Recursive Coupling, Tensor Amplification Networks, and the Tesseract Framework: A Theoretical Extension and Companion Paper

This paper presents a theoretical extension to the previously proposed Tesseract Framework. Rather than introducing new empirical constructs, the extension reinterprets the four original dimensions—Institutional Priming (IP), Intergenerational Stress (IS), Community Response (CR), and Digital Amplification (DA)—as functional roles operating within a recursively coupled multi-scale amplification network. Under this interpretation, IP functions as a boundary condition, IS as a gain parameter, CR as a meso-scale aggregation variable, and DA as a coupling coefficient modulating edge weights across the network. The extension introduces two pre-registrable hypotheses (H6, H7): cross-platform desynchronization following platform governance shocks, and post-surge hysteresis as residual baseline elevation beyond lagged-predictor expectation. Importantly, the extension does not empirically validate individual-level recursive dynamics directly; rather, it tests whether platform-scale synchronization behavior exhibits the signatures expected under a recursively coupled amplification system. All claims remain probabilistic rather than deterministic. This work is intended as a theoretical companion paper to “The Tesseract of Antisemitism: A Hybrid Geometric-Causal Framework.”