B1nger--Seeger's 200 Euro Conjecture

Let $A=(a_{ij})\in\mathbb{R}^{n\times n}$ with $n\ge 2$, and let $r_i=(a_{i1},\dots,a_{in})$ denote the $i$th row of $A$. Suppose that

$$\lVert r_i\rVert_2\ge \sqrt{n-1}\qquad (1\le i\le n).$$

B1nger--Seeger's 200 Euro Conjecture. There exists $x\in\mathbb{R}^n\setminus\{0\}$ such that

$$|Ax|\ge |x|.$$

This stronger conjecture was proposed by F. B1nger and A. Seeger in 2024 and is also called the 200 Euro Conjecture. The supplied text does not state that it has been resolved.