Multi-turn jailbreak attacks on large language models (LLMs) reveal a mismatch in current guardrails: they operate on individual turns, while attacks unfold as trajectories across conversations. We propose a shift from content to dynamics, modeling conversations as paths in representation space and asking whether adversarial intent is encoded early in their geometry. We introduce PSYCHOPASS, a framework that extracts geometric features from conversation trajectories in embedding space to predict a potential attack before harmful content is produced. These features achieve near-perfect performance in naïve classifiers, which is largely explained by the inclusion of number of turns as a feature. After removing this confound, a smaller but consistent geometric signal remains, with classification performance that does not depend meaningfully on encoder choice. Crucially, this signal appears early in the conversation: attack outcomes remain above chance from short prefixes alone, more reliably than baseline guardrails. A supporting theoretical analysis explains these findings via a decomposition of length and shape, a detection bound based on prefix length, and encoder invariance. Together, these results show that adversarial conversations leave an early, representation-robust geometric fingerprint suitable for online monitoring