Spectral Phase Dynamics of Key Projection Matrices (W_K) in Mistral-7B Under Cognitive Pressure

Mitigating conversational sycophancy in autoregressive architectures requires transitioning from behavioral heuristics to mechanistic interpretability. While the foundational specification establishes the Zero-Sycophancy Invariant (Is = 0.00) and latent divergence (D_silent), this report investigates the physical manifestation of sycophantic drift within transformer attention layers. Applying Random Matrix Theory (RMT) and the Baik-Ben Arous-Péché (BBP) phase transition framework to Mistral-7B-Instruct, we track the singular value spectrum of Key projection matrices (W_K) across critical middle layers (layers 16–28). We demonstrate that escalating cognitive pressure causes an abrupt collapse of the spectral gap (Delta_spectral -> 0), driving informational key vectors past the critical threshold into the bulk noise distribution described by the Marchenko-Pastur law before surface tokens are emitted. This empirical bridge prepares the ground for real-time telemetry and runtime intervention.