A multi-agent adversarial evaluation platform with six progressive attack strategies shows that role-playing LLMs degrade under sustained pressure, with automated judging correlating with human ratings.
Iwasawa module of the cyclotomic $\mathbb{Z}_{2}$-extension of certain real quadratic fields
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abstract
For a real quadratic field $K=\mathbb{Q}(\sqrt{D})$, let $K_{\infty}$ denote the cyclotomic $\mathbb{Z}_{p}$-extension of $K$. Greenberg conjectured that the corresponding Iwasawa module $X_{\infty}$ is finite. Building on the work of Mouhib and Movahhedi, we provide new examples of real quadratic fields for which the conjecture holds, when $X_{\infty}$ is cyclic and the prime is $p=2$. Furthermore, we find a fundamental system of units for certain biquadratic fields of the form $\mathbb{Q}(\sqrt{2}, \sqrt{D})$ and show how to use it to calculate the order of $X_{\infty}$.
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Adversarial Stress Testing of Role-Playing Language Agents using Multi-Agent Evaluation
A multi-agent adversarial evaluation platform with six progressive attack strategies shows that role-playing LLMs degrade under sustained pressure, with automated judging correlating with human ratings.