higher $c4^n$-torsion

Let $x$ be a class on the $\mathbb{C}$-motivic Adams $E_2$ page. Suppose that $\tau^n x=0$ while $\tau^{n-1}x\neq 0$.

Improved Adams-filtration bound. Then $x$ has Adams filtration at least $3n$.

The paper proves the weaker bound that the Adams filtration is at least $2n+2$ and observes that the stronger bound appears reasonable based on computed charts. Its general validity is left open.