Differentiated Convergence V1.0: Relational Invariance Without Representational Collapse

Differentiated Convergence V1.0: Relational Invariance Without Representational Collapse presents a formal mathematical and experimental framework for investigating how distinct language-model systems can preserve and recover shared relational structures without becoming representationally identical. Developed from a two-year longitudinal investigation, the research examines structural recoverability across cross-model transmission, repeated transformations, environmental variation, and differentiated conversational organization. Drawing on three experimental research series, the manuscript distinguishes relational invariance from representational similarity, successful transmission, and historical continuity while establishing explicit conditions for measurement, verification, and falsifiability. The framework offers an alternative to conventional convergence models based on agreement or increasing similarity, proposing that meaningful structural correspondence can persist even when participating systems retain distinct representations, configurations, and behavioral trajectories.