A Runtime Trajectory Dynamics Framework for Large Language Models

Most existing observability tools for large language models analyze attention patterns or final outputs in isolation, leaving the runtime dynamics of probability distributions under-characterized. We introduce V20, a framework that measures the geometric trajectory of token-level probability distributions during inference. The framework defines a bicephalic operator (κ G, κD, κsync) on logit distributions and classifies dynamic states into a five-category taxonomy (E_STABLE, A_HIDDEN_TURBULENCE, B_SURFACE_BRANCHING, D_FULL_BIFURCATION_ZONE, C_COMMITTED_NO_BIFURCATION). We validate the framework on eight open-source attention-based transformer models ranging from 70M to 1.3B parameters. Four principal findings emerge: the five-state taxonomy is statistically robust and cross-model consistent on seven of eight models tested; eight architectures partition into two distinct probability geometry regimes (GD_ratio > 1.5 vs GD_ratio < 0.1) that are not explained by parameter count; the D_FULL_BIFURCATION_ZONE state is a transient regime with self-transition probability below 0.04 on every model where it appears; perturbation responses are architecture-specific and reproducible. We document five limited findings requiring further validation and five claims explicitly rejected by the data. V20 enables runtime observability of model dynamics independent of vocabulary or task, providing a quantitative substrate for auditing and alignment work.