Kappa-LLM: Multi-Observable Topological Detection of Hallucinations in Large Language Models

We introduce Kappa-LLM, a multi-observable framework grounded in topological data analysis that detects hallucinations in LLMs during generation by monitoring attention dynamics. Building on the Kappa Method, we define five canonical observables (Ω, Φ, η, Ξ, Δ) capturing entropy, persistence, rigidity, diversity, and divergence in attention matrices. Key finding: hallucinations exhibit an "obsessive attractor" pattern — premature collapse onto spurious attractors with high confidence and low entropy (low Ω, high η, low Ξ, high Δ). Experiments on Phi-3, Mistral-7B, and Llama-3.1-8B (HaluEval benchmark): 85.0% accuracy and 94.2% AUC for Phi-3 (+36.5pp over topological baseline R-Score). Entropy-based observables achieve 93.1% AUC and generalize across architectures. Real-time detection with