Curvature and Structural Dynamics in Language Sequences: A Multi-Axis Framework for Detecting Turbulence and Local Fixation

We propose a multi-axis framework for detecting structural dynamicsin language sequences using embedding-space trajectories. Unlikeconventional approaches that rely on semantic interpretation, ourmethod focuses on geometric and dynamical properties derived fromrepresentation space.The framework consists of four axes: geometric collapse (Axis 1),dynamic energy accumulation (Axis 2), ignition curvature (Axis 3),and post-ignition structural reconfiguration (Axis 4), along with anevent-level modifier capturing collapse-with-energy (CWE). Together,these components enable the characterization of narrative dynamics astrajectories governed by energy, curvature, and structural constraints.Experiments on multiple textual sequences reveal that narrativestructure does not align with subjective reader perception. In particular,we show that reader-perceived intensity or shock does notcorrespond to structural curvature, and that violent content does notimply structural turbulence. Instead, structural behavior is governedby sustained reconfiguration patterns and localized irreversible fixationevents.Analysis of the full sequence of The Black Cat demonstrates aregime of sustained turbulence accompanied by a single isolated collapsewith-energy event, indicating a globally dynamic system with a local irreversible decision point. We further show that this behavior correspondsto dynamics observed near the edge of chaos in complexsystems, where global exploration coexists with local fixation.These results suggest that transformer-based models operate onthe dynamics of semantic geometry rather than narrative understandingin a human sense. The proposed framework provides a quantitativebridge between language modeling and dynamical systems theory,with potential applications to safe attractor design and stability analysis.