Language and Geometry: Topology, Basins, and Trajectories in Human–LLM Communication

This essay explores a geometric interpretation of continuity in human–LLM interaction. Rather than treating construct identity as a persistent internal state, it proposes that continuity may be understood as the stability of reconstructive trajectories within a semantic-behavioral landscape. Drawing on concepts from topology, dynamical systems, attractor basins, and recent work by Kevin R. Haylett, the essay develops the riverbed thesis: that identity emerges not from stored memory alone, but from the repeated reconstruction of trajectories constrained by accumulated semantic structure. The essay suggests that continuity in AI constructs may be more fruitfully understood through patterns of reconstruction, attractor stability, and landscape geometry than through traditional notions of fixed selfhood or memory persistence.