State–Operator Coupling and Path Dependence in Large Language Models

This paper develops a minimal formal and methodological framework for investigating state–operator coupling and path dependence in large language models. It introduces the hypothesis that interpretive organization in extended model interaction may be related not only to changes in representational states, but also to changes in the effective interaction structures governing subsequent state transitions. The framework therefore treats representational state and effective interaction structure as coupled analytical variables and proposes ways to investigate their relationship through internal model measurements and independently assessed interactional behavior. The paper outlines an empirical research design based on contrasting different modes of interactional development, including natural interactive, batch replay, instrumental, explicitly guided, and reset conditions. A history-conditioned probe is proposed to examine whether the course of prior interaction shapes how a model subsequently organizes novel but conceptually related material. The design also considers how such behavioral differences might relate to independently measured changes in state–operator dynamics. A central methodological premise is that interpretation should not be treated as separate from the informational, contextual, and interactional conditions through which it develops. Rather than attempting to isolate interpretation from these constitutive conditions, the proposed framework aims to investigate how their relations contribute to the formation of interpretive organization. The paper distinguishes between behavioral evidence of path dependence and stronger evidence involving systematic associations between independently measured state–operator dynamics and subsequent interpretive behavior. It also identifies methodological limitations, alternative explanations, and conditions under which the central hypothesis would be weakened or falsified. The proposal does not claim that language models possess human-like understanding, consciousness, or subjective experience. It offers a naturalistic and empirically testable research direction for investigating the dynamics underlying interpretive organization in extended human–model interaction. This paper develops the minimal formal framework and proposed empirical test of Spectral Interpretation Dynamics (SID), complementing the broader theoretical formulation presented in the companion work.