Trajectory Accessibility and Stability (TAS) A Unified Theoretical Construct for Human–AI Interaction Dynamics

This paper introduces Trajectory Accessibility and Stability (TAS) as a unified theoretical construct for describing and measuring the dynamic properties of reasoning trajectories in human–language model interaction. TAS proposes two separable dimensions: accessibility, defined as the ease with which a given reasoning trajectory can be entered from a given initialization state; and stability, defined as the persistence of an entered trajectory under perturbation and across interaction depth. TAS is not a new empirical claim. It is a theoretical consolidation of findings documented across four validation studies in the Human Recursive Interaction System (HRIS) series. Each study independently produced evidence bearing on one or both dimensions of TAS. Together they constitute converging empirical support for the construct. The contribution of this paper is to name the phenomenon, formalize its two dimensions, and establish TAS as the theoretical capstone of the HRIS research program. The implications of TAS extend beyond the HRIS framework. As a construct, TAS provides a vocabulary and measurement orientation for any researcher seeking to characterize the dynamic properties of human–AI interaction over time, without requiring adoption of the full HRIS methodology. It also reframes a long-standing practical question, why does structured interaction with language models produce reliably better reasoning outcomes, as a tractable empirical question with defined dimensions, measurable variables, and falsifiable predictions.