Wilkinson's complete-pivoting growth-factor bound conjecture

Let $g\big[\mathbf{CP}_n(\mathbb{R})\big]$ denote the maximum growth factor for complete pivoting over real $n\times n$ matrices. Wilkinson's conjecture.

$$g\big[\mathbf{CP}_n(\mathbb{R})\big] \le n,$$

with equality achieved only by Hadamard matrices. This historical conjecture was known to be false by 1991, so it is included as a refuted conjecture rather than an open claim.