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A pencil of quadratic forms in nine variables with no member of Witt index four
We exhibit an explicit pair $(A,B)$ of integral symmetric $9\times9$ matrices, defining a nonsingular pair of quadratic forms over $\mathbb{Q}$, such that no member of the rational pencil $λq_A+μq_B$ has Witt index $4$ over $\mathbb{Q}$. This refutes a conjecture from \cite{Que16a}, which predicted
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