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.
Lower bounds on the $\ell$-rank of ideal class groups
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abstract
For a prime number $\ell$ and an extension of number fields $K/F$, we prove new lower bounds on the $\ell$-rank of the ideal class group of $K$ based on prime ramification in $K/F$. Unlike related results from the literature, our bound is supported on prime ideals in $F$ over which at least one (rather than each) prime in $K$ has ramification index divisible by $\ell$. This bound holds with a proviso on the Galois group of the normal closure of $K/F$, which is satisfied by towers of Galois extensions, intermediate fields in nilpotent extensions, and intermediate fields in dihedral extensions of degree $8n$, to name a few. We also use our lower bound to prove a new density result on number fields with infinite class field towers.
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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.