Geometric Constraints on Transition Dynamics in Recursive Language Systems

This work investigates transition dynamics in recursive language systems using Fisher information geometry. States are embedded in a Fisher-geometric manifold, where transitions are shown to localize near a phase boundary rather than occurring uniformly throughout state space. Local curvature modulates transition likelihood within this boundary-adjacent region, producing a low-dimensional geometric transition law. A trajectory-level scalar observable, the Lazarus score, is introduced as a phase-sensitive measure of compression. Although correlated with boundary distance, Lazarus retains predictive power within fixed geometric strata: near the phase boundary, high-Lazarus states are substantially more transition-prone than distance-matched low-Lazarus states. The reported structure is stable across probe scales from 10 to 100,000 and is supported by supplementary analyses of geometric collapse, conditional transition structure, and initial-condition phase selection. The package includes the manuscript, supplementary information, and supporting materials for the study.