Most injection detectors score each prompt in isolation. I built one that tracks the geometric trajectory of the full session. Here is a concrete result.

I've been building Arc Gate, a monitoring proxy for deployed LLMs. One URL change routes your OpenAI or Anthropic traffic through it and you get injection blocking, behavioral monitoring, and a dashboard. The interesting part is the geometric layer. I published a five-paper series on a second-order Fisher information manifold (H2xH2, Ricci scalar R = -4) with a phase transition threshold t* = sqrt(3/2) approximately 1.2247. The same geometry that describes physical stability thresholds also describes prompt injection vulnerability patterns.